Mixed Effects Machine Learning with GPBoost for Grouped and Areal Spatial Econometric Data
<p>The <a href="https://www.jmlr.org/papers/v23/20-322.html" rel="noopener ugc nofollow" target="_blank">GPBoost algorithm</a> extends linear mixed effects and Gaussian process models by replacing the linear fixed effects function with a non-parametric non-linear function modeled using tree-boosting. This article shows how the GPBoost algorithm implemented in the <code><a href="https://github.com/fabsig/GPBoost" rel="noopener ugc nofollow" target="_blank">GPBoost</a></code><a href="https://github.com/fabsig/GPBoost" rel="noopener ugc nofollow" target="_blank"> library</a> can be used for modeling data with a spatial and grouped structure. We demonstrate the functionality of the <code>GPBoost</code> library using European GDP data which is an example of areal spatial econometric data.</p>
<h2>Table of contents</h2>
<p>∘ <a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#2d36" rel="noopener ugc nofollow">Introduction</a><br />
· · <a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#7b6e" rel="noopener ugc nofollow">Basic workflow of GPBoost</a><br />
· · <a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#d3b9" rel="noopener ugc nofollow">Data description</a><br />
· ·<a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#be54" rel="noopener ugc nofollow">Data loading and short visualization</a><br />
∘ <a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#ef69" rel="noopener ugc nofollow">Training a GPBoost model</a><br />
∘ <a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#e5e7" rel="noopener ugc nofollow">Choosing tuning parameters</a><br />
∘ <a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#b7b0" rel="noopener ugc nofollow">Model interpretation</a><br />
· ·<a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#54e9" rel="noopener ugc nofollow">Estimated random effects model</a><br />
· ·<a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#c547" rel="noopener ugc nofollow">Spatial effect map</a><br />
· ·<a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#0ff8" rel="noopener ugc nofollow">Understanding the fixed effects function</a><br />
∘ <a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#af79" rel="noopener ugc nofollow">Extensions</a><br />
· ·<a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#756a" rel="noopener ugc nofollow">Separate random effects for different time periods</a><br />
· ·<a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#7121" rel="noopener ugc nofollow">Interaction between space and fixed effects predictor variables</a><br />
· ·<a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#c6c4" rel="noopener ugc nofollow">Large data</a><br />
· ·<a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#24bc" rel="noopener ugc nofollow">Other spatial random effects models</a><br />
· ·<a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#4342" rel="noopener ugc nofollow">(Generalized) linear mixed effects and Gaussian process models</a><br />
∘ <a href="https://towardsdatascience.com/mixed-effects-machine-learning-with-gpboost-for-grouped-and-areal-spatial-econometric-data-b26f8bddd385#376a" rel="noopener ugc nofollow">References</a></p>
<h1>Introduction</h1>
<h2>Basic workflow of GPBoost</h2>
<p>Applying a GPBoost model (= combined tree-boosting and random effects / GP models) involves the following main steps:</p>
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