10-MY451-more.Rmd

# More statistics... {#c-more}

You will no doubt be pleased to learn that the topics covered on this
course have not quite exhausted the list of available statistical
methods. In this chapter we outline some of the most important further
areas of statistics, so that you are at least aware of their existence
and titles. For some of them, codes of LSE courses which cover these
methods are given in parentheses.

A very large part of advanced statistics is devoted to further types of
**regression models**. The basic idea of them is the same as for
multiple linear regression, i.e. modelling expected values of response
variables given several explanatory variables. The issues involved in
the form and treatment of explanatory variables are usually almost
exactly the same as for linear models. Different classes of regression
models are needed mainly to accommodate different types of response
variables:

-   Models for **categorical response variables**. These exist for
    situations where the response variable is dichotomous (**binary
    regression**, especially **logistic models**), has more than two
    unordered (**multinomial logistic models**) or ordered (**ordinal
    regression models**) categories, or is a count, for example in a
    contingency table (**Poisson regression**, **loglinear models**).
    Despite the many different titles, all of these models are closely
    connected (MY452)

-   Models for cases where the response is a length of time to some
    event, such as a spell of unemployment, interval between births of
    children or survival of a patient in a medical study. These
    techniques are known as **event history analysis**, **survival
    analysis** or **lifetime data analysis**. Despite the different
    terms, all refer to the same statistical models.

Techniques for the analysis of **dependent data**, which do not require
the assumption of statistically independent observations used by almost
all the methods on this course:

-   **Time series analysis** for one or more long sequence of
    observations of the same quantity over time. For example, each of
    the five temperature sequencies in Figure \@ref(fig:f-temperatures) is a
    time series of this kind.

-   Regression models for **hierarchical data**, where some sets of
    observations are not independent of each other. There are two main
    types of such data: **longitudinal** or **panel data** which consist
    of short time series for many units (e.g. answers by respondents in
    successive waves of a panel survey), and **nested** or **multilevel
    data** where basic units are grouped in natural groups or clusters
    (e.g. pupils in classes and schools in an educational study). Both
    of these can be analysed using the same general classes of models,
    which in turn are generalisations of linear and other regression
    models used for independent data (ST416 for models for multilevel
    data and ST442 for models for longitudinal data).

Methods for **multivariate data**. Roughly speaking, this means data
with several variables for comparable quantities treated on an equal
footing, so that none of them is obviously a response to the others. For
example, results for the ten events in the decathlon data of the week 7
computer class or, more seriously, the responses to a series of related
attitude items in a survey are multivariate data of this kind.

-   Various methods of **descriptive multivariate analysis** for jointly
    summarising and presenting information on the many variables,
    e.g. **cluster analysis**, **multidimensional scaling** and
    **principal component analysis** (MY455 for principal
    components analysis).

-   Model-based methods for multivariate data. These are typically
    **latent variable models**, which also involve variables which can
    never be directly observed. The simplest latent variable technique
    is **exploratory factor analysis**, and others include
    **confirmatory factor analysis**, **structural equation models**,
    and **latent trait** and **latent class** models (MY455).

Some types of **research design** may also involve particular
statistical considerations:

-   **Sampling theory** for the design of probability samples, e.g.  for
    surveys (part of MY456, which also covers methodology of surveys
    in general).

-   **Design of experiments** for more complex randomized experiments.

Finally, some areas of statistics are concerned with broader and more
fundamental aspects of statistical analysis, such as alternative forms
of model specification and inference (e.g. **nonparametric methods**) or
the basic ideas of inference itself (e.g. **Bayesian statistics**).
These and the more specific tools further build on the foundations of
all statistical methods, which are the subject of **probability theory**
and **mathematical statistics**. However, you are welcome, if you wish,
to leave the details of these fields to professional statisticians, if
only to keep them too in employment.