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

## TL;DR

This paper provides a tutorial on using Bayesian methods to compare multiple groups in growth curve models with count data, focusing on juvenile delinquency trajectories.

## Contribution

The paper introduces a Bayesian multiple-group comparison approach for latent growth models with count variables, simplifying moderation analysis.

## Key findings

- Group differences in delinquency trajectories were found based on gender and school type in the unconditional growth model.
- School type moderated the relationship between legal norm acceptance and delinquency trajectories in the conditional model.

## Abstract

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.