Bayesian Growth Curves Using Normal Mixtures With Nonparametric Weights

Bayesian variable selection for latent class models

In this article, we develop a latent class model with class probabilities that depend on subject-specific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection uncertainty. We propose a Bayesian variable selection approach and implement a stochastic search Gibbs sampler for posterior computation to obtain model-averaged estimates of quantities of interest such as marginal inclusion probabilities of predictors. Our methods are illustrated through simulation studies and application to data on weight gain during pregnancy, where it is of interest to identify important predictors of latent weight gain classes.

Power Prior Elicitation in Bayesian Quantile Regression

We address a quantile dependent prior for Bayesian quantile regression. We extend the idea of the power prior distribution in Bayesian quantile regression by employing the likelihood function that is based on a location-scale mixture representation of the asymmetric Laplace distribution. The propriety of the power prior is one of the critical issues in Bayesian analysis. Thus, we discuss the propriety of the power prior in Bayesian quantile regression. The methods are illustrated with both simulation and real data.

Application of finite mixture models for vehicle crash data analysis

Developing sound or reliable statistical models for analyzing motor vehicle crashes is very important in highway safety studies. However, a significant difficulty associated with the model development is related to the fact that crash data often exhibit over-dispersion. Sources of dispersion can be varied and are usually unknown to the transportation analysts. These sources could potentially affect the development of negative binomial (NB) regression models, which are often the model of choice in highway safety. To help in this endeavor, this paper documents an alternative formulation that could be used for capturing heterogeneity in crash count models through the use of finite mixture regression models. The finite mixtures of Poisson or NB regression models are especially useful where count data were drawn from heterogeneous populations. These models can help determine sub-populations or groups in the data among others. To evaluate these models, Poisson and NB mixture models were estimated using data collected in Toronto, Ontario. These models were compared to standard NB regression model estimated using the same data. The results of this study show that the dataset seemed to be generated from two distinct sub-populations, each having different regression coefficients and degrees of over-dispersion. Although over-dispersion in crash data can be dealt with in a variety of ways, the mixture model can help provide the nature of the over-dispersion in the data. It is therefore recommended that transportation safety analysts use this type of model before the traditional NB model, especially when the data are suspected to belong to different groups.