Skew t Mixture Latent State-Trait Analysis: A Monte Carlo Simulation Study on Statistical Performance

Abstract

This simulation study assessed the statistical performance of a skew t mixture latent state-trait (LST) model for the analysis of longitudinal data. The model aims to identify interpretable latent classes with class-specific LST model parameters. A skew t-distribution within classes is allowed to account for non-normal outcomes. This flexible function covers heavy tails and may reduce the risk of identifying spurious classes, e.g., in case of outliers. Sample size, number of occasions and skewness of the trait variable were varied. Generally, parameter estimation accuracy increases with increasing numbers of observations and occasions. Larger bias compared to other parameters occurs for parameters referring to the skew t-distribution and variances of the latent trait variables. Standard error estimation accuracy shows diffuse patterns across conditions and parameters. Overall model performance is acceptable for large conditions, even though none of the models is free from bias. The application of the skew t mixture model in case of large numbers of occasions and observations may be possible, but results should be treated with caution. Moreover, the skew t approach may be useful for other mixture models.