Robust Semiparametric Bayesian Methods in Growth Curve Modeling

Despite wide applications of growth curve models, few studies have dealt with a practical issue -- nonnormality of data. Previous studies have typically used Student's t distributions to remedy the nonnormal problems. In this dissertation, three types of robust distributionalgrowth curve models are proposed from a semiparametric Bayesian perspective, in which random coefficients or intraindividual measurement errors follow either normal distributions or unknown random distributionswith Dirichlet process priors. Based on Monte Carlo simulations, we evaluate the performance of the robust models and demonstrate that selecting an appropriate model for practical data analyses is very important, by comparing the three types of robust distributional models as well as the traditional growth curve models with the normalityassumption in analyzing different types of data. In addition, we compare the semiparametric Bayesian methods to the existing robust methods using Student's t distributions and conclude that the semiparametric Bayesian methods are more robust to nonnormal data. An example about the development of mathematical abilities is used to illustrate the application of semiparametric Bayesian growth curve models, using school children's Peabody Individual Achievement Test mathematical test scores from the National Longitudinal Survey of Youth 1997 Cohort.