A latent variable mixed‐effects location scale model that also considers between‐person differences in the autocorrelation

Abstract

In public health research an increasing number of studies is conducted in which intensive longitudinal data is collected in an experience sampling or a daily diary design. Typically, the resulting data is analyzed with a mixed‐effects model or mixed‐effects location scale model because they allow one to examine a host of interesting longitudinal research questions. Here, we introduce an extension of the mixed‐effects location scale model in which measurement error of the observed variables is considered by a latent factor model and in which—in addition to the mean‐or location‐related effects—the residual variance of the latent factor and the parameters of the autoregressive process of this latent factor can differ between persons. We show how to estimate the parameters of the model with a maximum likelihood approach, whose performance is also compared with a Bayesian approach in a small simulation study. We illustrate the models using a real data example and end with a discussion in which we suggest questions for future research.