A Comparison of Different Nonnormal Distributions in Growth Mixture Models

The purpose of the present study is to compare nonnormal distributions (i.e., t, skew-normal, skew-t with equal skew and skew-t with unequal skew) in growth mixture models (GMMs) based on diverse conditions of a number of time points, sample sizes, and skewness for intercepts. To carry out this research, two simulation studies were conducted with two different models: an unconditional GMM and a GMM with a continuous distal outcome variable. For the simulation, data were generated under the conditions of a different number of time points (4, 8), sample size (300, 800, 1,500), and skewness for intercept (1.2, 2, 4). Results demonstrate that it is not appropriate to fit nonnormal data to normal, t, or skew-normal distributions other than the skew-t distribution. It was also found that if there is skewness over time, it is necessary to model skewness in the slope as well.