Bayesian Approach to Zero-Inflated Bivariate Ordered Probit Regression Model, with an Application to Tobacco Use

Table 4

Posterior mean, standard deviation, and 95% credible intervals of parameters from zibop for smoking and chewing tobacco.

Variable	Mean	St. dev.	2.50%	Median	97.50%
Main (β 1,α 1): smoking (𝑦1):
Age/10	0.672	0.119	0.444	0.685
Age square/100	−0.070	0.012	−0.093	−0.071
Education	−0.071	0.014	−0.097	−0.071
Education square	0.001	0.001	−0.002	0.001
Income	0.000	0.002	−0.005	0.000
Male	2.092	0.086	1.925	2.091
Married	0.213	0.070	0.074	0.213
Muslim	−0.053	0.052	−0.157	−0.053
Region	−0.007	0.048	−0.102	−0.007
Urban	−0.096	0.051	−0.198	−0.097
Agriservice	−0.234	0.056	−0.345	−0.233
Self-employed	−0.246	0.087	−0.414	−0.247
student	−0.476	0.137	−0.742	−0.478
α 12	0.284	0.017	0.252	0.283
α 13	0.987	0.030	0.928	0.987
Main (β 2,α 2): chewing (𝑦2)
Age/10	0.649	0.133	0.382	0.658
Age square/100	−0.046	0.013	−0.071	−0.046
Education	−0.020	0.016	−0.052	−0.020
Education square	−0.002	0.001	−0.005	−0.002
Income	0.001	0.003	−0.004	0.002
Male	−0.479	0.081	−0.641	−0.479
Married	−0.025	0.075	−0.171	−0.025
Muslim	−0.072	0.056	−0.181	−0.072
Region	0.417	0.051	0.317	0.418
Urban	−0.080	0.058	−0.194	−0.079
Agriservice	0.052	0.074	−0.096	0.052
Self-employed	0.127	0.092	−0.058	0.126
Student	−0.450	0.221	−0.887	−0.448
α 22	0.484	0.023	0.439	0.484
Inflation (γ):
Age/10	−0.012	2.044	−4.755	0.253
Age square/100	0.509	0.552	−0.197	0.398
Education	−0.218	0.115	−0.476	−0.204
Education square	0.028	0.011	0.010	0.026
Income	0.006	0.022	−0.027	0.003
Male	0.239	0.827	−1.582	0.417
Married	2.306	4.478	−0.416	0.500
Muslim	−0.528	0.356	−1.331	−0.494
Mother	−0.170	0.267	−0.716	−0.164
Father	−0.119	0.330	−0.664	−0.160
Region	0.630	0.291	0.061	0.625
Urban	0.040	0.357	−0.737	0.071
Agrservice	5.312	5.416	1.017	2.674
Self-employed	3.783	5.025	0.124	1.275
Sstudent	−0.344	0.411	−1.154	−0.339
ρ 12	−0.185	0.033	−0.249	−0.186
Select probabilities:
𝑃 (𝑦1=0)	0.760	0.004	0.752	0.760
𝑃 (𝑦2=0)	0.871	0.004	0.864	0.871
𝑃 (𝑦1=0, 𝑦2=0)	0.662	0.005	0.652	0.662
𝑃 (zero-inflation)	0.242	0.048	0.151	0.243

Results for the constant terms in the main and inflation parts have been suppressed for brevity.