| Latent growth curves are an effective tool for describing the change or growth of an attribute over time. Interactive effects between two latent variables on the rate of change of a latent outcome of interest are of great interest to researchers. Several models have been utilized to conceptualize the interaction in latent growth curves, but as yet there has been a limited amount of empirical research to assess each of these models. The current study used a Monte Carlo simulation approach to investigate three latent growth interaction models -- those by Wen (Wen et al., 2000), Duncan (Duncan et al., 1999), and a longitudinal extension of the model by Schumacker (2002), under varying conditions, with 5000 replications per condition. The factors of missing data mechanism (Complete, Missing Completely At Random, Missing Not At Random), correlation between latent intercept and slope factors (small, medium, large), sample size (250,500, 1000), and the reliability of the observed variables (very low, low, average, high) were manipulated to determine their effects on overall model performance and model fit, bias of the estimates for the latent slope interaction effect, and rates of Type I error. Of the three models assessed, the Wen model showed the most reliable performance with respect to overall model fit, and the Duncan and Schumacker models showed the most reliable performance with respect to parameter estimation, and bias. The Schumacker model showed adequate Type I error control when the data was either Complete or Missing Completely at Random. When the missing data mechanism was Missing Not at Random none of the models performed well, however the Schumacker model showed the most promising behaviour with respect to bias and Type I error control. Recommendations for researchers utilizing these models are made, as well as considerations for their use. |
