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

Area of Science:

• Statistics
• Psychometrics
• Longitudinal Data Analysis

Background:

• Latent state-trait (LST) models are used for longitudinal data.
• Non-normal outcomes and outliers can complicate LST model analysis.
• Mixture models offer flexibility in capturing unobserved heterogeneity.

Purpose of the Study:

• To assess the statistical performance of a skew t mixture LST model.
• To evaluate the model's ability to identify latent classes with non-normal data.
• To investigate the impact of sample size, occasions, and skewness on model accuracy.

Main Methods:

• Simulation study design.
• Implementation of a skew t mixture latent state-trait (LST) model.
• Variation of sample size, number of occasions, and trait skewness.

Main Results:

• Parameter estimation accuracy improves with larger sample sizes and more occasions.
• Bias is more pronounced for parameters related to the skew t-distribution and latent trait variances.
• Standard error estimation accuracy varies across conditions and parameters.

Conclusions:

• The skew t mixture LST model demonstrates acceptable performance under large sample conditions.
• Results suggest caution when applying the model due to potential parameter bias.
• The skew t approach shows promise for enhancing other mixture models.