The Impact of Ignoring Time Series Processes in Linear Growth Mixture Modeling

Abstract

Growth mixture modeling (GMM) is a useful statistical method for longitudinal studies because it includes features of both latent growth modeling (LGM) and finite mixture modeling. This Monte Carlo simulation study explored the impact of ignoring 3 types of time series processes (i.e., AR(1), MA(1), and ARMA(1,1)) in GMM and manipulated the separation of the latent classes, the strength of the time series process, and whether the errors conformed to the time series process in 1 or 2 latent classes. The results showed that omitting time series processes resulted in more serious bias in parameter estimation as the distance between classes increased. However, when the class distances were small, ignoring time series processes contributed to the selection of the correct number of classes. When the GMM models correctly specified the time series process, only models with an AR(1) time series process produced unbiased parameter estimates in most conditions. It was also found that among design factors manipulated, the distance between classes prominently affected the identification of the number of classes and parameter estimation.

Keywords:

• class distance
• growth mixture modeling
• model assumptions
• Monte Carlo simulation study
• time series process