Bayesian Analysis of a Nonlinear Dynamic Latent Class Structural Equation Model: A Simulation Study

Abstract

In the past several decades, the so-called ambulatory assessment (AA) of in- tensive longitudinal data (ILD) has gained a substantial amount of attention. Recent advancements in data collection technologies such as smart phones and pedometers have catalysed the creation of richer and denser data sets. Such data sets enable the investigation of momentary dynamic processes underlying the data, but at the same time also pose more challenges in choosing appropriate modeling techniques to an- swer increasingly more complex research questions. Traditional modeling techniques such as structural equation models, latent class analysis, and time series analysis can each be applied to understand the dynamic relations from a particular perspective, but not comprehensively. Recently, Kelava and Brandt (2019) proposed a general nonlinear dynamic latent class structural equation model framework which can be used to examine the intraindividual processes of observed or latent variables using the ILD data set. This general framework allows the decomposition of the process data into individual- and time-specific components so that unobserved heterogeneity of intraindividual processes can be modeled via a latent Markov process which can be predicted by individual- and time-specific variables as random effects. Despite the theoretical advancements in modeling ILD data, little is known about the statistical properties of this general framework. The purpose of this study is to fill this gap by running an extensive Monte Carlo simulation study to investigate the simulation outcomes using various evaluation metrics under a series of conditions using representative submodels from the general framework. Recommendations are given according to the simulation results and findings from the simulation study can serve as useful guidance for both applied and methodological researchers alike.