A Nonparametric Bayesian Approach for Longitudinal Nonnormal and Missing Data in Growth Curve Models

Growth curve models (GCMs) are widely used to analyze longitudinal
data. This study highlights two aspects of novelties to GCMs. The first novelty
solves a practical issue. The study proposes a nonparametric Bayesian
selection GCM to simultaneously handle missing and nonnormal data in longitudinal
studies. Bayesian methods are used for the estimation. Multiple imputation and selection model approaches are used to handle the ignorable
and non-ignorable missing data, respectively. The second novelty advances
methodological theory. The proposed modeling framework is an infinite mixture
modeling. The study develops new Bayesian model selection criteria
to evaluate infinite mixture models in a Bayesian context and compares the
performance of new criteria with existing criteria in Bayesian infinite mixture
modeling. A Monte Carlo simulation study is conducted to assess the performance
of the proposed modeling approach and the corresponding model
selection criteria. Simulation results show that the nonparametric Bayesian
GCMs perform better than the traditional normal-distribution-based GCM
in analyzing the nonnormal and ignorable missing data. The BNP selection
GCM in general outperforms the other two GCMs when data are nonnormal
and non-ignorable missing. The new Bayesian model selection criteria have
the potential to select the Bayesian infinite mixture models. A real data example
using the NLSY97 survey data is provided to illustrate the application
of the proposed method and model selection criteria.