A Data Permutation Method for Testing Random Slopes of Bayesian Growth Curves

Abstract

Growth curve analysis is a popular method for modeling individual development across time. Specifying growth curve models in a Bayesian framework affords researchers the flexibility of including previous information as prior distributions of parameters. However, common choices of prior distribution for modeling slope variance in a Bayesian growth curve framework make determining the existence of meaningful interindividual differences in intraindividual change across time difficult due to boundary values of these priors. Additionally, many current methods are either technically difficult to implement or are sensitive to model specification. We present a simple data permutation method that reliably distinguishes between longitudinal data with individual slope variation and those without slope variation. We show situations in that the proposed data permutation testing outperforms DIC based model comparison through Monte Carlo simulations and apply this data permutation method to data derived from the National Longitudinal Study of Adolescent to Adult Health.