Comparison of general multivariate and random-effects models for growth curve analysis: incomplete-data smallsample situations

Abstract

This study investigates the application of general multivariate and the random-effects models under incomplete-data small-sample growth curve situations. The primary interest is testing hypotheses of parallelism and identity of linear growth curves for subjects in two groups. The null distributions of Wald statistics for the random-effects model are examined for appropriateness of asymptotic chi-square and recommendations are made for controlling type I error rates. Monte Carlo techniques are used to find an approximation of the null distribution. Simulations used each combination of one of three covariance structures, one of three missing data patterns (1/5, 1/3, and 2/5 proportion missing), one of two hypotheses (parallelism and identity), and one of four nominal significance levels (.05, .025,.01, and .005). This leads to a recommendation of an approximation of the null distribution for the random-effects procedure. Monte Carlo techniques are also used to compare the power performance of the procedure with the Generalized Growth Curve Multivariate (GGCM) model. Powers of the two procedures are compared over 48 cases which are combinations of covariance structures, missing data patterns, hypotheses, significance levels, and average deviation in means between two groups. The random-effects procedure has a slightly better power performance than the GGCM procedure, especially when using low significance levels when a larger proportion of data are missing.