A tutorial on bayesian multiple-group comparisons of latent growth curve models with count distributed variables.

Moderation effects in longitudinal structural equation models are often analysed using latent variable product terms, which can be complex and difficult to estimate, especially in large models with many panel waves. An alternative approach for categorical moderation variables is the simpler technique of multiple-group comparisons. This method allows for straightforward model specification and precise differentiation of effects in complex models. This tutorial demonstrates multiple-group comparisons using examples based on developmental trajectories of juvenile delinquency. These trajectories are modelled via a latent growth curve approach, treating the variables as count data and applying Bayesian estimation using the software Mplus. The results are processed using the R programming language. This method addresses challenges associated with maximum likelihood estimation, particularly for latent growth models with count variables and additional exogenous latent variables. The analysis examines group differences by gender and school type in the trajectories of an unconditional growth model. It also examines the effect of legal norm acceptance on these trajectories using a conditional growth model. The moderating effects of gender and school type on these effects are analysed separately. The results reveal group differences of gender and school type for the unconditional growth model, while the conditional growth model highlights a moderating effect of school type on the relationship between legal norm acceptance and growth trajectories.