Bayesian latent structure modeling of walking behavior in a physical activity intervention

Abstract

The analysis of walking behavior in a physical activity intervention is considered. A Bayesian latent structure modeling approach is proposed whereby the ability and willingness of participants is modeled via latent effects. The dropout process is jointly modeled via a linked survival model. Computational issues are addressed via posterior sampling and a simulated evaluation of the longitudinal model's ability to recover latent structure and predictor effects is considered. We evaluate the effect of a variety of socio-psychological and spatial neighborhood predictors on the propensity to walk and the estimation of latent ability and willingness in the full study.

Keywords: Bayesian; Latent structure; intervention; joint model; longitudinal data; physical activity.

Figure 1

Latent variable paradigm to illustrate a participant’s probability of walking based on their willingness and ability.

Figure 2

Percentages and counts of missingness per variable using in the PATH participant data. given that there is a set of walks from which a person chooses then if we denote the walk date as t_j, j = 1, …, M then we can denote y_ij as a binary indicator for the ith individual at the jth walk time (t_j). We can assume that at this data level we have

Figure 3

Comparison of the variance and bias associated with the primary and secondary simulation cases for model three.