Classical and Bayesian Approaches For the Zero-Inflated Dynamic Categorical Panel Ordered Probit Model
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Date
2023
Authors
Wanjiru, John Kung’u
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
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 substances such as drugs. 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
assumes that the cut points are known to address heaping in the data and therefore
cannot be used when the cut points are unknown. The Simulated maximum likelihood
was applied to evaluate the double integrals in the Semi-parametric zero inflated
dynamic panel probit model. This procedure could be very time-consuming even with
fast modern computer and imprecise even with the use of modern simulator like
Halton simulators. The aim of this research was to develop the Zero inflated dynamic
panel ordered probit models with independent and correlated error terms to address
the above challenges. Interpretation of the coefficients in the proposed models were
extra difficult than in the normal regression scheme because a shift in one of the
variables in the equation is conditioned on other variables and their parameters.
Average partial effects that gave the effects on the particular probabilities per unit
change in the covariates was proposed to address the above challenge. The integrals
were evaluated using Two step Gauss Hermite quadrature that is five times faster than
the Simulated maximum likelihood. Since the solutions are not of closed form,
maximum likelihood estimation based on Newton Raphson algorithm and Bayesian
approach were used to estimate the parameters of the proposed models. Monte Carlo
simulations were conducted to investigate the theoretical properties of the estimators
of the developed models. Using National Longitudinal Survey of Youth (1997) dataset
sponsored by the Bureau of labour Statistics of the U.S. Department of labour with
zero inflation, the study investigated the determinants of smoking tobacco among the
youths. The study found that the proposed models produced consistent estimators and
their estimates were more accurate than the Dynamic panel ordered probit model
estimates. The proposed models fitted the data better than dynamic panel ordered
probit model in both classical and Bayesian approaches in the simulated data. The
study found positive associations between the initial period participation decision and
consumption levels observations and unobserved latent participation decision and
consumption levels. Therefore, this indicated that it is essential to control for
participation decision and consumption levels at the initial period. The models
showed a strong and significant positive state dependence in both participation
decision and at various consumption levels. The unobserved individual effects
accounted for 49.90% of the unexplained variation in decision to participate in
smoking and 47.65% of the unexplained variation at all levels of consumption. The
main causes of persistence in smoking decision were the state dependence,
unobserved heterogeneity and race while the main causes of persistence at
consumption level were state dependence, unobserved heterogeneity, gender and age.
The study is significant to policy analyst in identifying the socioeconomic and
demographic factors associated with drug abuse and providing useful information to
facilitate well-targeted public health policies.
Description
A Thesis Submitted in Fulfillment of the Requirement for the Award of the Degree of Doctor of Philosophy (Statistics) in the School of Pure and Applied Sciences of Kenyatta University January, 2023
Keywords
Classical, Bayesian Approaches, Zero-Inflated, Dynamic, Categorical, Panel, Ordered, Probit, Model