Gaussian Process Panel Modeling—Machine Learning Inspired Analysis of Longitudinal Panel Data

Frontiers in Psychology, vol. 11, pp. 351

Abstract

In this article, we extend the Bayesian nonparametric regression method Gaussian Process Regression to the analysis of longitudinal panel data. We call this new approach Gaussian Process Panel Modeling (GPPM). GPPM provides great flexibility because of the large number of models it can represent. It allows classical statistical inference as well as machine learning inspired predictive modeling. GPPM offers frequentist and Bayesian inference without the need to resort to Markov chain Monte Carlo-based approximations, which makes the approach exact and fast. GPPMs are defined using the kernel-language, which can express many traditional modeling approaches for longitudinal data, such as linear structural equation models, multilevel models, or state-space models but also various commonly used machine learning approaches. As a result, GPPM is uniquely able to represent hybrid models combining traditional parametric longitudinal models and nonparametric machine learning models. In the present paper, we introduce GPPM and illustrate its utility through theoretical arguments as well as simulated and empirical data.

Authors 3

1. Julian David Karch Aachen Methodology and Statistics Institute of Psychology, Leiden University

   Leiden University · Max Planck Institute for Human Development

   Affiliation as printed

   Formal Methods in Lifespan Psychology, Center for Lifespan Psychology, Max Planck Institute for Human Development, Berlin, Germany

   Methodology and Statistics, Institute of Psychology, Leiden University, Leiden, Netherlands

2. Andreas M. Brandmaier corresponding

   University College London · Max Planck Institute for Human Development

   Affiliation as printed

   Formal Methods in Lifespan Psychology, Center for Lifespan Psychology, Max Planck Institute for Human Development, Berlin, Germany

   Max Planck UCL Centre for Computational Psychiatry and Ageing Research, Berlin, Germany

3. Manuel C. Voelkle

   Humboldt-Universität zu Berlin

   Affiliation as printed

   Psychological Research Methods, Department of Psychology, Humboldt University of Berlin, Berlin, Germany