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a & b: f 6.98622 0.107871 64.76 <1e-77 6.77197 7.20046
a & b: g 7.92541 0.109873 72.13 <1e-82 7.70719 8.14362
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</code></pre><p>Internally, this is accomplished in three steps:</p><ol><li>The expression passed to <code>@formula</code> is lowered to term constructors combined by <code>~</code>, <code>+</code>, and <code>&amp;</code>, which evaluate to create terms for the whole formula and any interaction terms.</li><li>A schema is extracted from the data, which determines whether each variable is continuous or categorical and extracts the summary statistics of each variable (mean/variance/min/max or unique levels respectively). This schema is then <em>applied</em> to the formula with <code>apply_schema(term, schema, ::Type{Model})</code>, which returns a new formula with each placeholder <code>Term</code> replaced with a concrete <code>ContinuousTerm</code> or <code>CategoricalTerm</code> as appropriate. This is also the stage where any custom syntax is applied (see <a href="../internals/#Internals-and-extending-the-formula-DSL">the section on extending the <code>@formula</code> language</a> for more details).</li><li>Numeric arrays are generated for the response and predictors from the full table using <code>modelcols(term, data)</code>.</li></ol><p>The <code>ModelFrame</code> and <code>ModelMatrix</code> types can still be used to do this transformation, but this is only to preserve some backwards compatibility. Package authors who would like to include support for fitting models from a <code>@formula</code> are <strong>strongly</strong> encouraged to directly use <code>schema</code>, <code>apply_schema</code>, and <code>modelcols</code> to handle the table-to-matrix transformations they need.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Introduction</a><a class="docs-footer-nextpage" href="../internals/">Internals and extending the <code>@formula</code> »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Friday 16 August 2024 08:51">Friday 16 August 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
</code></pre><p>Internally, this is accomplished in three steps:</p><ol><li>The expression passed to <code>@formula</code> is lowered to term constructors combined by <code>~</code>, <code>+</code>, and <code>&amp;</code>, which evaluate to create terms for the whole formula and any interaction terms.</li><li>A schema is extracted from the data, which determines whether each variable is continuous or categorical and extracts the summary statistics of each variable (mean/variance/min/max or unique levels respectively). This schema is then <em>applied</em> to the formula with <code>apply_schema(term, schema, ::Type{Model})</code>, which returns a new formula with each placeholder <code>Term</code> replaced with a concrete <code>ContinuousTerm</code> or <code>CategoricalTerm</code> as appropriate. This is also the stage where any custom syntax is applied (see <a href="../internals/#Internals-and-extending-the-formula-DSL">the section on extending the <code>@formula</code> language</a> for more details).</li><li>Numeric arrays are generated for the response and predictors from the full table using <code>modelcols(term, data)</code>.</li></ol><p>The <code>ModelFrame</code> and <code>ModelMatrix</code> types can still be used to do this transformation, but this is only to preserve some backwards compatibility. Package authors who would like to include support for fitting models from a <code>@formula</code> are <strong>strongly</strong> encouraged to directly use <code>schema</code>, <code>apply_schema</code>, and <code>modelcols</code> to handle the table-to-matrix transformations they need.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Introduction</a><a class="docs-footer-nextpage" href="../internals/">Internals and extending the <code>@formula</code> »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Friday 16 August 2024 09:05">Friday 16 August 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Introduction · StatsModels.jl</title><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>StatsModels.jl</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Introduction</a></li><li><a class="tocitem" href="formula/">Modeling tabular data</a></li><li><a class="tocitem" href="internals/">Internals and extending the <code>@formula</code></a></li><li><a class="tocitem" href="contrasts/">Contrast coding categorical variables</a></li><li><a class="tocitem" href="temporal_terms/">Temporal variables and Time Series Terms</a></li><li><a class="tocitem" href="api/">API documentation</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Introduction</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Introduction</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaStats/StatsModels.jl/blob/master/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="StatsModels-Documentation"><a class="docs-heading-anchor" href="#StatsModels-Documentation">StatsModels Documentation</a><a id="StatsModels-Documentation-1"></a><a class="docs-heading-anchor-permalink" href="#StatsModels-Documentation" title="Permalink"></a></h1><p>This package provides common abstractions and utilities for specifying, fitting, and evaluating statistical models. The goal is to provide an API for package developers implementing different kinds of statistical models (see the <a href="https://www.github.com/JuliaStats/GLM.jl">GLM</a> package for example), and utilities that are generally useful for both users and developers when dealing with statistical models and tabular data.</p><ul><li><a href="formula/#Modeling-tabular-data">Formula notation</a> for transforming tabular data into numerical arrays for modeling.</li><li>Mechanisms for <a href="internals/#Internals-and-extending-the-formula-DSL">extending the <code>@formula</code> notation</a> in external modeling packages.</li><li><a href="contrasts/#Modeling-categorical-data">Contrast coding</a> for categorical data</li><li>Types and <a href="api/#Modeling">API</a> for fitting and working with statistical models, extending <a href="http://juliastats.github.io/StatsBase.jl/stable/statmodels.html">StatsBase.jl&#39;s API</a> to tabular data.</li></ul><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Much of this package was formerly part of <a href="https://www.github.com/JuliaStats/DataFrames.jl">DataFrames.jl</a> and historically only handled tabular data in the form of a <code>DataFrame</code>, but currently supports any table that supports the minimal <a href="https://github.com/JuliaData/Tables.jl/">Tables.jl</a> interface. It&#39;s thus a relatively light dependency.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="formula/">Modeling tabular data »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Friday 16 August 2024 08:51">Friday 16 August 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Introduction · StatsModels.jl</title><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>StatsModels.jl</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Introduction</a></li><li><a class="tocitem" href="formula/">Modeling tabular data</a></li><li><a class="tocitem" href="internals/">Internals and extending the <code>@formula</code></a></li><li><a class="tocitem" href="contrasts/">Contrast coding categorical variables</a></li><li><a class="tocitem" href="temporal_terms/">Temporal variables and Time Series Terms</a></li><li><a class="tocitem" href="api/">API documentation</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Introduction</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Introduction</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaStats/StatsModels.jl/blob/master/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="StatsModels-Documentation"><a class="docs-heading-anchor" href="#StatsModels-Documentation">StatsModels Documentation</a><a id="StatsModels-Documentation-1"></a><a class="docs-heading-anchor-permalink" href="#StatsModels-Documentation" title="Permalink"></a></h1><p>This package provides common abstractions and utilities for specifying, fitting, and evaluating statistical models. The goal is to provide an API for package developers implementing different kinds of statistical models (see the <a href="https://www.github.com/JuliaStats/GLM.jl">GLM</a> package for example), and utilities that are generally useful for both users and developers when dealing with statistical models and tabular data.</p><ul><li><a href="formula/#Modeling-tabular-data">Formula notation</a> for transforming tabular data into numerical arrays for modeling.</li><li>Mechanisms for <a href="internals/#Internals-and-extending-the-formula-DSL">extending the <code>@formula</code> notation</a> in external modeling packages.</li><li><a href="contrasts/#Modeling-categorical-data">Contrast coding</a> for categorical data</li><li>Types and <a href="api/#Modeling">API</a> for fitting and working with statistical models, extending <a href="http://juliastats.github.io/StatsBase.jl/stable/statmodels.html">StatsBase.jl&#39;s API</a> to tabular data.</li></ul><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Much of this package was formerly part of <a href="https://www.github.com/JuliaStats/DataFrames.jl">DataFrames.jl</a> and historically only handled tabular data in the form of a <code>DataFrame</code>, but currently supports any table that supports the minimal <a href="https://github.com/JuliaData/Tables.jl/">Tables.jl</a> interface. It&#39;s thus a relatively light dependency.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="formula/">Modeling tabular data »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Friday 16 August 2024 09:05">Friday 16 August 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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