title: Modeling error distributions of growth curve models through Bayesian methods.
abstract: Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is proposed to flexibly model normal and non-normal data through the explicit specification of the error distributions. A simulation study shows when the distribution of the error is correctly specified, one can avoid the loss in the efficiency of standard error estimates. A real example on the analysis of mathematical ability growth data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 is used to show the application of the proposed methods. Instructions and code on how to conduct growth curve analysis with both normal and non-normal error distributions using the the MCMC procedure of SAS are provided.
authors.affiliation: Department of Psychology, University of Notre Dame, 118 Haggar Hall, Notre Dame, IN, 46556, USA. ZhiyongZhang@nd.edu.
authors.forename: Zhiyong
authors.initials: Z
authors.lastname: Zhang
mesh_terms: D001499:Bayes Theorem; D002657:Child Development; D002675:Child, Preschool; D003198:Computer Simulation; D006801:Humans; D008137:Longitudinal Studies; D015233:Models, Statistical
keywords: Bayesian estimation; Exponential power distribution; Growth curve models; Non-normal data; SAS PROC MCMC; Skew normal distribution; t-distribution