diff --git a/README.Rmd b/README.Rmd new file mode 100644 index 000000000..3b1952330 --- /dev/null +++ b/README.Rmd @@ -0,0 +1,6 @@ +## A short discription of the course +This course--Introduction to Open Data Science--is aimed to help students to understand the principles and advantages of using open research tools with open data and understand the possibilities of reproducible research. After learning this course the students should know how to use R, RStudio, RMarkdown and GitHUb and also know how to learn more of these open software tools. Beside, and also the most important for me, the students will also know how to apply certain statistical methods of data science. + + +*The link of my course diary is listed below:* +https://XiaodongAAA.github.io/IODS-project/ diff --git a/README.html b/README.html new file mode 100644 index 000000000..2eab5ea61 --- /dev/null +++ b/README.html @@ -0,0 +1,158 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + +
+

A short discription of the course

+

This course–Introduction to Open Data Science–is aimed to help students to understand the principles and advantages of using open research tools with open data and understand the possibilities of reproducible research. After learning this course the students should know how to use R, RStudio, RMarkdown and GitHUb and also know how to learn more of these open software tools. Beside, and also the most important for me, the students will also know how to apply certain statistical methods of data science.

+

The link of my course diary is listed below:
+https://XiaodongAAA.github.io/IODS-project/

+
+ + + + +
+ + + + + + + + diff --git a/_config.yml b/_config.yml new file mode 100644 index 000000000..c50ff38da --- /dev/null +++ b/_config.yml @@ -0,0 +1 @@ +theme: jekyll-theme-merlot \ No newline at end of file diff --git a/chapter1.Rmd b/chapter1.Rmd index e3c5c05f8..91d3d3493 100644 --- a/chapter1.Rmd +++ b/chapter1.Rmd @@ -1,4 +1,10 @@ # About the project -*Write a short description about the course and add a link to your github repository here. This is an R markdown (.Rmd) file so you can use R markdown syntax. See the 'Useful links' page in the mooc area (chapter 1) for instructions.* \ No newline at end of file +*Write a short description about the course and add a link to your github repository here. This is an R markdown (.Rmd) file so you can use R markdown syntax. See the 'Useful links' page in the mooc area (chapter 1) for instructions.* + +## A short discription of the course +This course--Introduction to Open Data Science--is aimed to help students to understand the principles and advantages of using open research tools with open data and understand the possibilities of reproducible research. After learning this course the students should know how to use R, RStudio, RMarkdown and GitHUb and also know how to learn more of these open software tools. Beside, and also the most important for me, the students will also know how to apply certain statistical methods of data science. + +*The link of my github repository is listed below:* +https://github.com/XiaodongAAA/IODS-project diff --git a/chapter1.html b/chapter1.html new file mode 100644 index 000000000..158b161cc --- /dev/null +++ b/chapter1.html @@ -0,0 +1,162 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + +
+

About the project

+

Write a short description about the course and add a link to your github repository here. This is an R markdown (.Rmd) file so you can use R markdown syntax. See the ‘Useful links’ page in the mooc area (chapter 1) for instructions.

+
+

A short discription of the course

+

This course–Introduction to Open Data Science–is aimed to help students to understand the principles and advantages of using open research tools with open data and understand the possibilities of reproducible research. After learning this course the students should know how to use R, RStudio, RMarkdown and GitHUb and also know how to learn more of these open software tools. Beside, and also the most important for me, the students will also know how to apply certain statistical methods of data science.

+

The link of my github repository is listed below:
+https://github.com/XiaodongAAA/IODS-project

+
+
+ + + + +
+ + + + + + + + diff --git a/chapter2.Rmd b/chapter2.Rmd index 1e36a6f14..3d96243d1 100644 --- a/chapter2.Rmd +++ b/chapter2.Rmd @@ -1,7 +1,83 @@ -# Insert chapter 2 title here +# Regression and model validation *Describe the work you have done this week and summarize your learning.* - Describe your work and results clearly. - Assume the reader has an introductory course level understanding of writing and reading R code as well as statistical methods - Assume the reader has no previous knowledge of your data or the more advanced methods you are using + +*Created at 10:00 12.11.2017* +*@author:Xiaodong Li* +*The script for RStudio Exercise 2 -- data analysis* + +**Import packages:** +```{r} +library(dplyr) +library(GGally) +library(ggplot2) +``` + +## Step 1:read data +```{r} +lrn2014 = read.table('/home/xiaodong/IODS_course/IODS-project/data/learning2014.txt',sep='\t',header = TRUE) +``` +Structure of the data +```{r} +str(lrn2014) +``` +Dimensions of the data +```{r} +dim(lrn2014) +``` +Data description +According to the structure and dimensions of the data, the data frame contains 7 variables which are `gender`,`age`,`attitude`,`deep`,`stra`,`surf`,`points`. In each variable, there are 166 observations. `gender` represents male (M) and female (F) surveyors. `age` is the ages (in years) of the people derived from the date of birth.In `attitude` column lists the global attitudes toward statistics. Columns `deep`,`surf` and `stra` list the questions related to deep, surface and strategic learning. The related question could be found in the following page, http://www.helsinki.fi/~kvehkala/JYTmooc/JYTOPKYS3-meta.txt +The `points` column list the exam points from the survey. + +## Step2: Explore the data +Plot the relationships between the variables +```{r} +p <- ggpairs(lrn2014, mapping = aes(col=gender,alpha=0.3)) +p +``` + +The figure shows relationships between different variables. From the figure we can see that, from the `gender` column, female surveyors are more than male surveyors. Most of the people being surveyed are young generations, aged around 20 years old. The `attitudes` of man are higher than those of wemon towards statistics, which reflects that man has more positive attitudes towards statistics than wemen. The questions of `deep` and `strategic learning` are almost the same for men and wemen. The mean scores for them are around 3 and 4. However, the `surface questions` are quite different between the men and wemen surveyors. For wemen, the answers are centered at around 3.0 while the answers of men are centered at around 2.3. The exam `points` got from male and female answerers are quite the same and the most points are about 23 for both of them. + +## Step 3: Multiple regression +```{r} +reg_model=lm(points~attitude+stra+surf,data=lrn2014) +summary(reg_model) +``` + +The target variable `point` is fitted to three explanatory variables: `attitude`, `stra` and `surf`. According to the results of the model, `surf` does not have a statistically significant relationship with the target variable. So, `surf` is removed from the fitting model and points is modelled according to `attitude` and `stra` again. + +## Step 4: Model again +```{r} +reg_model2=lm(points~attitude+stra, data=lrn2014) +summary(reg_model2) +``` + +The model is fitted with the target `points` and two explanatory variable, `attitude` and `stra`. According to the summary results, the relationship between these variable should be $points=8.9729+3.4658*attitude+0.9137*stra$. +* The `Std. Error` is the standard deviation of the sampling distribution of the estimate of the coefficient under the standard regression assumptions. +* The `t values` are the estimates divided by there standard errors. It is an estimation of how extreme the value you see is, relative to the standard error. +* `Pr.` is the `p-value` for the hypothesis for which the `t value` is the test statistic. It tell you the probability of a test statistic at least as unusual as the one you obtained, if the null hypothesis were true (the null hypothesis is usually 'no effect', unless something else is specified). So, if the `p-value` is very low, then there is a higher probability that you're see data that is counter-indicative of zero effect. +* `Residual standard error` represents the standard deviation of the residuals. It's a measure of how close the fit is to the points. +* `The Multiple R-squared` is the proportion of the variance in the data that's explained by the model. The more variables you add, the large this will be. The `Adjusted R-squared` reduces that to account for the number of variables in the model. +* The `F-statistic` on the last line is telling you whether the regression as a whole is performing 'better than random',in other words, it tells whether your model fits better than you'd expect if all your predictors had no relationship with the response. +* `The p-value` in the last row is the p-value for that test, essentially comparing the full model you fitted with an intercept-only model. + +## Step 5: Diagnostic plots +Residuals vs Fitted values, Normal QQ-plot and Residuals vs Leverage are plotted +```{r} +par(mfrow=c(2,2)) +plot(reg_model2, which=c(1,2,5)) +``` + +* The `Residuals vs Fitted` values plot examines if the errors have constant variance. The graph shows a reasonable constant variance without any pattern. +* The `Normal QQ-polt` checks if the errors are normally distributed. We see from the graph a very good linear model fit, indicating a normally distributed error set. +* The `Residuals vs Leverage` confirms if there are any outliers with high leverage. From the graph, it shows that all the leverage are below 0.06, indicating good model fitting. + +# Conclusion +The data `learning_2014` is explord and analysed by using graphical overview, data summary, multiple regression and diagnostic plots methods. The relationships between different variables are examined by a single plot which shows all possible scatter plots from the columns of `learning_2014` data. The exam points `Points` variable is fitted with combination variables `attitude` and `surf` and showed a reasonable good linear trend, despite the relatively low R-squared value. The validity of the model is checked by means of multiple residual analysis. The model predicts that the exam points of the students are positively correlated with their attitude and surface approaches. + + + diff --git a/chapter2.html b/chapter2.html new file mode 100644 index 000000000..876b1be28 --- /dev/null +++ b/chapter2.html @@ -0,0 +1,289 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + +
+

Regression and model validation

+

Describe the work you have done this week and summarize your learning.

+ +

Created at 10:00 12.11.2017
+@author:Xiaodong Li
+The script for RStudio Exercise 2 – data analysis

+

Import packages:

+
library(dplyr)
+
## 
+## Attaching package: 'dplyr'
+
## The following objects are masked from 'package:stats':
+## 
+##     filter, lag
+
## The following objects are masked from 'package:base':
+## 
+##     intersect, setdiff, setequal, union
+
library(GGally)
+
## 
+## Attaching package: 'GGally'
+
## The following object is masked from 'package:dplyr':
+## 
+##     nasa
+
library(ggplot2)
+
+

Step 1:read data

+
lrn2014 = read.table('/home/xiaodong/IODS_course/IODS-project/data/learning2014.txt',sep='\t',header = TRUE)
+

Structure of the data

+
str(lrn2014)
+
## 'data.frame':    166 obs. of  7 variables:
+##  $ gender  : Factor w/ 2 levels "F","M": 1 2 1 2 2 1 2 1 2 1 ...
+##  $ age     : int  53 55 49 53 49 38 50 37 37 42 ...
+##  $ attitude: num  3.7 3.1 2.5 3.5 3.7 3.8 3.5 2.9 3.8 2.1 ...
+##  $ deep    : num  3.58 2.92 3.5 3.5 3.67 ...
+##  $ stra    : num  3.38 2.75 3.62 3.12 3.62 ...
+##  $ surf    : num  2.58 3.17 2.25 2.25 2.83 ...
+##  $ points  : int  25 12 24 10 22 21 21 31 24 26 ...
+

Dimensions of the data

+
dim(lrn2014)
+
## [1] 166   7
+

Data description According to the structure and dimensions of the data, the data frame contains 7 variables which are gender,age,attitude,deep,stra,surf,points. In each variable, there are 166 observations. gender represents male (M) and female (F) surveyors. age is the ages (in years) of the people derived from the date of birth.In attitude column lists the global attitudes toward statistics. Columns deep,surf and stra list the questions related to deep, surface and strategic learning. The related question could be found in the following page, http://www.helsinki.fi/~kvehkala/JYTmooc/JYTOPKYS3-meta.txt The points column list the exam points from the survey.

+
+
+

Step2: Explore the data

+

Plot the relationships between the variables

+
p <- ggpairs(lrn2014, mapping = aes(col=gender,alpha=0.3))
+p
+
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
+## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
+## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
+## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
+## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
+## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
+

+

The figure shows relationships between different variables. From the figure we can see that, from the gender column, female surveyors are more than male surveyors. Most of the people being surveyed are young generations, aged around 20 years old. The attitudes of man are higher than those of wemon towards statistics, which reflects that man has more positive attitudes towards statistics than wemen. The questions of deep and strategic learning are almost the same for men and wemen. The mean scores for them are around 3 and 4. However, the surface questions are quite different between the men and wemen surveyors. For wemen, the answers are centered at around 3.0 while the answers of men are centered at around 2.3. The exam points got from male and female answerers are quite the same and the most points are about 23 for both of them.

+
+
+

Step 3: Multiple regression

+
reg_model=lm(points~attitude+stra+surf,data=lrn2014)
+summary(reg_model)
+
## 
+## Call:
+## lm(formula = points ~ attitude + stra + surf, data = lrn2014)
+## 
+## Residuals:
+##      Min       1Q   Median       3Q      Max 
+## -17.1550  -3.4346   0.5156   3.6401  10.8952 
+## 
+## Coefficients:
+##             Estimate Std. Error t value Pr(>|t|)    
+## (Intercept)  11.0171     3.6837   2.991  0.00322 ** 
+## attitude      3.3952     0.5741   5.913 1.93e-08 ***
+## stra          0.8531     0.5416   1.575  0.11716    
+## surf         -0.5861     0.8014  -0.731  0.46563    
+## ---
+## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+## 
+## Residual standard error: 5.296 on 162 degrees of freedom
+## Multiple R-squared:  0.2074, Adjusted R-squared:  0.1927 
+## F-statistic: 14.13 on 3 and 162 DF,  p-value: 3.156e-08
+

The target variable point is fitted to three explanatory variables: attitude, stra and surf. According to the results of the model, surf does not have a statistically significant relationship with the target variable. So, surf is removed from the fitting model and points is modelled according to attitude and stra again.

+
+
+

Step 4: Model again

+
reg_model2=lm(points~attitude+stra, data=lrn2014)
+summary(reg_model2)
+
## 
+## Call:
+## lm(formula = points ~ attitude + stra, data = lrn2014)
+## 
+## Residuals:
+##      Min       1Q   Median       3Q      Max 
+## -17.6436  -3.3113   0.5575   3.7928  10.9295 
+## 
+## Coefficients:
+##             Estimate Std. Error t value Pr(>|t|)    
+## (Intercept)   8.9729     2.3959   3.745  0.00025 ***
+## attitude      3.4658     0.5652   6.132 6.31e-09 ***
+## stra          0.9137     0.5345   1.709  0.08927 .  
+## ---
+## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+## 
+## Residual standard error: 5.289 on 163 degrees of freedom
+## Multiple R-squared:  0.2048, Adjusted R-squared:  0.1951 
+## F-statistic: 20.99 on 2 and 163 DF,  p-value: 7.734e-09
+

The model is fitted with the target points and two explanatory variable, attitude and stra. According to the summary results, the relationship between these variable should be \(points=8.9729+3.4658*attitude+0.9137*stra\).
+* The Std. Error is the standard deviation of the sampling distribution of the estimate of the coefficient under the standard regression assumptions.
+* The t values are the estimates divided by there standard errors. It is an estimation of how extreme the value you see is, relative to the standard error.
+* Pr. is the p-value for the hypothesis for which the t value is the test statistic. It tell you the probability of a test statistic at least as unusual as the one you obtained, if the null hypothesis were true (the null hypothesis is usually ‘no effect’, unless something else is specified). So, if the p-value is very low, then there is a higher probability that you’re see data that is counter-indicative of zero effect.
+* Residual standard error represents the standard deviation of the residuals. It’s a measure of how close the fit is to the points.
+* The Multiple R-squared is the proportion of the variance in the data that’s explained by the model. The more variables you add, the large this will be. The Adjusted R-squared reduces that to account for the number of variables in the model.
+* The F-statistic on the last line is telling you whether the regression as a whole is performing ‘better than random’,in other words, it tells whether your model fits better than you’d expect if all your predictors had no relationship with the response.
+* The p-value in the last row is the p-value for that test, essentially comparing the full model you fitted with an intercept-only model.

+
+
+

Step 5: Diagnostic plots

+

Residuals vs Fitted values, Normal QQ-plot and Residuals vs Leverage are plotted

+
par(mfrow=c(2,2))
+plot(reg_model2, which=c(1,2,5))
+

+
    +
  • The Residuals vs Fitted values plot examines if the errors have constant variance. The graph shows a reasonable constant variance without any pattern.
  • +
  • The Normal QQ-polt checks if the errors are normally distributed. We see from the graph a very good linear model fit, indicating a normally distributed error set.
  • +
  • The Residuals vs Leverage confirms if there are any outliers with high leverage. From the graph, it shows that all the leverage are below 0.06, indicating good model fitting.
  • +
+
+
+
+

Conclusion

+

The data learning_2014 is explord and analysed by using graphical overview, data summary, multiple regression and diagnostic plots methods. The relationships between different variables are examined by a single plot which shows all possible scatter plots from the columns of learning_2014 data. The exam points Points variable is fitted with combination variables attitude and surf and showed a reasonable good linear trend, despite the relatively low R-squared value. The validity of the model is checked by means of multiple residual analysis. The model predicts that the exam points of the students are positively correlated with their attitude and surface approaches.

+
+ + + + +
+ + + + + + + + diff --git a/chapter3.Rmd b/chapter3.Rmd new file mode 100644 index 000000000..521d5276c --- /dev/null +++ b/chapter3.Rmd @@ -0,0 +1,141 @@ +# Chapter 3 Logistic regression +Created on 18.11.2017 +@author: Xiaodong Li +This is the script for RStudio exercise 3 -- Data analysis +The work focuses on exploring data and performing and interpreting logistic regression analysis on the UCI Machine Learning Repository, Student Performance Data Set. + +## Step 0: import packages +```{r} +library(tidyr) +library(dplyr) +library(ggplot2) +``` + +## Step 1:read data +```{r} +alc=read.csv('/home/xiaodong/IODS_course/IODS-project/data/alc.csv',sep=',',header = TRUE) +colnames(alc) +``` +The data used in the exercise is a joined data set that combines the two student alcohol consumption data sets, student-mat.csv and student-por.csv. The two data sets are retrieved from the UCI Machine Learning Repository. The data are from two identical questionaires related to secondary school student alcohol consumption in Portugal. For more background information, please check [here.](https://archive.ics.uci.edu/ml/datasets/Student+Performance) The variables not used for joining the two data have been combined by averaging. The `alc_use` colume is the average of weekday (`Dalc`) and weekend (`Walc`) alcohol use. The `high_use` column records if the `alc_use` is higher than 2 or not. + +## Step 2:hypothesis about relationships with alcohol consumption +Choose four interesting variables in the data and present personal hypothesis about their relationships with alcohol consumption. +- `failures`: positive correlation, the more alcohol consumption, the more failures +- `absenses`: positive correlation, the more alcohol consumption, the more absenses +- `sex`: male is more than female students with high alcohol use +- `studytime`: negative correlation, the more alcohol consumption, the less studytime + +## Step 3: Explore the distributions of the chosen variables and there relationships with alcohol consumption + +### The relationship between sex and alcohol use +```{r} +bar_sex=ggplot(alc, aes(x=alc_use,fill=sex))+geom_bar(); bar_sex +``` +`sex`~`alc_use`: +According to the count~alc_use bar figure plotted according to different sexes, we can see that female students are the main low alcohol users (`alc_use` < 2.5), however, for high alcohol users (`alc_use` > 2.5), most of them are male students. The bar figure also tells us that most of the alcohol users are very light users and the numbers of them decrease quickly with the increasing alcohol use levels (except for the extreme high users). + +### The relationship between absences, failures, studytime and alcohol use +The failures, absences and studytime are scaled according to the counts of the alcohol users in different levels. +```{r} +alc2=group_by(alc,alc_use) +tab_sum=summarise(alc2,count=n(),absences=sum(absences),failures=sum(failures),studytime=sum(studytime)) +tab_sum=mutate(tab_sum,abs_count=absences/count,fai_count=failures/count,styt_count=studytime/count) +tab_sum +``` +```{r} +bar_absences=ggplot(tab_sum,aes(x=alc_use,y=abs_count))+geom_bar(stat='identity'); bar_absences +bar_failures=ggplot(tab_sum,aes(x=alc_use,y=fai_count))+geom_bar(stat='identity'); bar_failures +bar_studytime=ggplot(tab_sum,aes(x=alc_use,y=styt_count))+geom_bar(stat='identity'); bar_studytime +``` + +`absences`~`alc_use`: +There ia an increasing trend with absenses and alcohol use, which is in line with our hypothesis. When the alcohol use is 4.5, the absence is extremely high. The second high absence happens when the alcohol use is on the highest level. +`failures`~`alc_use`: +There is an positive correlation between failures and alcohol use. For light alcohol users, the failures are also in a low level, however, the failure reaches the highest mount when `alc_use`= 3. After that the failures fall down with incresing alcohol use, and we interpret this as lacking of enough samples. For extreme high alcohol users (`alc_use`=5), the failures are at the highest level, the same as `alc_use`=3. +`studytime`~`alc_use`: +The figure shows that there is no obvious relations between the study time and alcohol use. This is not in agreement with our hypothesis before. The lowest alcohol users have the most study time and the study time of the highest users are low compared with the other alcohol using levels. But the difference bwteen them are not quite obvious. + +### Box plots by goups +Box plots are an excellent way of displaying and comparing distributions. The box visualizes the percentiles of the 25th, 50th and 75th of the data, while the whiskers show the typical range and the ourliers of a variable. +```{r} +box_absences=ggplot(alc,aes(x=high_use,y=absences))+geom_boxplot(); box_absences +box_failures=ggplot(alc,aes(x=high_use,y=failures))+geom_boxplot(); box_failures +box_studytime=ggplot(alc,aes(x=high_use,y=studytime))+geom_boxplot(); box_studytime +``` + +From the box plot of `absences` vs. `high_use`, it is obvious that the high alcohol users (`alc_use` > 2) are most likely to be absent from school. The box plot of `studytime` vs. `high_use` shows that high alcohol use also reduces the study time of the students. The conclusiona are in line with our hypothesis before. + +## Step 4: Logistic regression +The logistic regression is used here to identify factors (failures,absences,sex and studytime) related to higher than average student alcohol consumption. +```{r} +m=glm(high_use~failures+absences+sex+studytime, data=alc,family='binomial') +summary(m) +coef(m) +``` + +According to the summary results, the estimated coefficients for failures, absences, sexM and studytime are 0.360, 0.087, 0.795 and -0.340 respectively. The results show that, for failures, absences and sexM, the correlations between them and alcohol use are positive while for studytime, the correlation is negative. This is in agreement with our previous hypothesis. According to the `P value` shown in the summary part, the biggest possibility happens between `absences` and `high_use`. The relation between `failures` and `high_use` may seem not quite convincing and this is in agreement with the box plot shown in the last part. + +```{r} +OR=coef(m) %>% exp +CI=confint(m) %>% exp +cbind(OR,CI) +``` + +The ratio of expected "success" to "failures" are called the odds: p/(1-p). Odds are an alternative way of expressing probabilities. Higher odds corresponds to a higher probability of success when OR > 1. Odds higher than 1 means that X is positively associated with "success". If OR < 1, lower odds corresponds to the higher probability of success. The computational target variable in the logistic regression model is the log of odds, so applying exponent function to the modelled values gives the odds. +From the summary of the odds one can see that sexM gives the largest odds. This means that sexM has higher probability to high alcolhol use compared to failures and absences. The odds of studytime is the lower than 1. The result indicate that higher alcohol use corresponds to less study time. +The confidence intervals of 2.5% and 97.5 % for the odd ratios are also listed in the data frame. + +## Step 5: Binary predictions +predict() the probability of high_use +```{r} +probabilities <- predict(m, type = "response") +alc <- mutate(alc, probability = probabilities) +alc <- mutate(alc, prediction = probability>0.5) +select(alc, failures, absences, sex, studytime, high_use, probability, prediction) %>% tail(10) +table(high_use = alc$high_use, prediction = alc$prediction)%>%addmargins +g=ggplot(alc, aes(x = probability, y = high_use, col=prediction)) +g=g+geom_point() +g +table(high_use = alc$high_use, prediction = alc$prediction)%>% prop.table%>%addmargins +``` +According to the last 10 rows of data, we can see that most of the predictions are correct, except for the last two one. The last two samples are high alcohol users however, the prediction show that they are not, which is incorrect. +The cross tabulation of predictions versus the actual values show that 256 out of 268 `FALSE`(non-high alcohol users) values were predicted correctly by the model, while only 34 of 114 `TRUE`(high alcohol users) were predicted correctly. The correct prediction rate of `FALSE` samples is 95.5% while the correct prediction rate of `TRUE` samples is only 29.8%. +The results show that the model could give relatively good predictions for `FALSE` results while for the prediction of `TRUE` results is not sensitive. + +## Step 6: Compute the average number of incorrect predictions +Accuracy: the average number of correctly classified observations. +Penalty (loss) function: the mean of incorrectly classified observations. +Less penalty function means better predictions. +```{r} +# define a loss function (mean prediction error) +loss_func <- function(class, prob) { + n_wrong <- abs(class - prob) > 0.5 + mean(n_wrong) +} +# call loss_func to compute the average number of wrong predictions in the data +loss_func(class = alc$high_use, prob = alc$probability) +``` +So, the wrong predictions of the model is about 24.1%. Combined with the analysis from step 5, we know that most of the wrong predictions are `TRUE` results (12 wrongly prediction for `FALSE` scenarios and 80 wrongly prediction for `TRUE` scenarios). + +## Step 7: Cross-validation +Cross-validation is a method of testing a predictive model on unseen data. In cross-validation, the value of a penalty (loss) function (mean prediction error) is computed on data not used for finding the model. The low value of cross-validation result means better model predictions. +Perform 10-fold cross-validation +```{r} +library(boot) +cv <- cv.glm(data = alc, cost = loss_func, glmfit = m, K = 10) +cv$delta[1] +``` +The 10-fold cross-validation result show that the test set performance are mostly between 0.25 and 0.26. There is no obvious smaller prediction error than the model introduced in DataCamp which has an error of about 0.26. + + + + + + + + + + + + + diff --git a/chapter3.html b/chapter3.html new file mode 100644 index 000000000..f89e8bb81 --- /dev/null +++ b/chapter3.html @@ -0,0 +1,354 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + +
+

Chapter 3 Logistic regression

+

Created on 18.11.2017 @author: Xiaodong Li This is the script for RStudio exercise 3 – Data analysis The work focuses on exploring data and performing and interpreting logistic regression analysis on the UCI Machine Learning Repository, Student Performance Data Set.

+
+

Step 0: import packages

+
library(tidyr)
+library(dplyr)
+
## 
+## Attaching package: 'dplyr'
+
## The following objects are masked from 'package:stats':
+## 
+##     filter, lag
+
## The following objects are masked from 'package:base':
+## 
+##     intersect, setdiff, setequal, union
+
library(ggplot2)
+
+
+

Step 1:read data

+
alc=read.csv('/home/xiaodong/IODS_course/IODS-project/data/alc.csv',sep=',',header = TRUE)
+colnames(alc)
+
##  [1] "school"     "sex"        "age"        "address"    "famsize"   
+##  [6] "Pstatus"    "Medu"       "Fedu"       "Mjob"       "Fjob"      
+## [11] "reason"     "nursery"    "internet"   "guardian"   "traveltime"
+## [16] "studytime"  "failures"   "schoolsup"  "famsup"     "paid"      
+## [21] "activities" "higher"     "romantic"   "famrel"     "freetime"  
+## [26] "goout"      "Dalc"       "Walc"       "health"     "absences"  
+## [31] "G1"         "G2"         "G3"         "alc_use"    "high_use"
+

The data used in the exercise is a joined data set that combines the two student alcohol consumption data sets, student-mat.csv and student-por.csv. The two data sets are retrieved from the UCI Machine Learning Repository. The data are from two identical questionaires related to secondary school student alcohol consumption in Portugal. For more background information, please check here. The variables not used for joining the two data have been combined by averaging. The alc_use colume is the average of weekday (Dalc) and weekend (Walc) alcohol use. The high_use column records if the alc_use is higher than 2 or not.

+
+
+

Step 2:hypothesis about relationships with alcohol consumption

+

Choose four interesting variables in the data and present personal hypothesis about their relationships with alcohol consumption. - failures: positive correlation, the more alcohol consumption, the more failures
+- absenses: positive correlation, the more alcohol consumption, the more absenses
+- sex: male is more than female students with high alcohol use
+- studytime: negative correlation, the more alcohol consumption, the less studytime

+
+
+

Step 3: Explore the distributions of the chosen variables and there relationships with alcohol consumption

+
+

The relationship between sex and alcohol use

+
bar_sex=ggplot(alc, aes(x=alc_use,fill=sex))+geom_bar(); bar_sex
+

sex~alc_use:
+According to the count~alc_use bar figure plotted according to different sexes, we can see that female students are the main low alcohol users (alc_use < 2.5), however, for high alcohol users (alc_use > 2.5), most of them are male students. The bar figure also tells us that most of the alcohol users are very light users and the numbers of them decrease quickly with the increasing alcohol use levels (except for the extreme high users).

+
+
+

The relationship between absences, failures, studytime and alcohol use

+

The failures, absences and studytime are scaled according to the counts of the alcohol users in different levels.

+
alc2=group_by(alc,alc_use)
+tab_sum=summarise(alc2,count=n(),absences=sum(absences),failures=sum(failures),studytime=sum(studytime))
+tab_sum=mutate(tab_sum,abs_count=absences/count,fai_count=failures/count,styt_count=studytime/count)
+tab_sum
+
## # A tibble: 9 x 8
+##   alc_use count absences failures studytime abs_count fai_count styt_count
+##     <dbl> <int>    <int>    <int>     <int>     <dbl>     <dbl>      <dbl>
+## 1     1.0   140      470       15       323  3.357143 0.1071429   2.307143
+## 2     1.5    69      292       10       136  4.231884 0.1449275   1.971014
+## 3     2.0    59      231       13       117  3.915254 0.2203390   1.983051
+## 4     2.5    44      283        6        85  6.431818 0.1363636   1.931818
+## 5     3.0    32      195       18        55  6.093750 0.5625000   1.718750
+## 6     3.5    17       96        8        25  5.647059 0.4705882   1.470588
+## 7     4.0     9       54        2        16  6.000000 0.2222222   1.777778
+## 8     4.5     3       36        0         6 12.000000 0.0000000   2.000000
+## 9     5.0     9       62        5        15  6.888889 0.5555556   1.666667
+
bar_absences=ggplot(tab_sum,aes(x=alc_use,y=abs_count))+geom_bar(stat='identity'); bar_absences
+

+
bar_failures=ggplot(tab_sum,aes(x=alc_use,y=fai_count))+geom_bar(stat='identity'); bar_failures
+

+
bar_studytime=ggplot(tab_sum,aes(x=alc_use,y=styt_count))+geom_bar(stat='identity'); bar_studytime
+

+

absences~alc_use:
+There ia an increasing trend with absenses and alcohol use, which is in line with our hypothesis. When the alcohol use is 4.5, the absence is extremely high. The second high absence happens when the alcohol use is on the highest level.
+failures~alc_use:
+There is an positive correlation between failures and alcohol use. For light alcohol users, the failures are also in a low level, however, the failure reaches the highest mount when alc_use= 3. After that the failures fall down with incresing alcohol use, and we interpret this as lacking of enough samples. For extreme high alcohol users (alc_use=5), the failures are at the highest level, the same as alc_use=3.
+studytime~alc_use:
+The figure shows that there is no obvious relations between the study time and alcohol use. This is not in agreement with our hypothesis before. The lowest alcohol users have the most study time and the study time of the highest users are low compared with the other alcohol using levels. But the difference bwteen them are not quite obvious.

+
+
+

Box plots by goups

+

Box plots are an excellent way of displaying and comparing distributions. The box visualizes the percentiles of the 25th, 50th and 75th of the data, while the whiskers show the typical range and the ourliers of a variable.

+
box_absences=ggplot(alc,aes(x=high_use,y=absences))+geom_boxplot(); box_absences
+

+
box_failures=ggplot(alc,aes(x=high_use,y=failures))+geom_boxplot(); box_failures
+

+
box_studytime=ggplot(alc,aes(x=high_use,y=studytime))+geom_boxplot(); box_studytime
+

+

From the box plot of absences vs. high_use, it is obvious that the high alcohol users (alc_use > 2) are most likely to be absent from school. The box plot of studytime vs. high_use shows that high alcohol use also reduces the study time of the students. The conclusiona are in line with our hypothesis before.

+
+
+
+

Step 4: Logistic regression

+

The logistic regression is used here to identify factors (failures,absences,sex and studytime) related to higher than average student alcohol consumption.

+
m=glm(high_use~failures+absences+sex+studytime, data=alc,family='binomial')
+summary(m)
+
## 
+## Call:
+## glm(formula = high_use ~ failures + absences + sex + studytime, 
+##     family = "binomial", data = alc)
+## 
+## Deviance Residuals: 
+##     Min       1Q   Median       3Q      Max  
+## -2.1213  -0.8226  -0.6017   1.0824   2.1185  
+## 
+## Coefficients:
+##             Estimate Std. Error z value Pr(>|z|)    
+## (Intercept) -1.11174    0.43028  -2.584 0.009773 ** 
+## failures     0.36048    0.19472   1.851 0.064126 .  
+## absences     0.08734    0.02296   3.803 0.000143 ***
+## sexM         0.79470    0.25212   3.152 0.001621 ** 
+## studytime   -0.34003    0.16259  -2.091 0.036499 *  
+## ---
+## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+## 
+## (Dispersion parameter for binomial family taken to be 1)
+## 
+##     Null deviance: 465.68  on 381  degrees of freedom
+## Residual deviance: 419.82  on 377  degrees of freedom
+## AIC: 429.82
+## 
+## Number of Fisher Scoring iterations: 4
+
coef(m)
+
## (Intercept)    failures    absences        sexM   studytime 
+## -1.11173770  0.36048380  0.08734126  0.79469663 -0.34003347
+

According to the summary results, the estimated coefficients for failures, absences, sexM and studytime are 0.360, 0.087, 0.795 and -0.340 respectively. The results show that, for failures, absences and sexM, the correlations between them and alcohol use are positive while for studytime, the correlation is negative. This is in agreement with our previous hypothesis. According to the P value shown in the summary part, the biggest possibility happens between absences and high_use. The relation between failures and high_use may seem not quite convincing and this is in agreement with the box plot shown in the last part.

+
OR=coef(m) %>% exp
+CI=confint(m) %>% exp
+
## Waiting for profiling to be done...
+
cbind(OR,CI)
+
##                    OR     2.5 %    97.5 %
+## (Intercept) 0.3289868 0.1402796 0.7609560
+## failures    1.4340230 0.9804979 2.1153252
+## absences    1.0912690 1.0455005 1.1442053
+## sexM        2.2137693 1.3559547 3.6508476
+## studytime   0.7117465 0.5129770 0.9721184
+

The ratio of expected “success” to “failures” are called the odds: p/(1-p). Odds are an alternative way of expressing probabilities. Higher odds corresponds to a higher probability of success when OR > 1. Odds higher than 1 means that X is positively associated with “success”. If OR < 1, lower odds corresponds to the higher probability of success. The computational target variable in the logistic regression model is the log of odds, so applying exponent function to the modelled values gives the odds.
+From the summary of the odds one can see that sexM gives the largest odds. This means that sexM has higher probability to high alcolhol use compared to failures and absences. The odds of studytime is the lower than 1. The result indicate that higher alcohol use corresponds to less study time.
+The confidence intervals of 2.5% and 97.5 % for the odd ratios are also listed in the data frame.

+
+
+

Step 5: Binary predictions

+

predict() the probability of high_use

+
probabilities <- predict(m, type = "response")
+alc <- mutate(alc, probability = probabilities)
+alc <- mutate(alc, prediction = probability>0.5)
+select(alc, failures, absences, sex, studytime, high_use, probability, prediction) %>% tail(10)
+
##     failures absences sex studytime high_use probability prediction
+## 373        1        0   M         1    FALSE   0.4263911      FALSE
+## 374        1        7   M         1     TRUE   0.5780560       TRUE
+## 375        0        1   F         3    FALSE   0.1146096      FALSE
+## 376        0        6   F         1    FALSE   0.2833868      FALSE
+## 377        1        2   F         3    FALSE   0.1684473      FALSE
+## 378        0        2   F         2    FALSE   0.1656021      FALSE
+## 379        2        2   F         2    FALSE   0.2898414      FALSE
+## 380        0        3   F         2    FALSE   0.1780258      FALSE
+## 381        0        4   M         1     TRUE   0.4236739      FALSE
+## 382        0        2   M         1     TRUE   0.3816874      FALSE
+
table(high_use = alc$high_use, prediction = alc$prediction)%>%addmargins
+
##         prediction
+## high_use FALSE TRUE Sum
+##    FALSE   256   12 268
+##    TRUE     80   34 114
+##    Sum     336   46 382
+
g=ggplot(alc, aes(x = probability, y = high_use, col=prediction))
+g=g+geom_point()
+g
+

+
table(high_use = alc$high_use, prediction = alc$prediction)%>% prop.table%>%addmargins
+
##         prediction
+## high_use      FALSE       TRUE        Sum
+##    FALSE 0.67015707 0.03141361 0.70157068
+##    TRUE  0.20942408 0.08900524 0.29842932
+##    Sum   0.87958115 0.12041885 1.00000000
+

According to the last 10 rows of data, we can see that most of the predictions are correct, except for the last two one. The last two samples are high alcohol users however, the prediction show that they are not, which is incorrect.
+The cross tabulation of predictions versus the actual values show that 256 out of 268 FALSE(non-high alcohol users) values were predicted correctly by the model, while only 34 of 114 TRUE(high alcohol users) were predicted correctly. The correct prediction rate of FALSE samples is 95.5% while the correct prediction rate of TRUE samples is only 29.8%.
+The results show that the model could give relatively good predictions for FALSE results while for the prediction of TRUE results is not sensitive.

+
+
+

Step 6: Compute the average number of incorrect predictions

+

Accuracy: the average number of correctly classified observations. Penalty (loss) function: the mean of incorrectly classified observations. Less penalty function means better predictions.

+
# define a loss function (mean prediction error)
+loss_func <- function(class, prob) {
+  n_wrong <- abs(class - prob) > 0.5
+  mean(n_wrong)
+}
+# call loss_func to compute the average number of wrong predictions in the data
+loss_func(class = alc$high_use, prob = alc$probability)
+
## [1] 0.2408377
+

So, the wrong predictions of the model is about 24.1%. Combined with the analysis from step 5, we know that most of the wrong predictions are TRUE results (12 wrongly prediction for FALSE scenarios and 80 wrongly prediction for TRUE scenarios).

+
+
+

Step 7: Cross-validation

+

Cross-validation is a method of testing a predictive model on unseen data. In cross-validation, the value of a penalty (loss) function (mean prediction error) is computed on data not used for finding the model. The low value of cross-validation result means better model predictions.
+Perform 10-fold cross-validation

+
library(boot)
+cv <- cv.glm(data = alc, cost = loss_func, glmfit = m, K = 10)
+cv$delta[1]
+
## [1] 0.2696335
+

The 10-fold cross-validation result show that the test set performance are mostly between 0.25 and 0.26. There is no obvious smaller prediction error than the model introduced in DataCamp which has an error of about 0.26.

+
+
+ + + + +
+ + + + + + + + diff --git a/chapter4.Rmd b/chapter4.Rmd new file mode 100644 index 000000000..96c1a2c7f --- /dev/null +++ b/chapter4.Rmd @@ -0,0 +1,150 @@ +# Chapter 4 Clustering and classification +Created on 26.11.2017 +@author: Xiaodong Li +This is the script for RStudio exercise 4 -- Clustering and classification +The work focuses on exploring data and performing clustering methods which try to find the clusters (or groups) from the data. Clustering means that some points (or observations) of the data are in some sense closer to each other than some other points. Based on a successful clustering, we may try to classify new observations to these clusters and hence validate the results of clustering. This week's data is the Boston data from the MASS package. + +## Step 0: Import packages +```{r} +library(MASS) +library(corrplot) +library(tidyr) +library(dplyr) +library(ggplot2) +``` + +##Step 1: Load and explore the data +```{r} +data("Boston") +str(Boston) +dim(Boston) +``` +The `Boston` data describes the housing values in the suburs of Boston. Is contains 14 variables which describe the situations of the housing environment like `crim`: per capita crime rate by town; `lstat`: lower status of the population (percent). In each variable there are 506 observations giving the detailed data of the coresponding variable. + +## Step 2: The correlations between variables +The function `cor()` can be used to create the correlation matrix. A more visual way to look at the correlations is to use `corrplot()` function (from the corrplot package). +```{r} +cor_matrix<-cor(Boston) %>% round(2) +corrplot(cor_matrix, method="circle",type='upper',cl.pos='b',tl.pos='d',tl.cex=0.6) +``` + +The corrplot shows the correlations between variables of the Boston dataset. The darker color in the corrplot indicates more straight corelation. Blue color means a positive correlation while red color means a negative correlation. Then from the figure we can summarise that `rad` (index of accessibility to radial highways) and `tax` (full-value property-tax rate per \$10000) have very strong positive correlation. And `dis` (weighted mean of distances to five Boston employment centres) very strong negative correlations with `nox` (nitrogen oxides concentration), `age` (proportion of owner-occupied units built prior to 1940) and `indux` (proportion of non-retail business acres per town). `medv` (meidan value of owner-occupied homes in \$1000) and `lstat` (lower status of the population) have very strong negative correlation too. + +## Step 3: Scale the whole dataset +In the scaling we subtract the column means from the corresponding columns and divide the difference with standard deviation. +$scaled(x) = \frac{x - mean(x)}{ sd(x)}$ +```{r} +boston_scaled <- scale(Boston) +summary(boston_scaled) +``` +The variables changed according to the formula shown above. After the scaling, we can see that the data are all quite near 0 which is the mean value of the variable. Negative values mean that the data are less than the mean value while the positive figures mean that the data are bigger values than the mean value. +We want to cut the variable by quantiles to get the high, low and middle rates of crime into their own categories. +```{r} +boston_scaled=as.data.frame(boston_scaled) +bins=quantile(boston_scaled$crim) +crime=cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label = c('low','med_low','med_high','high')) +table(crime) +boston_scaled=dplyr::select(boston_scaled, -crim) +boston_scaled=data.frame(boston_scaled, crime) +n <- nrow(boston_scaled) +ind <- sample(n, size = n * 0.8) +train <- boston_scaled[ind,] +test <- boston_scaled[-ind,] +correct_classes <- test$crime +test <- dplyr::select(test, -crime) +``` +First, we use the quantiles as the break points and creat a categorical variable of the crime rate in the Boston dataset. Then the old crime rate variable is dropped from the old crime rate variable. And then the dataset is divided into train and test sets where 80% of the data belongs to the train set. + +## Step 4: Linear discriminant analysis +**Linear Discriminant analysis** is a classification (and dimension reduction) method. It finds the (linear) combination of the variables that separate the target variable classes. The target can be binary or multiclass variable. +```{r} +lda.fit <- lda(crime~., data = train) +lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){ + heads <- coef(x) + arrows(x0 = 0, y0 = 0, + x1 = myscale * heads[,choices[1]], + y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads) + text(myscale * heads[,choices], labels = row.names(heads), + cex = tex, col=color, pos=3) +} +classes <- as.numeric(train$crime) +plot(lda.fit, dimen = 2,col=classes,pch=classes) +lda.arrows(lda.fit, myscale = 3) +``` + +LDA can be visualized with a biplot. A Biplot is an enhanced scatterplot that uses both points and vectors to represent structure. A biplot uses points to represent the scores of the observations on the principal components, and it uses vectors to represent the coefficients of the variables on the principal components. +`Points`: Points that are close together correspond to observations that have similar scores on the components displayed in the plot. To the extent that these components fit the data well, the points also correspond to observations that have similar values on the variables. +`Vectors`: A vector points in the direction which is most like the variable represented by the vector. This is the direction which has the highest squared multiple correlation with the principal components. The length of the vector is proportional to the squared multiple correlation between the fitted values for the variable and the variable itself. + +## Step 5: Predict LDA +The function `predict()` can be used to predict values based on a model. +We used the test data got from Step 3 where the crime categories is saved as `correct_classes` and the categorical crime variable is removed from the the test dataset. +```{r} +lda.pred=predict(lda.fit,newdata=test) +table(correct=correct_classes,predicted=lda.pred$class) %>% addmargins +``` +From the cross table we can see that the model could give relatively good predictions of the crime rate especially at high rate district. The correct prediction rates are shown below: +```{r} +correct=c(16,23,13,26) +correct=c(correct,sum(correct)) +sumdata=c(27,30,18,27) +sumdata=c(sumdata,sum(sumdata)) +index=c('low','med_low','med_high','high','sum') +t=data.frame(correct=index,predict=correct,sum=sumdata) +t$percentage=t$predict/t$sum +t +``` +From the table we can see that on the whole the corrected prediction precentage is 76.5% and the percentage increases with the increase of crime rate. The model is more suitable for predict high crime rate area. + +## Step 6: Distance measures and clustering +**Distance measurements** +Similarity and dissimilarity of objects can be measured with distance measures. There are many different measures for different types of data. Here we perform *Euclidean distance* and *Manhattan distance* for the data. +```{r} +data('Boston') +boston_scaled=scale(Boston) +dist_eu=dist(boston_scaled,method='euclidean') +summary(dist_eu) +dist_man=dist(boston_scaled,method='manhattan') +summary(dist_man) +``` +The calculations of thest two distances are: +![distance figure](images/distance.png) + +**K-means** +K-means is maybe the most used and known clustering method. It is an unsupervised method, that assighs observations to groups or cluster based on similarity of the objects. +Three clusters is tried first. +```{r} +km=kmeans(boston_scaled,centers = 3) +pairs(boston_scaled,col=km$cluster) +``` + +**Find the optimal number of cluster** +One way to determine the number of clusters is to look at how the total of within cluster sum of squares (WCSS) behaves when the number of cluster changes. When you plot the number of clusters and the total WCSS, the optimal number of clusters is when the total WCSS drops radically. +```{r} +set.seed(123) +k_max=10 +twcss=sapply(1:k_max,function(k){kmeans(boston_scaled,k)$tot.withinss}) +qplot(x=1:k_max,y=twcss,geom='line') +``` + +According to the line figure shown above, the most radically drop of the line happens when the K value is 2. So the optimal number of clusters is 2. +```{r} +km=kmeans(boston_scaled,centers=2) +pairs(boston_scaled,col=km$cluster) +``` + +From the figure we can see that, for most of the variables, the k-means method could classify the results quite well. +The method of calculating K-means: +1. Choose the number of clusters and initial centroids. +2. Calculate distances between centroids and data points. +3. For all the data points: assign data point to clusters based on which centroid is closest. +4. Update centroids: within each cluster, calculate new centroid. +5. Update cluster: calculate distances between data points and updated centroids. If some other centroid is closer than the cluster centroid where the data point belongs, the data point changes cluster. +Continue updating steps until the centroids or the clusters do not change. +K-means is a quick and simple method to cluster analysis. It aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster. +However, the number of clusters k is very unpredictable. In this example, we used a simple way to find the optimal k value. But we must remember that, an inappropriate choice of k may yield poor results. +The choice of the initial cluster center has a great impact on the clustering result. Once the initial value is not chosen well, it may not be able to get a valid clustering result. The K-means method randomly assigns the initial cluster centers and this is a major issue of K-means algorithms. We used the function `set.seed()` to deal with the problem, but usually we need to choose the initial centers quite well. + + + + diff --git a/chapter4.html b/chapter4.html new file mode 100644 index 000000000..0781370ea --- /dev/null +++ b/chapter4.html @@ -0,0 +1,357 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + +
+

Chapter 4 Clustering and classification

+

Created on 26.11.2017 @author: Xiaodong Li This is the script for RStudio exercise 4 – Clustering and classification The work focuses on exploring data and performing clustering methods which try to find the clusters (or groups) from the data. Clustering means that some points (or observations) of the data are in some sense closer to each other than some other points. Based on a successful clustering, we may try to classify new observations to these clusters and hence validate the results of clustering. This week’s data is the Boston data from the MASS package.

+
+

Step 0: Import packages

+
library(MASS)
+library(corrplot)
+
## corrplot 0.84 loaded
+
library(tidyr)
+library(dplyr)
+
## 
+## Attaching package: 'dplyr'
+
## The following object is masked from 'package:MASS':
+## 
+##     select
+
## The following objects are masked from 'package:stats':
+## 
+##     filter, lag
+
## The following objects are masked from 'package:base':
+## 
+##     intersect, setdiff, setequal, union
+
library(ggplot2)
+
+
+

Step 1: Load and explore the data

+
data("Boston")
+str(Boston)
+
## 'data.frame':    506 obs. of  14 variables:
+##  $ crim   : num  0.00632 0.02731 0.02729 0.03237 0.06905 ...
+##  $ zn     : num  18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
+##  $ indus  : num  2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
+##  $ chas   : int  0 0 0 0 0 0 0 0 0 0 ...
+##  $ nox    : num  0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
+##  $ rm     : num  6.58 6.42 7.18 7 7.15 ...
+##  $ age    : num  65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
+##  $ dis    : num  4.09 4.97 4.97 6.06 6.06 ...
+##  $ rad    : int  1 2 2 3 3 3 5 5 5 5 ...
+##  $ tax    : num  296 242 242 222 222 222 311 311 311 311 ...
+##  $ ptratio: num  15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
+##  $ black  : num  397 397 393 395 397 ...
+##  $ lstat  : num  4.98 9.14 4.03 2.94 5.33 ...
+##  $ medv   : num  24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...
+
dim(Boston)
+
## [1] 506  14
+

The Boston data describes the housing values in the suburs of Boston. Is contains 14 variables which describe the situations of the housing environment like crim: per capita crime rate by town; lstat: lower status of the population (percent). In each variable there are 506 observations giving the detailed data of the coresponding variable.

+
+
+

Step 2: The correlations between variables

+

The function cor() can be used to create the correlation matrix. A more visual way to look at the correlations is to use corrplot() function (from the corrplot package).

+
cor_matrix<-cor(Boston) %>% round(2)
+corrplot(cor_matrix, method="circle",type='upper',cl.pos='b',tl.pos='d',tl.cex=0.6)
+

+

The corrplot shows the correlations between variables of the Boston dataset. The darker color in the corrplot indicates more straight corelation. Blue color means a positive correlation while red color means a negative correlation. Then from the figure we can summarise that rad (index of accessibility to radial highways) and tax (full-value property-tax rate per $10000) have very strong positive correlation. And dis (weighted mean of distances to five Boston employment centres) very strong negative correlations with nox (nitrogen oxides concentration), age (proportion of owner-occupied units built prior to 1940) and indux (proportion of non-retail business acres per town). medv (meidan value of owner-occupied homes in $1000) and lstat (lower status of the population) have very strong negative correlation too.

+
+
+

Step 3: Scale the whole dataset

+

In the scaling we subtract the column means from the corresponding columns and divide the difference with standard deviation.
+\(scaled(x) = \frac{x - mean(x)}{ sd(x)}\)

+
boston_scaled <- scale(Boston)
+summary(boston_scaled)
+
##       crim                 zn               indus        
+##  Min.   :-0.419367   Min.   :-0.48724   Min.   :-1.5563  
+##  1st Qu.:-0.410563   1st Qu.:-0.48724   1st Qu.:-0.8668  
+##  Median :-0.390280   Median :-0.48724   Median :-0.2109  
+##  Mean   : 0.000000   Mean   : 0.00000   Mean   : 0.0000  
+##  3rd Qu.: 0.007389   3rd Qu.: 0.04872   3rd Qu.: 1.0150  
+##  Max.   : 9.924110   Max.   : 3.80047   Max.   : 2.4202  
+##       chas              nox                rm               age         
+##  Min.   :-0.2723   Min.   :-1.4644   Min.   :-3.8764   Min.   :-2.3331  
+##  1st Qu.:-0.2723   1st Qu.:-0.9121   1st Qu.:-0.5681   1st Qu.:-0.8366  
+##  Median :-0.2723   Median :-0.1441   Median :-0.1084   Median : 0.3171  
+##  Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
+##  3rd Qu.:-0.2723   3rd Qu.: 0.5981   3rd Qu.: 0.4823   3rd Qu.: 0.9059  
+##  Max.   : 3.6648   Max.   : 2.7296   Max.   : 3.5515   Max.   : 1.1164  
+##       dis               rad               tax             ptratio       
+##  Min.   :-1.2658   Min.   :-0.9819   Min.   :-1.3127   Min.   :-2.7047  
+##  1st Qu.:-0.8049   1st Qu.:-0.6373   1st Qu.:-0.7668   1st Qu.:-0.4876  
+##  Median :-0.2790   Median :-0.5225   Median :-0.4642   Median : 0.2746  
+##  Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
+##  3rd Qu.: 0.6617   3rd Qu.: 1.6596   3rd Qu.: 1.5294   3rd Qu.: 0.8058  
+##  Max.   : 3.9566   Max.   : 1.6596   Max.   : 1.7964   Max.   : 1.6372  
+##      black             lstat              medv        
+##  Min.   :-3.9033   Min.   :-1.5296   Min.   :-1.9063  
+##  1st Qu.: 0.2049   1st Qu.:-0.7986   1st Qu.:-0.5989  
+##  Median : 0.3808   Median :-0.1811   Median :-0.1449  
+##  Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
+##  3rd Qu.: 0.4332   3rd Qu.: 0.6024   3rd Qu.: 0.2683  
+##  Max.   : 0.4406   Max.   : 3.5453   Max.   : 2.9865
+

The variables changed according to the formula shown above. After the scaling, we can see that the data are all quite near 0 which is the mean value of the variable. Negative values mean that the data are less than the mean value while the positive figures mean that the data are bigger values than the mean value.
+We want to cut the variable by quantiles to get the high, low and middle rates of crime into their own categories.

+
boston_scaled=as.data.frame(boston_scaled)
+bins=quantile(boston_scaled$crim)
+crime=cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label = c('low','med_low','med_high','high'))
+table(crime)
+
## crime
+##      low  med_low med_high     high 
+##      127      126      126      127
+
boston_scaled=dplyr::select(boston_scaled, -crim)
+boston_scaled=data.frame(boston_scaled, crime)
+n <- nrow(boston_scaled)
+ind <- sample(n,  size = n * 0.8)
+train <- boston_scaled[ind,]
+test <- boston_scaled[-ind,]
+correct_classes <- test$crime
+test <- dplyr::select(test, -crime)
+

First, we use the quantiles as the break points and creat a categorical variable of the crime rate in the Boston dataset. Then the old crime rate variable is dropped from the old crime rate variable. And then the dataset is divided into train and test sets where 80% of the data belongs to the train set.

+
+
+

Step 4: Linear discriminant analysis

+

Linear Discriminant analysis is a classification (and dimension reduction) method. It finds the (linear) combination of the variables that separate the target variable classes. The target can be binary or multiclass variable.

+
lda.fit <- lda(crime~., data = train)
+lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){
+  heads <- coef(x)
+  arrows(x0 = 0, y0 = 0, 
+         x1 = myscale * heads[,choices[1]], 
+         y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads)
+  text(myscale * heads[,choices], labels = row.names(heads), 
+       cex = tex, col=color, pos=3)
+}
+classes <- as.numeric(train$crime)
+plot(lda.fit, dimen = 2,col=classes,pch=classes)
+lda.arrows(lda.fit, myscale = 3)
+

+

LDA can be visualized with a biplot. A Biplot is an enhanced scatterplot that uses both points and vectors to represent structure. A biplot uses points to represent the scores of the observations on the principal components, and it uses vectors to represent the coefficients of the variables on the principal components.
+Points: Points that are close together correspond to observations that have similar scores on the components displayed in the plot. To the extent that these components fit the data well, the points also correspond to observations that have similar values on the variables.
+Vectors: A vector points in the direction which is most like the variable represented by the vector. This is the direction which has the highest squared multiple correlation with the principal components. The length of the vector is proportional to the squared multiple correlation between the fitted values for the variable and the variable itself.

+
+
+

Step 5: Predict LDA

+

The function predict() can be used to predict values based on a model.
+We used the test data got from Step 3 where the crime categories is saved as correct_classes and the categorical crime variable is removed from the the test dataset.

+
lda.pred=predict(lda.fit,newdata=test)
+table(correct=correct_classes,predicted=lda.pred$class) %>% addmargins
+
##           predicted
+## correct    low med_low med_high high Sum
+##   low       15       8        3    0  26
+##   med_low    4       9        7    0  20
+##   med_high   1      11       17    1  30
+##   high       0       0        0   26  26
+##   Sum       20      28       27   27 102
+

From the cross table we can see that the model could give relatively good predictions of the crime rate especially at high rate district. The correct prediction rates are shown below:

+
correct=c(16,23,13,26)
+correct=c(correct,sum(correct))
+sumdata=c(27,30,18,27)
+sumdata=c(sumdata,sum(sumdata))
+index=c('low','med_low','med_high','high','sum')
+t=data.frame(correct=index,predict=correct,sum=sumdata)
+t$percentage=t$predict/t$sum
+t
+
##    correct predict sum percentage
+## 1      low      16  27  0.5925926
+## 2  med_low      23  30  0.7666667
+## 3 med_high      13  18  0.7222222
+## 4     high      26  27  0.9629630
+## 5      sum      78 102  0.7647059
+

From the table we can see that on the whole the corrected prediction precentage is 76.5% and the percentage increases with the increase of crime rate. The model is more suitable for predict high crime rate area.

+
+
+

Step 6: Distance measures and clustering

+

Distance measurements
+Similarity and dissimilarity of objects can be measured with distance measures. There are many different measures for different types of data. Here we perform Euclidean distance and Manhattan distance for the data.

+
data('Boston')
+boston_scaled=scale(Boston)
+dist_eu=dist(boston_scaled,method='euclidean')
+summary(dist_eu)
+
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
+##  0.1343  3.4625  4.8241  4.9111  6.1863 14.3970
+
dist_man=dist(boston_scaled,method='manhattan')
+summary(dist_man)
+
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
+##  0.2662  8.4832 12.6090 13.5488 17.7568 48.8618
+

The calculations of thest two distances are:
+distance figure

+

K-means
+K-means is maybe the most used and known clustering method. It is an unsupervised method, that assighs observations to groups or cluster based on similarity of the objects.
+Three clusters is tried first.

+
km=kmeans(boston_scaled,centers = 3)
+pairs(boston_scaled,col=km$cluster)
+

+

Find the optimal number of cluster
+One way to determine the number of clusters is to look at how the total of within cluster sum of squares (WCSS) behaves when the number of cluster changes. When you plot the number of clusters and the total WCSS, the optimal number of clusters is when the total WCSS drops radically.

+
set.seed(123)
+k_max=10
+twcss=sapply(1:k_max,function(k){kmeans(boston_scaled,k)$tot.withinss})
+qplot(x=1:k_max,y=twcss,geom='line')
+

+

According to the line figure shown above, the most radically drop of the line happens when the K value is 2. So the optimal number of clusters is 2.

+
km=kmeans(boston_scaled,centers=2)
+pairs(boston_scaled,col=km$cluster)
+

+

From the figure we can see that, for most of the variables, the k-means method could classify the results quite well.
+The method of calculating K-means:
+1. Choose the number of clusters and initial centroids.
+2. Calculate distances between centroids and data points.
+3. For all the data points: assign data point to clusters based on which centroid is closest.
+4. Update centroids: within each cluster, calculate new centroid.
+5. Update cluster: calculate distances between data points and updated centroids. If some other centroid is closer than the cluster centroid where the data point belongs, the data point changes cluster.
+Continue updating steps until the centroids or the clusters do not change.
+K-means is a quick and simple method to cluster analysis. It aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster.
+However, the number of clusters k is very unpredictable. In this example, we used a simple way to find the optimal k value. But we must remember that, an inappropriate choice of k may yield poor results.
+The choice of the initial cluster center has a great impact on the clustering result. Once the initial value is not chosen well, it may not be able to get a valid clustering result. The K-means method randomly assigns the initial cluster centers and this is a major issue of K-means algorithms. We used the function set.seed() to deal with the problem, but usually we need to choose the initial centers quite well.

+
+
+ + + + +
+ + + + + + + + diff --git a/chapter5.Rmd b/chapter5.Rmd new file mode 100644 index 000000000..8e41e134b --- /dev/null +++ b/chapter5.Rmd @@ -0,0 +1,151 @@ +# Chapter 5 Dimensionality reduction technique +Created on 01.12.2017 +@author: Xiaodong Li +This is the script for RStudio exercise 5 -- Dimensionality reduction technique + +## Step 0: Import packages +```{r} +library(GGally) +library(corrplot) +``` + +## Step 1: Read and explore data +```{r} +human = read.table('/home/xiaodong/IODS_course/IODS-project/data/human.txt',sep='\t',header = TRUE) +str(human) +dim(human) +``` +The `human` data describes the Human Development Index (HDI) and Gross National Income (GNI) situation in different countries together with the education, labour and health experiences. The goal is to show that the people and the their capabilities should be the ultimate criteria for assessing the development of a country, not economic growth alone. +The meaning of different variables are shown below: + +* `Edu2.FM`: The ratio of Female and Male populations with secondary education + +* `Labo.FM`: The ratio of labour force participation of females and males + +* `life.Exp`: Life expectancy at birth + +* `Edu.Exp`: Expected years of education + +* `GNI`: Gross national income per capita + +* `Mat.Mor`: Maternal mortality ratio + +* `Ado.Birth`: Adolescent birth rate + +* `Parli.F`: Percent Representation in Parliament n + +## Step 2: Graphical overview of the data +Visuualize the `human` data with ggpairs() +```{r} +ggpairs(human) +``` + +Visualize the `human` data with correlation plots +```{r} +cor_matrix=cor(human) +corrplot(cor_matrix,type='upper') +``` + +The scatter plots and correlation plots between all the variables shown above give information about the relationships and distributions of all the data. From the plots we can see that `Life.Exp` has strong positive relation with `Edu.Exp` and also very strong negative relation with `Mat.Mor` and `Ado.Birth`. `Edu2.Fm` has strong negative relation with `Mat.Mor` too. + +## Step 3: Perform PCA on not standardized data +Perform Principal Component Analysis (PCA) with the SVD method +```{r} +pca_human=prcomp(human) +s=summary(pca_human) +s +pca_pr=round(100*s$importance[2,],digits=1) +pc_lab=paste0(names(pca_pr),'(',pca_pr,'%)') +biplot(pca_human,choices=1:2,cex=c(0.8,1),xlab=pc_lab[1],ylab=pc_lab[2]) +``` + +The biplot figure with not standardized variable is not clear because the varialbes have different scales and are not compariable. + +## Step 4: Perform PCA on standardized data +```{r} +human_std=scale(human) +pca_human=prcomp(human_std) +s=summary(pca_human) +s +pca_pr=round(100*s$importance[2,],digits=1) +pc_lab=paste0(names(pca_pr),'(',pca_pr,'%)') +biplot(pca_human,choices = 1:2,cex=c(0.8,1),xlab=pc_lab[1],ylab=pc_lab[2]) +``` + +The biplots got from `Step 3` and `Step 4` give different PCA results. For the data that was not standardized, the `GNI` variable has very big variance and all the data could be transformed to the first principal component (PC1). However, for the data that was standardized, all the variables have similar vairance and the features of the original data are comprised in several pricipal components. The different distributions of the data in these two different situations are shown clearly in the two biplots. +The biplot is a way of visualizing two representations of the same data. The biplot displays, + +1. The observations in a lower 2-dimensional representation. + A scatter plot is drawn where the observations are placed on X and Y coordinates defined by two pricipal components. + +2. The original features and their relationships with both each other and the pricipal components. + Arrows and/or labels are drawn to visualize the connections between the original features and pricipal components. +* The angle between arrows representing the original features can be interpreted as the corelation between the features. Small angle = high positive correlation. + +* The angle between a feature and a principal component axis can be interpreted as the correlation between the two. Small angle = high positive correlation. + +* The length of the arrows are proportional to the standard deviation of the features. +According to the description of the features of biplot we can summarize the relationship between the observations. +* `Mat.Mor` and `Ado.Birth` have high positive relationship between each other. + +* `Edu.Exp`,`Edu2.FM`,`GNI` and `Life.Exp` have high positive relationship between other. + +* The above two groups have high negative relationship between each other. + +* The standard deviation of the observations are quite similar because of the scaling process. + +## Step 5: Perform MCA on tea dataset +Load the tea dataset +```{r} +library(FactoMineR) +library(ggplot2) +library(dplyr) +library(tidyr) +data('tea') +str(tea) +dim(tea) +``` +The tea dataset contains the answers of a questionnaire on tea consumption for 300 individuals. Although the data contains 36 columns for demonstration purposes I will only consider 6 of the following columns: +```{r} +keep_columns=c('Tea','How','how','sugar','where','lunch') +tea_time=dplyr::select(tea,one_of(keep_columns)) +summary(tea_time) +str(tea_time) +gather(tea_time) %>% ggplot(aes(value))+geom_bar()+facet_wrap('key',scales='free')+theme(axis.text=element_text(angle=45,hjust = 1,size=8)) +``` + +Perform MCA on the selected tea dateset--`tea_time` +```{r} +mca=MCA(tea_time,graph=FALSE) +summary(mca) +plot(mca,invisible=c('ind'),habillage='quali') +``` + +Multiple Correspondence Analysis (MCA) is an extension of simple CA to analyse a data table containing more than two categorical variables. MCA is generally used to analyse a data from survey. +The objectives are to identify: + +* A group of individuals with similar profile in their answers to the questions + +* The associations between variable categories + +The result of the function summary() contains 4 tables: + +* Table 1 - Eigenvalues: table 1 contains the variances and the percentage of variances retained by each dimension. + +* Table 2 contains the coordinates, the contribution and the cos2 (quality of representation [in 0-1]) of the first 10 active individuals on the dimensions 1 and 2. +* Table 3 contains the coordinates, the contribution and the cos2 (quality of representation [in 0-1]) of the first 10 active variable categories on the dimensions 1 and 2. This table contains also a column called v.test. The value of the v.test is generally comprised between 2 and -2. For a given variable category, if the absolute value of the v.test is superior to 2, this means that the coordinate is significantly different from 0. + +* Table 4 - categorical variables (eta2): contains the squared correlation between each variable and the dimensions. + +The MCA graph shows a global pattern within the data. Rows (individuals) are usually represented by blue points and columns (variable categories) by red triangles. +The distance between any row points or column points gives a measure of their similarity (or dissimilarity). +Row points with similar profile are closed on the factor map. The same holds true for column points. +In the situation of our results shown above, we can conclude that, variable `tea shop` and `unpackaged` are the most correlated with dimension 1. Similarly, the variables `other` and `chain store+tea shop` are the most correlated with dimension 2. + + + + + + + + diff --git a/chapter5.html b/chapter5.html new file mode 100644 index 000000000..25b949664 --- /dev/null +++ b/chapter5.html @@ -0,0 +1,457 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + +
+

Chapter 5 Dimensionality reduction technique

+

Created on 01.12.2017 @author: Xiaodong Li This is the script for RStudio exercise 5 – Dimensionality reduction technique

+
+

Step 0: Import packages

+
library(GGally)
+library(corrplot)
+
## corrplot 0.84 loaded
+
+
+

Step 1: Read and explore data

+
human = read.table('/home/xiaodong/IODS_course/IODS-project/data/human.txt',sep='\t',header = TRUE)
+str(human)
+
## 'data.frame':    155 obs. of  8 variables:
+##  $ Edu2.FM  : num  1.007 0.997 0.983 0.989 0.969 ...
+##  $ Labo.FM  : num  0.891 0.819 0.825 0.884 0.829 ...
+##  $ Life.Exp : num  81.6 82.4 83 80.2 81.6 80.9 80.9 79.1 82 81.8 ...
+##  $ Edu.Exp  : num  17.5 20.2 15.8 18.7 17.9 16.5 18.6 16.5 15.9 19.2 ...
+##  $ GNI      : int  64992 42261 56431 44025 45435 43919 39568 52947 42155 32689 ...
+##  $ Mat.Mor  : int  4 6 6 5 6 7 9 28 11 8 ...
+##  $ Ado.Birth: num  7.8 12.1 1.9 5.1 6.2 3.8 8.2 31 14.5 25.3 ...
+##  $ Parli.F  : num  39.6 30.5 28.5 38 36.9 36.9 19.9 19.4 28.2 31.4 ...
+
dim(human)
+
## [1] 155   8
+

The human data describes the Human Development Index (HDI) and Gross National Income (GNI) situation in different countries together with the education, labour and health experiences. The goal is to show that the people and the their capabilities should be the ultimate criteria for assessing the development of a country, not economic growth alone. The meaning of different variables are shown below:

+
    +
  • Edu2.FM: The ratio of Female and Male populations with secondary education

  • +
  • Labo.FM: The ratio of labour force participation of females and males

  • +
  • life.Exp: Life expectancy at birth

  • +
  • Edu.Exp: Expected years of education

  • +
  • GNI: Gross national income per capita

  • +
  • Mat.Mor: Maternal mortality ratio

  • +
  • Ado.Birth: Adolescent birth rate

  • +
  • Parli.F: Percent Representation in Parliament n

  • +
+
+
+

Step 2: Graphical overview of the data

+

Visuualize the human data with ggpairs()

+
ggpairs(human)
+

+

Visualize the human data with correlation plots

+
cor_matrix=cor(human)
+corrplot(cor_matrix,type='upper')
+

+

The scatter plots and correlation plots between all the variables shown above give information about the relationships and distributions of all the data. From the plots we can see that Life.Exp has strong positive relation with Edu.Exp and also very strong negative relation with Mat.Mor and Ado.Birth. Edu2.Fm has strong negative relation with Mat.Mor too.

+
+
+

Step 3: Perform PCA on not standardized data

+

Perform Principal Component Analysis (PCA) with the SVD method

+
pca_human=prcomp(human)
+s=summary(pca_human)
+s
+
## Importance of components:
+##                              PC1      PC2   PC3   PC4   PC5   PC6    PC7
+## Standard deviation     1.854e+04 185.5219 25.19 11.45 3.766 1.566 0.1912
+## Proportion of Variance 9.999e-01   0.0001  0.00  0.00 0.000 0.000 0.0000
+## Cumulative Proportion  9.999e-01   1.0000  1.00  1.00 1.000 1.000 1.0000
+##                           PC8
+## Standard deviation     0.1591
+## Proportion of Variance 0.0000
+## Cumulative Proportion  1.0000
+
pca_pr=round(100*s$importance[2,],digits=1)
+pc_lab=paste0(names(pca_pr),'(',pca_pr,'%)')
+biplot(pca_human,choices=1:2,cex=c(0.8,1),xlab=pc_lab[1],ylab=pc_lab[2])
+
## Warning in arrows(0, 0, y[, 1L] * 0.8, y[, 2L] * 0.8, col = col[2L], length
+## = arrow.len): zero-length arrow is of indeterminate angle and so skipped
+
+## Warning in arrows(0, 0, y[, 1L] * 0.8, y[, 2L] * 0.8, col = col[2L], length
+## = arrow.len): zero-length arrow is of indeterminate angle and so skipped
+
+## Warning in arrows(0, 0, y[, 1L] * 0.8, y[, 2L] * 0.8, col = col[2L], length
+## = arrow.len): zero-length arrow is of indeterminate angle and so skipped
+
+## Warning in arrows(0, 0, y[, 1L] * 0.8, y[, 2L] * 0.8, col = col[2L], length
+## = arrow.len): zero-length arrow is of indeterminate angle and so skipped
+
+## Warning in arrows(0, 0, y[, 1L] * 0.8, y[, 2L] * 0.8, col = col[2L], length
+## = arrow.len): zero-length arrow is of indeterminate angle and so skipped
+

+

The biplot figure with not standardized variable is not clear because the varialbes have different scales and are not compariable.

+
+
+

Step 4: Perform PCA on standardized data

+
human_std=scale(human)
+pca_human=prcomp(human_std)
+s=summary(pca_human)
+s
+
## Importance of components:
+##                           PC1    PC2     PC3     PC4     PC5     PC6
+## Standard deviation     2.0708 1.1397 0.87505 0.77886 0.66196 0.53631
+## Proportion of Variance 0.5361 0.1624 0.09571 0.07583 0.05477 0.03595
+## Cumulative Proportion  0.5361 0.6984 0.79413 0.86996 0.92473 0.96069
+##                            PC7     PC8
+## Standard deviation     0.45900 0.32224
+## Proportion of Variance 0.02634 0.01298
+## Cumulative Proportion  0.98702 1.00000
+
pca_pr=round(100*s$importance[2,],digits=1)
+pc_lab=paste0(names(pca_pr),'(',pca_pr,'%)')
+biplot(pca_human,choices = 1:2,cex=c(0.8,1),xlab=pc_lab[1],ylab=pc_lab[2])
+

+

The biplots got from Step 3 and Step 4 give different PCA results. For the data that was not standardized, the GNI variable has very big variance and all the data could be transformed to the first principal component (PC1). However, for the data that was standardized, all the variables have similar vairance and the features of the original data are comprised in several pricipal components. The different distributions of the data in these two different situations are shown clearly in the two biplots.
+The biplot is a way of visualizing two representations of the same data. The biplot displays,

+
    +
  1. The observations in a lower 2-dimensional representation.
    +A scatter plot is drawn where the observations are placed on X and Y coordinates defined by two pricipal components.

  2. +
  3. The original features and their relationships with both each other and the pricipal components.
    +Arrows and/or labels are drawn to visualize the connections between the original features and pricipal components.
    +
  4. +
+
    +
  • The angle between arrows representing the original features can be interpreted as the corelation between the features. Small angle = high positive correlation.

  • +
  • The angle between a feature and a principal component axis can be interpreted as the correlation between the two. Small angle = high positive correlation.

  • +
  • The length of the arrows are proportional to the standard deviation of the features.
    +According to the description of the features of biplot we can summarize the relationship between the observations.
    +
  • +
  • Mat.Mor and Ado.Birth have high positive relationship between each other.

  • +
  • Edu.Exp,Edu2.FM,GNI and Life.Exp have high positive relationship between other.

  • +
  • The above two groups have high negative relationship between each other.

  • +
  • The standard deviation of the observations are quite similar because of the scaling process.

  • +
+
+
+

Step 5: Perform MCA on tea dataset

+

Load the tea dataset

+
library(FactoMineR)
+library(ggplot2)
+library(dplyr)
+
## 
+## Attaching package: 'dplyr'
+
## The following object is masked from 'package:GGally':
+## 
+##     nasa
+
## The following objects are masked from 'package:stats':
+## 
+##     filter, lag
+
## The following objects are masked from 'package:base':
+## 
+##     intersect, setdiff, setequal, union
+
library(tidyr)
+data('tea')
+str(tea)
+
## 'data.frame':    300 obs. of  36 variables:
+##  $ breakfast       : Factor w/ 2 levels "breakfast","Not.breakfast": 1 1 2 2 1 2 1 2 1 1 ...
+##  $ tea.time        : Factor w/ 2 levels "Not.tea time",..: 1 1 2 1 1 1 2 2 2 1 ...
+##  $ evening         : Factor w/ 2 levels "evening","Not.evening": 2 2 1 2 1 2 2 1 2 1 ...
+##  $ lunch           : Factor w/ 2 levels "lunch","Not.lunch": 2 2 2 2 2 2 2 2 2 2 ...
+##  $ dinner          : Factor w/ 2 levels "dinner","Not.dinner": 2 2 1 1 2 1 2 2 2 2 ...
+##  $ always          : Factor w/ 2 levels "always","Not.always": 2 2 2 2 1 2 2 2 2 2 ...
+##  $ home            : Factor w/ 2 levels "home","Not.home": 1 1 1 1 1 1 1 1 1 1 ...
+##  $ work            : Factor w/ 2 levels "Not.work","work": 1 1 2 1 1 1 1 1 1 1 ...
+##  $ tearoom         : Factor w/ 2 levels "Not.tearoom",..: 1 1 1 1 1 1 1 1 1 2 ...
+##  $ friends         : Factor w/ 2 levels "friends","Not.friends": 2 2 1 2 2 2 1 2 2 2 ...
+##  $ resto           : Factor w/ 2 levels "Not.resto","resto": 1 1 2 1 1 1 1 1 1 1 ...
+##  $ pub             : Factor w/ 2 levels "Not.pub","pub": 1 1 1 1 1 1 1 1 1 1 ...
+##  $ Tea             : Factor w/ 3 levels "black","Earl Grey",..: 1 1 2 2 2 2 2 1 2 1 ...
+##  $ How             : Factor w/ 4 levels "alone","lemon",..: 1 3 1 1 1 1 1 3 3 1 ...
+##  $ sugar           : Factor w/ 2 levels "No.sugar","sugar": 2 1 1 2 1 1 1 1 1 1 ...
+##  $ how             : Factor w/ 3 levels "tea bag","tea bag+unpackaged",..: 1 1 1 1 1 1 1 1 2 2 ...
+##  $ where           : Factor w/ 3 levels "chain store",..: 1 1 1 1 1 1 1 1 2 2 ...
+##  $ price           : Factor w/ 6 levels "p_branded","p_cheap",..: 4 6 6 6 6 3 6 6 5 5 ...
+##  $ age             : int  39 45 47 23 48 21 37 36 40 37 ...
+##  $ sex             : Factor w/ 2 levels "F","M": 2 1 1 2 2 2 2 1 2 2 ...
+##  $ SPC             : Factor w/ 7 levels "employee","middle",..: 2 2 4 6 1 6 5 2 5 5 ...
+##  $ Sport           : Factor w/ 2 levels "Not.sportsman",..: 2 2 2 1 2 2 2 2 2 1 ...
+##  $ age_Q           : Factor w/ 5 levels "15-24","25-34",..: 3 4 4 1 4 1 3 3 3 3 ...
+##  $ frequency       : Factor w/ 4 levels "1/day","1 to 2/week",..: 1 1 3 1 3 1 4 2 3 3 ...
+##  $ escape.exoticism: Factor w/ 2 levels "escape-exoticism",..: 2 1 2 1 1 2 2 2 2 2 ...
+##  $ spirituality    : Factor w/ 2 levels "Not.spirituality",..: 1 1 1 2 2 1 1 1 1 1 ...
+##  $ healthy         : Factor w/ 2 levels "healthy","Not.healthy": 1 1 1 1 2 1 1 1 2 1 ...
+##  $ diuretic        : Factor w/ 2 levels "diuretic","Not.diuretic": 2 1 1 2 1 2 2 2 2 1 ...
+##  $ friendliness    : Factor w/ 2 levels "friendliness",..: 2 2 1 2 1 2 2 1 2 1 ...
+##  $ iron.absorption : Factor w/ 2 levels "iron absorption",..: 2 2 2 2 2 2 2 2 2 2 ...
+##  $ feminine        : Factor w/ 2 levels "feminine","Not.feminine": 2 2 2 2 2 2 2 1 2 2 ...
+##  $ sophisticated   : Factor w/ 2 levels "Not.sophisticated",..: 1 1 1 2 1 1 1 2 2 1 ...
+##  $ slimming        : Factor w/ 2 levels "No.slimming",..: 1 1 1 1 1 1 1 1 1 1 ...
+##  $ exciting        : Factor w/ 2 levels "exciting","No.exciting": 2 1 2 2 2 2 2 2 2 2 ...
+##  $ relaxing        : Factor w/ 2 levels "No.relaxing",..: 1 1 2 2 2 2 2 2 2 2 ...
+##  $ effect.on.health: Factor w/ 2 levels "effect on health",..: 2 2 2 2 2 2 2 2 2 2 ...
+
dim(tea)
+
## [1] 300  36
+

The tea dataset contains the answers of a questionnaire on tea consumption for 300 individuals. Although the data contains 36 columns for demonstration purposes I will only consider 6 of the following columns:

+
keep_columns=c('Tea','How','how','sugar','where','lunch')
+tea_time=select(tea,one_of(keep_columns))
+summary(tea_time)
+
##         Tea         How                      how           sugar    
+##  black    : 74   alone:195   tea bag           :170   No.sugar:155  
+##  Earl Grey:193   lemon: 33   tea bag+unpackaged: 94   sugar   :145  
+##  green    : 33   milk : 63   unpackaged        : 36                 
+##                  other:  9                                          
+##                   where           lunch    
+##  chain store         :192   lunch    : 44  
+##  chain store+tea shop: 78   Not.lunch:256  
+##  tea shop            : 30                  
+## 
+
str(tea_time)
+
## 'data.frame':    300 obs. of  6 variables:
+##  $ Tea  : Factor w/ 3 levels "black","Earl Grey",..: 1 1 2 2 2 2 2 1 2 1 ...
+##  $ How  : Factor w/ 4 levels "alone","lemon",..: 1 3 1 1 1 1 1 3 3 1 ...
+##  $ how  : Factor w/ 3 levels "tea bag","tea bag+unpackaged",..: 1 1 1 1 1 1 1 1 2 2 ...
+##  $ sugar: Factor w/ 2 levels "No.sugar","sugar": 2 1 1 2 1 1 1 1 1 1 ...
+##  $ where: Factor w/ 3 levels "chain store",..: 1 1 1 1 1 1 1 1 2 2 ...
+##  $ lunch: Factor w/ 2 levels "lunch","Not.lunch": 2 2 2 2 2 2 2 2 2 2 ...
+
gather(tea_time) %>% ggplot(aes(value))+geom_bar()+facet_wrap('key',scales='free')+theme(axis.text=element_text(angle=45,hjust = 1,size=8))
+
## Warning: attributes are not identical across measure variables;
+## they will be dropped
+

+

Perform MCA on the selected tea dateset–tea_time

+
mca=MCA(tea_time,graph=FALSE)
+summary(mca)
+
## 
+## Call:
+## MCA(X = tea_time, graph = FALSE) 
+## 
+## 
+## Eigenvalues
+##                        Dim.1   Dim.2   Dim.3   Dim.4   Dim.5   Dim.6
+## Variance               0.279   0.261   0.219   0.189   0.177   0.156
+## % of var.             15.238  14.232  11.964  10.333   9.667   8.519
+## Cumulative % of var.  15.238  29.471  41.435  51.768  61.434  69.953
+##                        Dim.7   Dim.8   Dim.9  Dim.10  Dim.11
+## Variance               0.144   0.141   0.117   0.087   0.062
+## % of var.              7.841   7.705   6.392   4.724   3.385
+## Cumulative % of var.  77.794  85.500  91.891  96.615 100.000
+## 
+## Individuals (the 10 first)
+##                       Dim.1    ctr   cos2    Dim.2    ctr   cos2    Dim.3
+## 1                  | -0.298  0.106  0.086 | -0.328  0.137  0.105 | -0.327
+## 2                  | -0.237  0.067  0.036 | -0.136  0.024  0.012 | -0.695
+## 3                  | -0.369  0.162  0.231 | -0.300  0.115  0.153 | -0.202
+## 4                  | -0.530  0.335  0.460 | -0.318  0.129  0.166 |  0.211
+## 5                  | -0.369  0.162  0.231 | -0.300  0.115  0.153 | -0.202
+## 6                  | -0.369  0.162  0.231 | -0.300  0.115  0.153 | -0.202
+## 7                  | -0.369  0.162  0.231 | -0.300  0.115  0.153 | -0.202
+## 8                  | -0.237  0.067  0.036 | -0.136  0.024  0.012 | -0.695
+## 9                  |  0.143  0.024  0.012 |  0.871  0.969  0.435 | -0.067
+## 10                 |  0.476  0.271  0.140 |  0.687  0.604  0.291 | -0.650
+##                       ctr   cos2  
+## 1                   0.163  0.104 |
+## 2                   0.735  0.314 |
+## 3                   0.062  0.069 |
+## 4                   0.068  0.073 |
+## 5                   0.062  0.069 |
+## 6                   0.062  0.069 |
+## 7                   0.062  0.069 |
+## 8                   0.735  0.314 |
+## 9                   0.007  0.003 |
+## 10                  0.643  0.261 |
+## 
+## Categories (the 10 first)
+##                        Dim.1     ctr    cos2  v.test     Dim.2     ctr
+## black              |   0.473   3.288   0.073   4.677 |   0.094   0.139
+## Earl Grey          |  -0.264   2.680   0.126  -6.137 |   0.123   0.626
+## green              |   0.486   1.547   0.029   2.952 |  -0.933   6.111
+## alone              |  -0.018   0.012   0.001  -0.418 |  -0.262   2.841
+## lemon              |   0.669   2.938   0.055   4.068 |   0.531   1.979
+## milk               |  -0.337   1.420   0.030  -3.002 |   0.272   0.990
+## other              |   0.288   0.148   0.003   0.876 |   1.820   6.347
+## tea bag            |  -0.608  12.499   0.483 -12.023 |  -0.351   4.459
+## tea bag+unpackaged |   0.350   2.289   0.056   4.088 |   1.024  20.968
+## unpackaged         |   1.958  27.432   0.523  12.499 |  -1.015   7.898
+##                       cos2  v.test     Dim.3     ctr    cos2  v.test  
+## black                0.003   0.929 |  -1.081  21.888   0.382 -10.692 |
+## Earl Grey            0.027   2.867 |   0.433   9.160   0.338  10.053 |
+## green                0.107  -5.669 |  -0.108   0.098   0.001  -0.659 |
+## alone                0.127  -6.164 |  -0.113   0.627   0.024  -2.655 |
+## lemon                0.035   3.226 |   1.329  14.771   0.218   8.081 |
+## milk                 0.020   2.422 |   0.013   0.003   0.000   0.116 |
+## other                0.102   5.534 |  -2.524  14.526   0.197  -7.676 |
+## tea bag              0.161  -6.941 |  -0.065   0.183   0.006  -1.287 |
+## tea bag+unpackaged   0.478  11.956 |   0.019   0.009   0.000   0.226 |
+## unpackaged           0.141  -6.482 |   0.257   0.602   0.009   1.640 |
+## 
+## Categorical variables (eta2)
+##                      Dim.1 Dim.2 Dim.3  
+## Tea                | 0.126 0.108 0.410 |
+## How                | 0.076 0.190 0.394 |
+## how                | 0.708 0.522 0.010 |
+## sugar              | 0.065 0.001 0.336 |
+## where              | 0.702 0.681 0.055 |
+## lunch              | 0.000 0.064 0.111 |
+
plot(mca,invisible=c('ind'),habillage='quali')
+

+

Multiple Correspondence Analysis (MCA) is an extension of simple CA to analyse a data table containing more than two categorical variables. MCA is generally used to analyse a data from survey.
+The objectives are to identify:

+
    +
  • A group of individuals with similar profile in their answers to the questions

  • +
  • The associations between variable categories

  • +
+

The result of the function summary() contains 4 tables:

+
    +
  • Table 1 - Eigenvalues: table 1 contains the variances and the percentage of variances retained by each dimension.

  • +
  • Table 2 contains the coordinates, the contribution and the cos2 (quality of representation [in 0-1]) of the first 10 active individuals on the dimensions 1 and 2.
    +
  • +
  • Table 3 contains the coordinates, the contribution and the cos2 (quality of representation [in 0-1]) of the first 10 active variable categories on the dimensions 1 and 2. This table contains also a column called v.test. The value of the v.test is generally comprised between 2 and -2. For a given variable category, if the absolute value of the v.test is superior to 2, this means that the coordinate is significantly different from 0.

  • +
  • Table 4 - categorical variables (eta2): contains the squared correlation between each variable and the dimensions.

  • +
+

The MCA graph shows a global pattern within the data. Rows (individuals) are usually represented by blue points and columns (variable categories) by red triangles.
+The distance between any row points or column points gives a measure of their similarity (or dissimilarity).
+Row points with similar profile are closed on the factor map. The same holds true for column points.
+In the situation of our results shown above, we can conclude that, variable tea shop and unpackaged are the most correlated with dimension 1. Similarly, the variables other and chain store+tea shop are the most correlated with dimension 2.

+
+
+ + + + +
+ + + + + + + + diff --git a/data/.RData b/data/.RData new file mode 100644 index 000000000..7bf071629 Binary files /dev/null and b/data/.RData differ diff --git a/data/.Rhistory b/data/.Rhistory new file mode 100644 index 000000000..fd19f6508 --- /dev/null +++ b/data/.Rhistory @@ -0,0 +1,512 @@ +library(MASS) +library(corrplot) +library(tidyr) +data("Boston") +str(Boston) +dim(Boston) +cor_matrix<-cor(Boston) %>% round(2) +corrplot(cor_matrix, method="circle",type='upper',cl.pos='b',tl.pos='d',tl.cex=0.6) +boston_scaled <- scale(Boston) +summary(boston_scaled) +bins <- quantile(boston_scaled$crim) +boston_scaled=as.data.frame(boston_scaled) +bins <- quantile(boston_scaled$crim) +crime <- cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label = c('low','med_low','med_high','high')) +table(crime) +library(dplyr) +boston_scaled=select(boston_scaled, -crim) +boston_scaled=data.frame(boston_scaled, crime) +boston_scaled=as.data.frame(boston_scaled) +bins=quantile(boston_scaled$crim) +boston_scaled=as.data.frame(boston_scaled) +bins=quantile(boston_scaled$crim) +library(MASS) +library(corrplot) +library(tidyr) +library(dplyr) +data("Boston") +str(Boston) +dim(Boston) +cor_matrix<-cor(Boston) %>% round(2) +corrplot(cor_matrix, method="circle",type='upper',cl.pos='b',tl.pos='d',tl.cex=0.6) +boston_scaled <- scale(Boston) +summary(boston_scaled) +boston_scaled=as.data.frame(boston_scaled) +bins=quantile(boston_scaled$crim) +crime=cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label = c('low','med_low','med_high','high')) +table(crime) +boston_scaled=select(boston_scaled, -crim) +boston_scaled=data.frame(boston_scaled, crime) +n <- nrow(boston_scaled) +ind <- sample(n, size = n * 0.8) +train <- boston_scaled[ind,] +test <- boston_scaled[-ind,] +correct_classes <- test$crime +test <- select(test, -crime) +lda.fit <- lda(crime~., data = train) +lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){ +heads <- coef(x) +arrows(x0 = 0, y0 = 0, +x1 = myscale * heads[,choices[1]], +y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads) +text(myscale * heads[,choices], labels = row.names(heads), +cex = tex, col=color, pos=3) +} +classes <- as.numeric(train$crime) +plot(lda.fit, dimen = 2,col=classes,pch=classes) +lda.arrows(lda.fit, myscale = 3) +library(MASS) +library(corrplot) +library(tidyr) +library(dplyr) +data("Boston") +str(Boston) +dim(Boston) +cor_matrix<-cor(Boston) %>% round(2) +corrplot(cor_matrix, method="circle",type='upper',cl.pos='b',tl.pos='d',tl.cex=0.6) +boston_scaled <- scale(Boston) +summary(boston_scaled) +boston_scaled=as.data.frame(boston_scaled) +bins=quantile(boston_scaled$crim) +crime=cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label = c('low','med_low','med_high','high')) +table(crime) +boston_scaled=select(boston_scaled, -crim) +boston_scaled=data.frame(boston_scaled, crime) +n <- nrow(boston_scaled) +ind <- sample(n, size = n * 0.8) +train <- boston_scaled[ind,] +test <- boston_scaled[-ind,] +correct_classes <- test$crime +test <- select(test, -crime) +lda.fit <- lda(crime~., data = train) +lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){ +heads <- coef(x) +arrows(x0 = 0, y0 = 0, +x1 = myscale * heads[,choices[1]], +y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads) +text(myscale * heads[,choices], labels = row.names(heads), +cex = tex, col=color, pos=3) +} +classes <- as.numeric(train$crime) +plot(lda.fit, dimen = 2,col=classes,pch=classes) +lda.arrows(lda.fit, myscale = 3) +library(MASS) +library(corrplot) +library(tidyr) +library(dplyr) +data("Boston") +str(Boston) +dim(Boston) +cor_matrix<-cor(Boston) %>% round(2) +corrplot(cor_matrix, method="circle",type='upper',cl.pos='b',tl.pos='d',tl.cex=0.6) +boston_scaled <- scale(Boston) +summary(boston_scaled) +boston_scaled=as.data.frame(boston_scaled) +bins=quantile(boston_scaled$crim) +crime=cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label = c('low','med_low','med_high','high')) +table(crime) +boston_scaled=select(boston_scaled, -crim) +boston_scaled=data.frame(boston_scaled, crime) +n <- nrow(boston_scaled) +ind <- sample(n, size = n * 0.8) +train <- boston_scaled[ind,] +test <- boston_scaled[-ind,] +correct_classes <- test$crime +test <- select(test, -crime) +lda.fit <- lda(crime~., data = train) +lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){ +heads <- coef(x) +arrows(x0 = 0, y0 = 0, +x1 = myscale * heads[,choices[1]], +y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads) +text(myscale * heads[,choices], labels = row.names(heads), +cex = tex, col=color, pos=3) +} +classes <- as.numeric(train$crime) +plot(lda.fit, dimen = 2,col=classes,pch=classes) +lda.arrows(lda.fit, myscale = 3) +train +library(MASS) +library(corrplot) +library(tidyr) +library(dplyr) +data("Boston") +str(Boston) +dim(Boston) +cor_matrix<-cor(Boston) %>% round(2) +corrplot(cor_matrix, method="circle",type='upper',cl.pos='b',tl.pos='d',tl.cex=0.6) +boston_scaled <- scale(Boston) +summary(boston_scaled) +boston_scaled=as.data.frame(boston_scaled) +bins=quantile(boston_scaled$crim) +crime=cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label = c('low','med_low','med_high','high')) +table(crime) +boston_scaled=select(boston_scaled, -crim) +boston_scaled=data.frame(boston_scaled, crime) +n <- nrow(boston_scaled) +ind <- sample(n, size = n * 0.8) +train <- boston_scaled[ind,] +test <- boston_scaled[-ind,] +correct_classes <- test$crime +test <- select(test, -crime) +lda.fit <- lda(crime~., data = train) +lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){ +heads <- coef(x) +arrows(x0 = 0, y0 = 0, +x1 = myscale * heads[,choices[1]], +y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads) +text(myscale * heads[,choices], labels = row.names(heads), +cex = tex, col=color, pos=3) +} +classes <- as.numeric(train$crime) +plot(lda.fit, dimen = 2,col=classes,pch=classes) +lda.arrows(lda.fit, myscale = 3) +train +library(MASS) +library(corrplot) +library(tidyr) +library(dplyr) +data("Boston") +str(Boston) +dim(Boston) +cor_matrix<-cor(Boston) %>% round(2) +corrplot(cor_matrix, method="circle",type='upper',cl.pos='b',tl.pos='d',tl.cex=0.6) +boston_scaled <- scale(Boston) +summary(boston_scaled) +boston_scaled=as.data.frame(boston_scaled) +bins=quantile(boston_scaled$crim) +crime=cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label = c('low','med_low','med_high','high')) +table(crime) +boston_scaled=select(boston_scaled, -crim) +boston_scaled=data.frame(boston_scaled, crime) +n <- nrow(boston_scaled) +ind <- sample(n, size = n * 0.8) +train <- boston_scaled[ind,] +test <- boston_scaled[-ind,] +correct_classes <- test$crime +test <- select(test, -crime) +lda.fit <- lda(crime~., data = train) +lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){ +heads <- coef(x) +arrows(x0 = 0, y0 = 0, +x1 = myscale * heads[,choices[1]], +y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads) +text(myscale * heads[,choices], labels = row.names(heads), +cex = tex, col=color, pos=3) +} +classes <- as.numeric(train$crime) +plot(lda.fit, dimen = 2,col=classes,pch=classes) +lda.arrows(lda.fit, myscale = 3) +lad.pred=predict(lad.fit,newdata=test) +lda.pred=predict(lad.fit,newdata=test) +lda.pred=predict(lda.fit,newdata=test) +table(correct=correct_classes,predicted=lad.pred$class) +table(correct=correct_classes,predicted=lda.pred$class) +table(correct=correct_classes,predicted=lda.pred$class) %>% prop.table %>% addmargins +table(correct=correct_classes,predicted=lda.pred$class) %>% addmargins +correct=c(16,23,13,26) +correct=c(correct,sum(correct)) +correct +sumdata=c(27,30,18,27) +sumdata=c(sumdata,sum(sumdata)) +t=data.frame(correct=correct,sum=sumdata) +t +index=c('low','med_low','med_high','high','sum') +t=data.frame(correct=index,correct_pred=correct,sum=sumdata) +t +t=data.frame(correct=index,predict(=correct,sum=sumdata) +t=data.frame(correct=index,predict=correct,sum=sumdata) +t +t$perc=t$predict/t$sum +t +correct=c(16,23,13,26) +correct=c(correct,sum(correct)) +sumdata=c(27,30,18,27) +sumdata=c(sumdata,sum(sumdata)) +index=c('low','med_low','med_high','high','sum') +t=data.frame(correct=index,predict=correct,sum=sumdata) +t$percentage=t$predict/t$sum +t +data('Boston') +boston_scaled=scale(Boston) +dist_eu=dist(boston_scaled,method='euclidean') +summary(dist_eu) +dist_man=dist(boston_scaled,method='manhattan') +summary(dist_man) +summary(boston_scaled) +dist_eu +km=kmeans(boston_scaled,centers = 3) +pairs(boston_scaled,col=km$cluster) +km=kmeans(boston_scaled,centers = 3) +pairs(boston_scaled[6:10],col=km$cluster) +pairs(boston_scaled,col=km$cluster) +k_max=10 +twcss=sapply(1:k_max,function(k){kmeans(boston_scaled,k)$tot.withinss}) +qplot(x=1:k_max,y=twcss,goem='line') +library(ggplot2) +k_max=10 +twcss=sapply(1:k_max,function(k){kmeans(boston_scaled,k)$tot.withinss}) +qplot(x=1:k_max,y=twcss,goem='line') +qplot(x=1:k_max,y=twcss,geom=line') +qplot(x=1:k_max,y=twcss,geom='line') +k_max=10 +twcss=sapply(1:k_max,function(k){kmeans(boston_scaled,k)$tot.withinss}) +qplot(x=1:k_max,y=twcss,geom='line') +set.seed(123) +set.seed(123) +k_max=10 +twcss=sapply(1:k_max,function(k){kmeans(boston_scaled,k)$tot.withinss}) +qplot(x=1:k_max,y=twcss,geom='line') +km=kmeans(boston_scaled,centers=2) +pairs(boston_scaled,col=km$cluster) +pairs(boston_scaled,col=km$cluster) +pairs(boston_scaled[1:5],col=km$cluster) +library(MASS) +library(corrplot) +library(tidyr) +library(dplyr) +library(ggplot2) +data("Boston") +str(Boston) +dim(Boston) +cor_matrix<-cor(Boston) %>% round(2) +corrplot(cor_matrix, method="circle",type='upper',cl.pos='b',tl.pos='d',tl.cex=0.6) +boston_scaled <- scale(Boston) +summary(boston_scaled) +boston_scaled=as.data.frame(boston_scaled) +bins=quantile(boston_scaled$crim) +crime=cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label = c('low','med_low','med_high','high')) +table(crime) +boston_scaled=select(boston_scaled, -crim) +boston_scaled=data.frame(boston_scaled, crime) +n <- nrow(boston_scaled) +ind <- sample(n, size = n * 0.8) +train <- boston_scaled[ind,] +test <- boston_scaled[-ind,] +correct_classes <- test$crime +test <- select(test, -crime) +lda.fit <- lda(crime~., data = train) +lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){ +heads <- coef(x) +arrows(x0 = 0, y0 = 0, +x1 = myscale * heads[,choices[1]], +y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads) +text(myscale * heads[,choices], labels = row.names(heads), +cex = tex, col=color, pos=3) +} +classes <- as.numeric(train$crime) +plot(lda.fit, dimen = 2,col=classes,pch=classes) +lda.arrows(lda.fit, myscale = 3) +lda.pred=predict(lda.fit,newdata=test) +table(correct=correct_classes,predicted=lda.pred$class) %>% addmargins +correct=c(16,23,13,26) +correct=c(correct,sum(correct)) +sumdata=c(27,30,18,27) +sumdata=c(sumdata,sum(sumdata)) +index=c('low','med_low','med_high','high','sum') +t=data.frame(correct=index,predict=correct,sum=sumdata) +t$percentage=t$predict/t$sum +t +data('Boston') +boston_scaled=scale(Boston) +dist_eu=dist(boston_scaled,method='euclidean') +summary(dist_eu) +dist_man=dist(boston_scaled,method='manhattan') +summary(dist_man) +km=kmeans(boston_scaled,centers = 3) +pairs(boston_scaled,col=km$cluster) +set.seed(123) +k_max=10 +twcss=sapply(1:k_max,function(k){kmeans(boston_scaled,k)$tot.withinss}) +qplot(x=1:k_max,y=twcss,geom='line') +km=kmeans(boston_scaled,centers=2) +pairs(boston_scaled,col=km$cluster) +library(MASS) +library(corrplot) +library(tidyr) +library(dplyr) +library(ggplot2) +data("Boston") +str(Boston) +dim(Boston) +cor_matrix<-cor(Boston) %>% round(2) +corrplot(cor_matrix, method="circle",type='upper',cl.pos='b',tl.pos='d',tl.cex=0.6) +boston_scaled <- scale(Boston) +summary(boston_scaled) +boston_scaled=as.data.frame(boston_scaled) +bins=quantile(boston_scaled$crim) +crime=cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label = c('low','med_low','med_high','high')) +table(crime) +boston_scaled=select(boston_scaled, -crim) +boston_scaled=data.frame(boston_scaled, crime) +n <- nrow(boston_scaled) +ind <- sample(n, size = n * 0.8) +train <- boston_scaled[ind,] +test <- boston_scaled[-ind,] +correct_classes <- test$crime +test <- select(test, -crime) +lda.fit <- lda(crime~., data = train) +lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){ +heads <- coef(x) +arrows(x0 = 0, y0 = 0, +x1 = myscale * heads[,choices[1]], +y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads) +text(myscale * heads[,choices], labels = row.names(heads), +cex = tex, col=color, pos=3) +} +classes <- as.numeric(train$crime) +plot(lda.fit, dimen = 2,col=classes,pch=classes) +lda.arrows(lda.fit, myscale = 3) +lda.pred=predict(lda.fit,newdata=test) +table(correct=correct_classes,predicted=lda.pred$class) %>% addmargins +correct=c(16,23,13,26) +correct=c(correct,sum(correct)) +sumdata=c(27,30,18,27) +sumdata=c(sumdata,sum(sumdata)) +index=c('low','med_low','med_high','high','sum') +t=data.frame(correct=index,predict=correct,sum=sumdata) +t$percentage=t$predict/t$sum +t +data('Boston') +boston_scaled=scale(Boston) +dist_eu=dist(boston_scaled,method='euclidean') +summary(dist_eu) +dist_man=dist(boston_scaled,method='manhattan') +summary(dist_man) +km=kmeans(boston_scaled,centers = 3) +pairs(boston_scaled,col=km$cluster) +set.seed(123) +k_max=10 +twcss=sapply(1:k_max,function(k){kmeans(boston_scaled,k)$tot.withinss}) +qplot(x=1:k_max,y=twcss,geom='line') +km=kmeans(boston_scaled,centers=2) +pairs(boston_scaled,col=km$cluster) +library(MASS) +library(corrplot) +library(tidyr) +library(dplyr) +library(ggplot2) +data("Boston") +str(Boston) +dim(Boston) +cor_matrix<-cor(Boston) %>% round(2) +corrplot(cor_matrix, method="circle",type='upper',cl.pos='b',tl.pos='d',tl.cex=0.6) +boston_scaled <- scale(Boston) +summary(boston_scaled) +boston_scaled=as.data.frame(boston_scaled) +bins=quantile(boston_scaled$crim) +crime=cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label = c('low','med_low','med_high','high')) +table(crime) +boston_scaled=dplyr::select(boston_scaled, -crim) +boston_scaled=data.frame(boston_scaled, crime) +n <- nrow(boston_scaled) +ind <- sample(n, size = n * 0.8) +train <- boston_scaled[ind,] +test <- boston_scaled[-ind,] +correct_classes <- test$crime +test <- dplyr::select(test, -crime) +lda.fit <- lda(crime~., data = train) +lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){ +heads <- coef(x) +arrows(x0 = 0, y0 = 0, +x1 = myscale * heads[,choices[1]], +y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads) +text(myscale * heads[,choices], labels = row.names(heads), +cex = tex, col=color, pos=3) +} +classes <- as.numeric(train$crime) +plot(lda.fit, dimen = 2,col=classes,pch=classes) +lda.arrows(lda.fit, myscale = 3) +lda.pred=predict(lda.fit,newdata=test) +table(correct=correct_classes,predicted=lda.pred$class) %>% addmargins +correct=c(16,23,13,26) +correct=c(correct,sum(correct)) +sumdata=c(27,30,18,27) +sumdata=c(sumdata,sum(sumdata)) +index=c('low','med_low','med_high','high','sum') +t=data.frame(correct=index,predict=correct,sum=sumdata) +t$percentage=t$predict/t$sum +t +data('Boston') +boston_scaled=scale(Boston) +dist_eu=dist(boston_scaled,method='euclidean') +summary(dist_eu) +dist_man=dist(boston_scaled,method='manhattan') +summary(dist_man) +km=kmeans(boston_scaled,centers = 3) +pairs(boston_scaled,col=km$cluster) +set.seed(123) +k_max=10 +twcss=sapply(1:k_max,function(k){kmeans(boston_scaled,k)$tot.withinss}) +qplot(x=1:k_max,y=twcss,geom='line') +km=kmeans(boston_scaled,centers=2) +pairs(boston_scaled,col=km$cluster) +# Read the human data +#human=read.table(' +hd <- read.csv("http://s3.amazonaws.com/assets.datacamp.com/production/course_2218/datasets/human_development.csv", stringsAsFactors = F) +hd +head(hd) +source('~/IODS_course/IODS-project/data/creat_human.R', echo=TRUE) +#head(gii) +head(gii) +source('~/IODS_course/IODS-project/data/creat_human.R', echo=TRUE) +head(hd) +head(gii) +colnames(hd) +colnames_hd=colnames(hd) +colnames_hd[3]=HDI +colnames_hd[3]='HDI' +source('~/IODS_course/IODS-project/data/creat_human.R', echo=TRUE) +head(hd) +colnames(gii) +source('~/IODS_course/IODS-project/data/creat_human.R', echo=TRUE) +names(gii) +# Calculate the ratio of female and male populations with secondary education and labour force participation in each country +gii=mutate(gii,Edu2.FM=Edu2.F/Edu2.M,Labo.FM=Labo.F/Labo.M) +gii +dim(hd) +dim(gii) +# Join the two datasets +human=inner_join(hd,gii,by='Country') +source('~/IODS_course/IODS-project/data/creat_human.R', echo=TRUE) +tail(human) +summary(human) +source('~/IODS_course/IODS-project/data/creat_human.R', echo=TRUE) +library(dplyr) +source('~/IODS_course/IODS-project/data/creat_human.R', echo=TRUE) +tail(human) +dim(human) +head(human) +library(stringr) +# Mutate the GNI data in 'human' dataset +str(human$GNI) +str_replace(human$GNI,pattern=',',replace='') %>% as.numeric +human$GNI=str_replace(human$GNI,pattern=',',replace='') %>% as.numeric +str(human) +# Dealing with not available (NA) values +keep=c("Country", "Edu2.FM", "Labo.FM", "Life.Exp", "Edu.Exp", "GNI", "Mat.Mor", "Ado.Birth", "Parli.F") +human=select(human,one_of(keep)) +human=filter(human,complete.cases(human)) +tail(human,10) +human$Country +# Remove observations with related to regions instead of countries +last=nrow(human)-7 +human_=human[1:last,] +head(human_) +# Define the row names of the data by the country names +rownames(human_)=human$Country +# Define the row names of the data by the country names +rownames(human_)=human_$Country +human_=human_(-1) +human_=human_[-1] +head(human_) +dim(human_) +human=human_[-1] +# Save data +setwd('/home/xiaodong/IODS_course/IODS-project/data') +source('~/IODS_course/IODS-project/data/creat_human.R', echo=TRUE) +source('~/IODS_course/IODS-project/data/creat_human.R', echo=TRUE) +human +source('~/IODS_course/IODS-project/data/creat_human.R', echo=TRUE) +human = read.table('/home/xiaodong/IODS_course/IODS-project/data/human.txt',sep='\t',header = TRUE) +head(human) diff --git a/data/alc.csv b/data/alc.csv new file mode 100644 index 000000000..90b3dd689 --- /dev/null +++ b/data/alc.csv @@ -0,0 +1,383 @@ +school,sex,age,address,famsize,Pstatus,Medu,Fedu,Mjob,Fjob,reason,nursery,internet,guardian,traveltime,studytime,failures,schoolsup,famsup,paid,activities,higher,romantic,famrel,freetime,goout,Dalc,Walc,health,absences,G1,G2,G3,alc_use,high_use +GP,F,18,U,GT3,A,4,4,at_home,teacher,course,yes,no,mother,2,2,0,yes,no,no,no,yes,no,4,3,4,1,1,3,5,2,8,8,1,FALSE +GP,F,17,U,GT3,T,1,1,at_home,other,course,no,yes,father,1,2,0,no,yes,no,no,yes,no,5,3,3,1,1,3,3,7,8,8,1,FALSE +GP,F,15,U,LE3,T,1,1,at_home,other,other,yes,yes,mother,1,2,2,yes,no,yes,no,yes,no,4,3,2,2,3,3,8,10,10,11,2.5,TRUE +GP,F,15,U,GT3,T,4,2,health,services,home,yes,yes,mother,1,3,0,no,yes,yes,yes,yes,yes,3,2,2,1,1,5,1,14,14,14,1,FALSE +GP,F,16,U,GT3,T,3,3,other,other,home,yes,no,father,1,2,0,no,yes,yes,no,yes,no,4,3,2,1,2,5,2,8,12,12,1.5,FALSE +GP,M,16,U,LE3,T,4,3,services,other,reputation,yes,yes,mother,1,2,0,no,yes,yes,yes,yes,no,5,4,2,1,2,5,8,14,14,14,1.5,FALSE +GP,M,16,U,LE3,T,2,2,other,other,home,yes,yes,mother,1,2,0,no,no,no,no,yes,no,4,4,4,1,1,3,0,12,12,12,1,FALSE +GP,F,17,U,GT3,A,4,4,other,teacher,home,yes,no,mother,2,2,0,yes,yes,no,no,yes,no,4,1,4,1,1,1,4,8,9,10,1,FALSE +GP,M,15,U,LE3,A,3,2,services,other,home,yes,yes,mother,1,2,0,no,yes,yes,no,yes,no,4,2,2,1,1,1,0,16,17,18,1,FALSE +GP,M,15,U,GT3,T,3,4,other,other,home,yes,yes,mother,1,2,0,no,yes,yes,yes,yes,no,5,5,1,1,1,5,0,13,14,14,1,FALSE +GP,F,15,U,GT3,T,4,4,teacher,health,reputation,yes,yes,mother,1,2,0,no,yes,yes,no,yes,no,3,3,3,1,2,2,1,12,11,12,1.5,FALSE +GP,F,15,U,GT3,T,2,1,services,other,reputation,yes,yes,father,3,3,0,no,yes,no,yes,yes,no,5,2,2,1,1,4,2,10,12,12,1,FALSE +GP,M,15,U,LE3,T,4,4,health,services,course,yes,yes,father,1,1,0,no,yes,yes,yes,yes,no,4,3,3,1,3,5,1,13,14,13,2,FALSE +GP,M,15,U,GT3,T,4,3,teacher,other,course,yes,yes,mother,2,2,0,no,yes,yes,no,yes,no,5,4,3,1,2,3,1,11,11,12,1.5,FALSE +GP,M,15,U,GT3,A,2,2,other,other,home,yes,yes,other,1,3,0,no,yes,no,no,yes,yes,4,5,2,1,1,3,0,14,15,16,1,FALSE +GP,F,16,U,GT3,T,4,4,health,other,home,yes,yes,mother,1,1,0,no,yes,no,no,yes,no,4,4,4,1,2,2,5,16,16,16,1.5,FALSE +GP,F,16,U,GT3,T,4,4,services,services,reputation,yes,yes,mother,1,3,0,no,yes,yes,yes,yes,no,3,2,3,1,2,2,8,13,14,14,1.5,FALSE +GP,F,16,U,GT3,T,3,3,other,other,reputation,yes,no,mother,3,2,0,yes,yes,no,yes,yes,no,5,3,2,1,1,4,3,10,12,12,1,FALSE +GP,M,17,U,GT3,T,3,2,services,services,course,yes,yes,mother,1,1,3,no,yes,no,yes,yes,no,5,5,5,2,4,5,9,7,6,6,3,TRUE +GP,M,16,U,LE3,T,4,3,health,other,home,yes,yes,father,1,1,0,no,no,yes,yes,yes,no,3,1,3,1,3,5,5,10,11,11,2,FALSE +GP,M,15,U,GT3,T,4,3,teacher,other,reputation,yes,yes,mother,1,2,0,no,no,no,no,yes,no,4,4,1,1,1,1,0,12,14,14,1,FALSE +GP,M,15,U,GT3,T,4,4,health,health,other,yes,yes,father,1,1,0,no,yes,yes,no,yes,no,5,4,2,1,1,5,0,12,14,14,1,FALSE 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100644 index 000000000..a9e4e4bb7 --- /dev/null +++ b/data/chapter2_data_analysis.R @@ -0,0 +1,68 @@ +#' Created at 10:00 12.11.2017 +#' +#' @author:Xiaodong Li +#' +#' The script for RStudio Exercise 2 -- analysis + +library(dplyr) +library(GGally) +library(ggplot2) +#read data +lrn2014 = read.table('/home/xiaodong/IODS_course/IODS-project/data/learning2014.txt',sep='\t',header = TRUE) +# Structure of the data +str(lrn2014) +# Dimensions of the data +dim(lrn2014) +# Data description +# According to the structure and dimensions of the data, the data frame contains 7 variables which are 'gender', +# 'age','attitude','deep','stra','surf','points'. In each variable, there are 166 observations. 'gender' represents +# male (M) and female (F) surveyors. 'age' is the ages (in years) of the people derived from the date of birth. +# In 'attitude' column lists the global attitudes toward statistics. Columns 'deep','surf' and 'stra' list the questions +# related to deep, surface and strategic learning. The related question could be found in the following page, http://www.helsinki.fi/~kvehkala/JYTmooc/JYTOPKYS3-meta.txt +# The 'points' column list the exam points from the survey. + +# Explore the data +# Plot the relationships between the variables +p <- ggpairs(lrn2014, mapping = aes(col=gender,alpha=0.3)) +p + +# The figure shows relationships between different variables. From the figure we can see that, from the gender column, +# female surveyors are more than male surveyors. Most of the people being surveyed are young generations, aged around 20 years old. +# The attitudes of man are higher than those of wemon towards statistics, which reflects that man has more positive attitudes towards +# statistics than wemen. The questions of deep and strategic learning are almost the same for men and wemen. The mean scores for +# them are around 3 and 4. However, the surface questions are quite different between the men and wemen surveyors. For wemen, the answers are centered +# at around 3.0 while the answers of men are centered at around 2.3. The exam points got from male and female answerers are quite the same and the most +# points are about 23 for both of them. + +# Multiple regression +reg_model=lm(points~attitude+stra+surf,data=lrn2014) +summary(reg_model) + +# The target variable point is fitted to three explanatory variables: attitude, stra and surf. According to +# the results of the model, surf does not have a statistically significant relationship with the target variable. +# So, surf is removed from the fitting model and points is modelled according to attitude and stra again. + +# Model again +reg_model2=lm(points~attitude+stra, data=lrn2014) +summary(reg_model2) + +# The model is fitted with the target points and two explanatory variable, attitude and stra. According to the summary results, the +# relationship between these variable should be points=8.9729+3.4658*attitude+0.9137*stra. The Std. Error is the standard deviation of the sampling distribution of +# the estimate of the coefficient under the standard regression assumptions. The t values are the estimates divided by there standard errors. It is an estimation of how +# extreme the value you see is, relative to the standard error. Pr. is the p-value for the hypothesis for which the t value is the test statistic. It tell you the probability +# of a test statistic at least as unusual as the one you obtained, if the null hypothesis were true (the null hypothesis is usually 'no effect', unless something else is specified). +# So, if the p-value is very low, then there is a higher probability that you're see data that is counter-indicative of zero effect. +# Residual standard error represents the standard deviation of the residuals. It's a measure of how close the fit is to the points. The Multiple R-squared is the proportion of the variance +# in the data that's explained by the model. The more variables you add, the large this will be. The Adjusted R-squared reduces that to account for the number of variables in the model. +# The F-statistic on the last line is telling you whether the regression as a whole is performing 'better than random',in other words, it tells whether your model fits better +# than you'd expect if all your predictors had no relationship with the response. The p-value in the last row is the p-value for that test, essentially comparing the full model you fitted with an intercept-only model. + +# Diagnostic plots +# Residuals vs Fitted values, Normal QQ-plot and Residuals vs Leverage are plotted +par(mfrow=c(2,2)) +plot(reg_model2, which=c(1,2,5)) + +# The Residuals vs Fitted values plot examines if the errors have constant variance. The graph shows a reasonable constant variance without any pattern. +# The Normal QQ-polt checks if the errors are normally distributed. We see from the graph a very good linear model fit, indicating a normally distributed error set. +# The Residuals vs Leverage confirms if there are any outliers with high leverage. From the graph, it shows that all the leverage are below 0.06, indicating good model fitting. + diff --git a/data/creat_alc.R b/data/creat_alc.R new file mode 100644 index 000000000..d9ef46c36 --- /dev/null +++ b/data/creat_alc.R @@ -0,0 +1,50 @@ +#Created on 18.11.2017 +#@author: Xiaodong Li +#This is the script for RStudio exercise 3 -- Data wrangling +#The data is from the UCI Machine Learning Repository, Student Performance Data Set. +# + +# Import packages +library(dplyr) + +# Read data +math=read.csv('student-mat.csv',sep=';',header=T) +por=read.csv('student-por.csv',sep=';',header=T) + +# Explore the data +str(math) +dim(math) +str(por) +dim(por) + +# Join the two datasets together and explore the data +join_by = c("school","sex","age","address","famsize","Pstatus","Medu","Fedu","Mjob","Fjob","reason","nursery","internet") +math_por = inner_join(math, por, by = join_by, suffix=c('.math','.por')) +str(math_por) +dim(math_por) + +# Combine the two 'duplicated' answers +alc = select(math_por, one_of(join_by)) +notjoined_columns <- colnames(math)[!colnames(math) %in% join_by] +for (column_name in notjoined_columns) { + two_columns=select(math_por,starts_with(column_name)) + first_column=select(two_columns,1)[[1]] + + if(is.numeric(first_column)) { + alc[column_name]=round(rowMeans(two_columns)) + } else { + alc[column_name]=first_column +} +} + +str(alc) +dim(alc) + +# Take the average of the answers related to weekday and weekend alcohol consumption. +alc = mutate(alc, alc_use = (Dalc + Walc) / 2) +alc = mutate(alc, high_use = alc_use > 2) +glimpse(alc) + +# Save the data +write.csv(alc,'alc.csv',row.names=F,quote=F) + diff --git a/data/creat_human.R b/data/creat_human.R new file mode 100644 index 000000000..c8dfe4311 --- /dev/null +++ b/data/creat_human.R @@ -0,0 +1,55 @@ +#Created on 28.11.2017 +#@author: Xiaodong Li +#This is the script for RStudio exercise 5 -- Data wrangling +#The data originates from the United Nations Development Programme. +# + +library(dplyr) +library(stringr) +# Read the human development data +#human=read.table(' +hd <- read.csv("http://s3.amazonaws.com/assets.datacamp.com/production/course_2218/datasets/human_development.csv", stringsAsFactors = F) +str(hd) +dim(hd) +summary(hd) + +# Read the Gender inequality data +gii <- read.csv("http://s3.amazonaws.com/assets.datacamp.com/production/course_2218/datasets/gender_inequality.csv", stringsAsFactors = F, na.strings = "..") +str(gii) +dim(gii) +summary(gii) + +# Modify the column names of Human Development dataset and Gender inequality data +column_names_hd=c('HDI.Rank','Country','HDI','Life.Exp','Edu.Exp','Edu.Mean','GNI','GNI.Minus.Rank') +colnames(hd)=column_names_hd +column_names_gii=c('GII.Rank','Country','GII','Mat.Mor','Ado.Birth','Parli.F','Edu2.F','Edu2.M','Labo.F','Labo.M') +colnames(gii)=column_names_gii + +# Calculate the ratio of female and male populations with secondary education and labour force participation in each country +gii=mutate(gii,Edu2.FM=Edu2.F/Edu2.M,Labo.FM=Labo.F/Labo.M) + +# Join the two datasets +human=inner_join(hd,gii,by='Country') +dim(human) +summary(human) + +# Mutate the GNI data in 'human' dataset +str(human$GNI) +human$GNI=str_replace(human$GNI,pattern=',',replace='') %>% as.numeric + +# Dealing with not available (NA) values +keep=c("Country", "Edu2.FM", "Labo.FM", "Life.Exp", "Edu.Exp", "GNI", "Mat.Mor", "Ado.Birth", "Parli.F") +human=select(human,one_of(keep)) +human=filter(human,complete.cases(human)) + +# Remove observations with related to regions instead of countries +last=nrow(human)-7 +human_=human[1:last,] + +# Define the row names of the data by the country names +rownames(human_)=human_$Country +human=human_[-1] + +# Save data +setwd('/home/xiaodong/IODS_course/IODS-project/data') +write.table(human,file='human.txt',row.names=T,sep = '\t') \ No newline at end of file diff --git a/data/creat_learning2014.R b/data/creat_learning2014.R new file mode 100644 index 000000000..4c96adae4 --- /dev/null +++ b/data/creat_learning2014.R @@ -0,0 +1,44 @@ +#' Created at 21:00 11.11.2017 +#' +#' @author:Xiaodong Li +#' +#' The script for RStudio Exercise 2 + +library(dplyr) +# Read data +lrn14=read.table('http://www.helsinki.fi/~kvehkala/JYTmooc/JYTOPKYS3-data.txt', sep='\t',header=TRUE) +# Structure of the data +str(lrn14) +# Dimensions of the data +dim(lrn14) +# The data has 183 obsversions and each observation has 60 variables. Nearly all the data are 'int' format except the 'gender' observation, which is a 'Factor'. + +# Modify column names +column_names=c('age','attitude','points') +colnames(lrn14)[57:59]=column_names + +# Sacling variables +lrn14$attitude=lrn14$attitude/10 +# questions related to deep, surface and strategic learning +deep_questions <- c("D03", "D11", "D19", "D27", "D07", "D14", "D22", "D30","D06", "D15", "D23", "D31") +surface_questions <- c("SU02","SU10","SU18","SU26", "SU05","SU13","SU21","SU29","SU08","SU16","SU24","SU32") +strategic_questions <- c("ST01","ST09","ST17","ST25","ST04","ST12","ST20","ST28") +# select the columns related to deep learning and create column 'deep' by averaging +deep_columns <- select(lrn14, one_of(deep_questions)) +lrn14$deep <- rowMeans(deep_columns) +# select the columns related to surface learning and create column 'surf' by averaging +surface_columns <- select(lrn14, one_of(surface_questions)) +lrn14$surf <- rowMeans(surface_columns) +# select the columns related to strategic learning and create column 'stra' by averaging +strategic_columns <- select(lrn14, one_of(strategic_questions)) +lrn14$stra = rowMeans(strategic_columns) + +# Select columns +selected_col=c('gender','age','attitude','deep','stra','surf','points') +learning2014=select(lrn14,one_of(selected_col)) + +# Exclude observations where the exam points variable is zero +learning2014=filter(learning2014,points!=0) + +# Save data +write.table(learning2014,file='learning2014.txt',row.names=F,sep = '\t') diff --git a/data/human.txt b/data/human.txt new file mode 100644 index 000000000..b86f48b46 --- /dev/null +++ b/data/human.txt @@ -0,0 +1,156 @@ +"Edu2.FM" "Labo.FM" "Life.Exp" "Edu.Exp" "GNI" "Mat.Mor" "Ado.Birth" "Parli.F" +"Norway" 1.00723888314374 0.890829694323144 81.6 17.5 64992 4 7.8 39.6 +"Australia" 0.996828752642706 0.818941504178273 82.4 20.2 42261 6 12.1 30.5 +"Switzerland" 0.98343685300207 0.825100133511348 83 15.8 56431 6 1.9 28.5 +"Denmark" 0.988612836438924 0.884036144578313 80.2 18.7 44025 5 5.1 38 +"Netherlands" 0.969060773480663 0.828611898016997 81.6 17.9 45435 6 6.2 36.9 +"Germany" 0.992783505154639 0.807228915662651 80.9 16.5 43919 7 3.8 36.9 +"Ireland" 1.02417302798982 0.779735682819383 80.9 18.6 39568 9 8.2 19.9 +"United States" 1.00316455696203 0.817126269956459 79.1 16.5 52947 28 31 19.4 +"Canada" 1 0.867605633802817 82 15.9 42155 11 14.5 28.2 +"New Zealand" 0.99685204616999 0.840108401084011 81.8 19.2 32689 8 25.3 31.4 +"Singapore" 0.914814814814815 0.761658031088083 83 15.4 76628 6 6 25.3 +"Sweden" 0.990836197021764 0.888070692194403 82.2 15.8 45636 4 6.5 43.6 +"United Kingdom" 0.998998998998999 0.810771470160116 80.7 16.2 39267 8 25.8 23.5 +"Iceland" 0.993449781659389 0.910852713178295 82.6 19 35182 4 11.5 41.3 +"Korea (Republic of)" 0.864197530864198 0.694868238557559 81.9 16.9 33890 27 2.2 16.3 +"Israel" 0.966781214203895 0.837916063675832 82.4 16 30676 2 7.8 22.5 +"Luxembourg" 1 0.784829721362229 81.7 13.9 58711 11 8.3 28.3 +"Japan" 1.01398601398601 0.693181818181818 83.5 15.3 36927 6 5.4 11.6 +"Belgium" 0.934861278648975 0.801011804384486 80.8 16.3 41187 6 6.7 42.4 +"France" 0.9375 0.823051948051948 82.2 16 38056 12 5.7 25.7 +"Austria" 1 0.806499261447563 81.4 15.7 43869 4 4.1 30.3 +"Finland" 1 0.8703125 80.8 17.1 38695 4 9.2 42.5 +"Slovenia" 0.977551020408163 0.82753164556962 80.4 16.8 27852 7 0.6 27.7 +"Spain" 0.913816689466484 0.797872340425532 82.6 17.3 32045 4 10.6 38 +"Italy" 0.884472049689441 0.665546218487395 83.1 16 33030 4 4 30.1 +"Czech Republic" 1.00200601805416 0.748169838945827 78.6 16.4 26660 5 4.9 18.9 +"Greece" 0.888059701492537 0.7072 80.9 17.6 24524 5 11.9 21 +"Estonia" 1 0.815674891146589 76.8 16.5 25214 11 16.8 19.8 +"Cyprus" 0.930232558139535 0.787623066104079 80.2 14 28633 10 5.5 12.5 +"Qatar" 1.13050847457627 0.531937172774869 78.2 13.8 123124 6 9.5 0 +"Slovakia" 0.995979899497487 0.744897959183674 76.3 15.1 25845 7 15.9 18.7 +"Poland" 0.928654970760234 0.75346687211094 77.4 15.5 23177 3 12.2 22.1 +"Lithuania" 0.944856839872746 0.829123328380386 73.3 16.4 24500 11 10.6 23.4 +"Malta" 0.877237851662404 0.571644042232277 80.6 14.4 27930 9 18.2 13 +"Saudi Arabia" 0.860597439544808 0.257982120051086 74.3 16.3 52821 16 10.2 19.9 +"Argentina" 0.977430555555555 0.633333333333333 76.3 17.9 22050 69 54.4 36.8 +"United Arab Emirates" 1.19444444444444 0.505434782608696 77 13.3 60868 8 27.6 17.5 +"Chile" 0.959424083769633 0.657754010695187 81.7 15.2 21290 22 55.3 15.8 +"Portugal" 0.989626556016598 0.829305135951662 80.9 16.3 25757 8 12.6 31.3 +"Hungary" 0.991894630192503 0.746666666666667 75.2 15.4 22916 14 12.1 10.1 +"Bahrain" 1.10311284046693 0.451093210586881 76.6 14.4 38599 22 13.8 15 +"Latvia" 0.998989898989899 0.812130177514793 74.2 15.2 22281 13 13.5 18 +"Croatia" 0.908119658119658 0.76541095890411 77.3 14.8 19409 13 12.7 25.8 +"Kuwait" 0.987566607460036 0.524669073405536 74.4 14.7 83961 14 14.5 1.5 +"Montenegro" 0.889123548046463 0.75043630017452 76.2 15.2 14558 7 15.2 17.3 +"Belarus" 0.943600867678959 0.793977812995246 71.3 15.7 16676 1 20.6 30.1 +"Russian Federation" 0.968648648648649 0.796373779637378 70.1 14.7 22352 24 25.7 14.5 +"Oman" 0.82661996497373 0.351089588377724 76.8 13.6 34858 11 10.6 9.6 +"Romania" 0.935869565217391 0.750385208012327 74.7 14.2 18108 33 31 12 +"Uruguay" 1.08151093439364 0.723958333333333 77.2 15.5 19283 14 58.3 11.5 +"Bahamas" 1.04109589041096 0.873896595208071 75.4 12.6 21336 37 28.5 16.7 +"Kazakhstan" 0.964574898785425 0.869062901155327 69.4 15 20867 26 29.9 20.1 +"Barbados" 1.02052451539339 0.860313315926893 75.6 15.4 12488 52 48.4 19.6 +"Bulgaria" 0.971786833855799 0.811864406779661 74.2 14.4 15596 5 35.9 20.4 +"Panama" 1.08216432865731 0.599022004889976 77.6 13.3 18192 85 78.5 19.3 +"Malaysia" 0.91304347826087 0.588079470198675 74.7 12.7 22762 29 5.7 14.2 +"Mauritius" 0.851724137931034 0.587601078167116 74.4 15.6 17470 73 30.9 11.6 +"Trinidad and Tobago" 0.980295566502463 0.701986754966887 70.4 12.3 26090 84 34.8 24.7 +"Serbia" 0.793478260869565 0.730706075533662 74.9 14.4 12190 16 16.9 34 +"Cuba" 0.942893401015228 0.62 79.4 13.8 7301 80 43.1 48.9 +"Lebanon" 0.956678700361011 0.328631875881523 79.3 13.8 16509 16 12 3.1 +"Costa Rica" 1.0039603960396 0.589873417721519 79.4 13.9 13413 38 60.8 33.3 +"Iran (Islamic Republic of)" 0.920118343195266 0.22554347826087 75.4 15.1 15440 23 31.6 3.1 +"Venezuela (Bolivarian Republic of)" 1.11417322834646 0.64520202020202 74.2 14.2 16159 110 83.2 17 +"Turkey" 0.65 0.415254237288136 75.3 14.5 18677 20 30.9 14.4 +"Sri Lanka" 0.951570680628272 0.46002621231979 74.9 13.7 9779 29 16.9 5.8 +"Mexico" 0.919141914191419 0.564455569461827 76.8 13.1 16056 49 63.4 37.1 +"Brazil" 1.04198473282443 0.735148514851485 74.5 15.2 15175 69 70.8 9.6 +"Georgia" 0.967637540453074 0.752330226364847 74.9 13.8 7164 41 46.8 11.3 +"Azerbaijan" 0.962012320328542 0.903735632183908 70.8 11.9 16428 26 40 15.6 +"Jordan" 0.885350318471338 0.234234234234234 74 13.5 11365 50 26.5 11.6 +"The former Yugoslav Republic of Macedonia" 0.723021582733813 0.638518518518518 75.4 13.4 11780 7 18.3 33.3 +"Ukraine" 0.956204379562044 0.795216741405082 71 15.1 8178 23 25.7 11.8 +"Algeria" 0.861290322580645 0.210526315789474 74.8 14 13054 89 10 25.7 +"Peru" 0.851739788199697 0.808056872037915 74.6 13.1 11015 89 50.7 22.3 +"Albania" 0.930602957906712 0.685496183206107 77.8 11.8 9943 21 15.3 20.7 +"Armenia" 0.989473684210526 0.746556473829201 74.7 12.3 8124 29 27.1 10.7 +"Bosnia and Herzegovina" 0.643266475644699 0.595113438045375 76.5 13.6 9638 8 15.1 19.3 +"Ecuador" 1.01776649746193 0.66142684401451 75.9 14.2 10605 87 77 41.6 +"China" 0.816411682892907 0.816091954022989 75.8 13.1 12547 32 8.6 23.6 +"Fiji" 0.995348837209302 0.520833333333333 70 15.7 7493 59 42.8 14 +"Mongolia" 1.01426872770511 0.816738816738817 69.4 14.6 10729 68 18.7 14.9 +"Thailand" 0.875 0.796778190830235 74.4 13.5 13323 26 41 6.1 +"Libya" 1.32458233890215 0.392670157068063 71.6 14 14911 15 2.5 16 +"Tunisia" 0.711496746203904 0.354019746121298 74.8 14.6 10404 46 4.6 31.3 +"Colombia" 1.02338129496403 0.700125470514429 74 13.5 12040 83 68.5 20.9 +"Jamaica" 1.05413105413105 0.791255289139633 75.7 12.4 7415 80 70.1 16.7 +"Tonga" 0.990939977349943 0.7171581769437 72.8 14.7 5069 120 18.1 0 +"Belize" 1.00791556728232 0.597812879708384 70 13.6 7614 45 71.4 13.3 +"Dominican Republic" 1.04708097928437 0.652671755725191 73.5 13.1 11883 100 99.6 19.1 +"Suriname" 0.94692144373673 0.588662790697674 71.1 12.7 15617 130 35.2 11.8 +"Maldives" 0.834862385321101 0.725161290322581 76.8 13 12328 31 4.2 5.9 +"Samoa" 1.07166666666667 0.402397260273973 73.4 12.9 5327 58 28.3 6.1 +"Botswana" 0.944801026957638 0.881127450980392 64.5 12.5 16646 170 44.2 9.5 +"Moldova (Republic of)" 0.968944099378882 0.850678733031674 71.6 11.9 5223 21 29.3 20.8 +"Egypt" 0.724422442244224 0.316844919786096 71.1 13.5 10512 45 43 2.2 +"Gabon" 1.49307479224377 0.859327217125382 64.4 12.5 16367 240 103 16.2 +"Indonesia" 0.810975609756098 0.610451306413302 68.9 13 9788 190 48.3 17.1 +"Paraguay" 0.855813953488372 0.65683962264151 72.9 11.9 7643 110 67 16.8 +"Philippines" 1.03453689167975 0.641154328732748 68.2 11.3 7915 120 46.8 27.1 +"El Salvador" 0.844036697247706 0.605063291139241 73 12.3 7349 69 76 27.4 +"South Africa" 0.957839262187088 0.735537190082645 57.4 13.6 12122 140 50.9 40.7 +"Viet Nam" 0.834269662921348 0.888077858880779 75.8 11.9 5092 49 29 24.3 +"Bolivia (Plurinational State of)" 0.805414551607445 0.793572311495674 68.3 13.2 5760 200 71.9 51.8 +"Kyrgyzstan" 0.976239669421488 0.70440251572327 70.6 12.5 3044 75 29.3 23.3 +"Iraq" 0.553784860557769 0.213467048710602 69.4 10.1 14003 67 68.7 26.5 +"Guyana" 1.26150627615063 0.529192546583851 66.4 10.3 6522 250 88.5 31.3 +"Nicaragua" 1.02872062663185 0.590286425902864 74.9 11.5 4457 100 100.8 39.1 +"Morocco" 0.685430463576159 0.349604221635884 74 11.6 6850 120 35.8 11 +"Namibia" 0.968023255813953 0.858712715855573 64.8 11.3 9418 130 54.9 37.7 +"Guatemala" 0.943965517241379 0.558956916099773 71.8 10.7 6929 140 97.2 13.3 +"Tajikistan" 1.04276315789474 0.763942931258106 69.4 11.2 2517 44 42.8 15.2 +"India" 0.477031802120141 0.337922403003755 68 11.7 5497 190 32.8 12.2 +"Honduras" 1.08527131782946 0.516284680337756 73.1 11.1 3938 120 84 25.8 +"Bhutan" 0.985507246376812 0.863989637305699 69.5 12.6 7176 120 40.9 8.3 +"Syrian Arab Republic" 0.728395061728395 0.185694635488308 69.6 12.3 2728 49 41.6 12.4 +"Congo" 0.84468085106383 0.938356164383562 62.3 11.1 6012 410 126.7 11.5 +"Zambia" 0.586363636363636 0.853971962616822 60.1 13.5 3734 280 125.4 12.7 +"Ghana" 0.698608964451314 0.942577030812325 61.4 11.5 3852 380 58.4 10.9 +"Bangladesh" 0.825665859564165 0.682520808561237 71.6 10 3191 170 80.6 20 +"Cambodia" 0.432314410480349 0.910982658959538 68.4 10.9 2949 170 44.3 19 +"Kenya" 0.805732484076433 0.859116022099447 61.6 11 2762 400 93.6 20.8 +"Nepal" 0.463350785340314 0.917336394948335 69.6 12.4 2311 190 73.7 29.5 +"Pakistan" 0.418655097613883 0.296743063932449 66.2 7.8 4866 170 27.3 19.7 +"Myanmar" 1.49673202614379 0.913730255164034 65.9 8.6 4608 200 12.1 4.7 +"Swaziland" 0.842307692307692 0.613128491620112 49 11.3 5542 310 72 14.7 +"Tanzania (United Republic of)" 0.589473684210526 0.976718403547672 65 9.2 2411 410 122.7 36 +"Cameroon" 0.610315186246418 0.830729166666667 55.5 10.4 2803 590 115.8 27.1 +"Zimbabwe" 0.785483870967742 0.927536231884058 57.5 10.9 1615 470 60.3 35.1 +"Mauritania" 0.397129186602871 0.36283185840708 63.1 8.5 3560 320 73.3 22.2 +"Papua New Guinea" 0.524137931034483 0.952702702702703 62.6 9.9 2463 220 62.1 2.7 +"Yemen" 0.322097378277154 0.35180055401662 63.8 9.2 3519 270 47 0.7 +"Lesotho" 1.15263157894737 0.802721088435374 49.8 11.1 3306 490 89.4 26.8 +"Togo" 0.399503722084367 0.991389913899139 59.7 12.2 1228 450 91.5 17.6 +"Haiti" 0.636363636363636 0.857746478873239 62.8 8.7 1669 380 42 3.5 +"Rwanda" 0.909090909090909 1.01289566236811 64.2 10.3 1458 320 33.6 57.5 +"Uganda" 0.683582089552239 0.957070707070707 58.5 9.8 1613 360 126.6 35 +"Benin" 0.418518518518519 0.863346104725415 59.6 11.1 1767 340 90.2 8.4 +"Sudan" 0.664835164835165 0.411842105263158 63.5 7 3809 360 84 23.8 +"Senegal" 0.467532467532468 0.75 66.5 7.9 2188 320 94.4 42.7 +"Afghanistan" 0.197986577181208 0.19874213836478 60.4 9.3 1885 400 86.8 27.6 +"Côte d'Ivoire" 0.465116279069767 0.643734643734644 51.5 8.9 3171 720 130.3 9.2 +"Malawi" 0.513888888888889 1.03803680981595 62.8 10.8 747 510 144.8 16.7 +"Ethiopia" 0.428571428571429 0.875699888017917 64.1 8.5 1428 420 78.4 25.5 +"Gambia" 0.552380952380952 0.870928829915561 60.2 8.8 1507 430 115.8 9.4 +"Congo (Democratic Republic of the)" 0.395061728395062 0.965846994535519 58.7 9.8 680 730 135.3 8.2 +"Liberia" 0.391857506361323 0.898148148148148 60.9 9.5 805 640 117.4 10.7 +"Mali" 0.509933774834437 0.624078624078624 58 8.4 1583 550 175.6 9.5 +"Mozambique" 0.225806451612903 1.03260869565217 55.1 9.3 1123 480 137.8 39.6 +"Sierra Leone" 0.460829493087558 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+26,16 @@ output: ``` *** +```{r child = "chapter3.Rmd"} +``` + +*** +```{r child = "chapter4.Rmd"} +``` + +*** +```{r child = "chapter5.Rmd"} +``` + + + diff --git a/index.html b/index.html index 64770ef40..b25f11d91 100644 --- a/index.html +++ b/index.html @@ -4,40 +4,72 @@ - + + IODS course project - + - - - - + + + + - -