Bayesian Hierarchical Growth Model for Experimental Data on the Effectiveness of an Incentive-Based Weight Reduction Method

Abstract

The objective of this current research is to model the experimental data on the effectiveness of an incentive-based weight reduction method by using Bayesian hierarchical growth models. Three Bayesian hierarchical growth models are proposed, namely parametric Bayesian hierarchical growth model with correlated intercept and slope random effects model, parametric Bayesian hierarchical growth model with no correlated intercept and slope random effects model and semi-parametric Bayesian hierarchical growth model with Dirichlet process mixture prior model. The data is obtained from forty eight (48) students who had participated in an experiment on weight reduction method. The students were divided equally into two groups: single and pair groups. The experiment was carried out over the period of three months with a weight reading session for every two weeks. At the end of the study, we had six repeated measures of each student’s weight in kg and some measures of covariates and factors. Our results showed that the best model for the above data based on the Bayesian fit indexes and the models’ flexibility is the semi-parametric Bayesian hierarchical growth model with Dirichlet process mixture prior model. The results of the semi-parametric model showed that the ‘growth’ or reduction rates of the weight reduction experiment relate to the students’ gender, height in cm, experimental group (single or pair) and time in term of weeks.