A Comparison of LTA Models with and Without Residual Correlation in Estimating Transition Probabilities

In longitudinal mixture models like latent transition analysis (LTA), identical items are often repeatedly measured across multiple time points to define latent classes and individuals' similar response patterns across multiple time points, which attributes to residual correlations. Therefore, this study hypothesized that an LTA model assuming residual correlations among indicator variables measured repeatedly across multiple time points would provide more accurate estimates of transition probabilities than a traditional LTA model. To test this hypothesis, a Monte Carlo simulation was conducted to generate data both with and without specified residual correlations among the repeatedly measured indicator variables, and the two LTA models-one that accounted for residual correlations and one that did not-were compared. This study included transition probabilities, numbers of indicator variables, sample sizes, and levels of residual correlations as the simulation conditions. The estimation performances were compared based on parameter estimate bias, mean squared error, and coverage. The results demonstrate that LTA with residual correlations outperforms traditional LTA in estimating transition probabilities, and the differences between the two models become prominent when the residual correlation is .3 or higher. This research integrates the characteristics of longitudinal data in an LTA simulation study and suggests an improved version of LTA estimation.