Skew T Based Maximum Likelihood Estimation of Latent Growth Curve Models with Non-Normal and Missing Data

Abstract

Latent growth curve models (LGM) are widely used in educational research to analyze longitudinal data. Typical normal-based maximum likelihood estimation (nMLE) assumes that data are normally distributed. Violations to the normality assumption have grave consequences on the accuracy of parameter estimates, which are augmented when missing data are present. Several robust modifications have been proposed to remedy the effects of the violation of the normality assumptions, the most common being robust normal based maximum likelihood (nMLR). However, these methods have serious limitations. Assuming that the data follow skew t distribution within the maximum likelihood framework (stMLE) provides a more parsimonious alternative. Recently, Mplus has implemented a distribution option that makes implementing stMLE more feasible. This study was conducted to evaluate the performance of stMLE in the estimation of LGM through a Monte Carlo simulation. Application of stMLE was also illustrated through estimation of LGM with math achievement test data from the National Longitudinal Survey of Youth. Results confirmed that nMLR can still produce biased parameter estimates when data are non-normally distributed. On the other hand, stMLE resulted in many estimation issues. Although stMLE presents a theoretically appropriate framework to estimate LGM with non-normal data, more research is needed to determine the conditions under which it performs well.