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.
Highlights
Longitudinal data are crucial for addressing various psychological research questions, including questions related to child development, aging, and intervention research
This is the case considering the statistical learning as well as the explanatory perspective. We demonstrate this by showing that the random intercept model leads to more accurate predictions as well as a higher model probability of the model compared to the continuous-time random intercept autoregressive model of order 1, which was previously used to analyze the example data set
We have introduced Gaussian process panel modeling (GPPM), an extension of Gaussian process regression (GPR) for the analysis of panel data
Summary
Longitudinal data are crucial for addressing various psychological research questions, including questions related to child development, aging, and intervention research. While Hall et al (2008) did not discuss how to extend GPR for N > 1, they used Gaussian processes as a mathematical tool to implement a functional analysis method for panel data Given this entirely different focus, their method is very different from GPPM, as introduced in this paper. An important consequence of the latter point are novel models for the analysis of panel data; in particular, the hierarchical version of models typically used in machine learning, as well as hybrid models that consist of a combination of a parametric (theory-based) model and a nonparametric statistical learning (data-driven) model We demonstrate that these models provide advantages from a predictive (they can outperform existing models in terms of predictive accuracy) as well as explanatory (they can have a higher Bayesian posterior model probability than existing models) perspective.
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