Bayesian approach to zero-inflated dynamic panel ordered probit model with an application in drug abuse

Abstract

The Zero inflated ordered categorical data with time series structure are often a characteristic of behavioral research attributed to non-participation decision and zero consumption of substance such as drugs among the participants. The existing Semi-parametric zero inflated dynamic panel probit model with selectivity have exhibited biasness and inconsistency in estimators as a result of poor treatment of initial condition and exclusion of selectivity in the unobserved individual effects respectively. The model assumed that the cut points are known to address heaping in the data and therefore cannot be used when the cut points are unknown. In this paper, a Zero inflated dynamic panel ordered probit model have been developed to address the above challenges. Average partial effects that presents the impacts on the specific probabilities per unit change in the covariates are also given. Since the solutions are not of closed form, Bayesian approach was used to estimate the parameters of the model since it allows sampling from the conditional distributions. Bayesian approach does not need a large sample to ensure the adequacy of asymptotic approximations and incorporate prior information in estimation. A Monte Carlo study was carried out to investigate some theoretical properties of the estimators in the models. The study found that the Zero inflated dynamic panel ordered probit models with independent and correlated error terms produced consistent estimators. The Zero inflated dynamic panel ordered probit models with independent and correlated error terms had more accurate estimators than the Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with independent error terms fitted the National Longitudinal Survey of Youth 1997 better than Zero inflated dynamic panel ordered probit model with correlated error terms and Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with correlated error terms fitted the National Longitudinal Survey of Youth 1997 better than Dynamic panel ordered probit model.