A penalized nonparametric regression approach to fitting generalized additive mixed effects models

Abstract

The frequency with which longitudinal data is collected from individuals continues to increase rapidly within psychology, but many questions remain regarding the best analytical techniques for this rich intensive longitudinal data. One potential approach is to use generalized nonparametric mixed models, which can model correlated data with potentially complex nonlinear mean functions from non-normal response distributions. Current implementations of these techniques, however, have numerous limitations, including slow computation times and limited flexibility. This dissertation proposes an alternative technique for estimating these models by leveraging penalized spline regression to include random effects using the equivalency between smoothing spline and mixed effect regression, but using a cross-validation approach to select the smoothing parameter rather than maximum likelihood. Best practices for implementing the proposed technique, as well as its relative performance to the current standard modeling implementation, are investigated through a series of simulation studies and real data analysis. In general, compared to the current standard approach, we find that the proposed technique has similar recovery of both fixed and random effects in a number of simulated data-generating scenarios, and nearly identical within-sample and out-of-sample predictive accuracy in real data. However, the proposed technique has estimation times up to 70 times faster than the current standard, indicating a potentially huge computational advantage. Numerous recommendations are also made regarding best practices for implementing the proposed technique. Finally, the ability of the proposed technique to investigate complex analytical questions in practice is highlighted by analyzing the impact of the COVID-19 pandemic on young adult mobility patterns in the US using the Colorado Online Twins (CoTwins) Study.