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Table 4 Summary statistic of the posterior distribution of the model parameters

From: Bayesian negative binomial logit hurdle and zero-inflated model for characterizing smoking intensity

Para Bayesian negative binomial-logit hurdle (BNBLH)
Count model coefficients Para Zero hurdle model coefficients
Mean SD HPD of 95% CrI OR   Mean SD HPD of 95% CrI OR
\(\varnothing \) 0.029 0.016 (0.003, 0.065) 1.029      
\({\upbeta }_{0}\) 0.869 0.163 (0.558, 1.189) 2.385 \({\upgamma }_{0}\) −  3.299 0.298 (− 3.902, − 2.753) 0.037
\({\upbeta }_{1}\) 0.026 0.085 (− 0.139, 0.193) 1.026 \({\upgamma }_{1}\) 1.022 0.156 (0.721, 1.334) 2.779
\({\upbeta }_{2}\) 0.090 0.087 (− 0.078, 0.257) 1.094 \({\upgamma }_{2}\) 1.434 0.164 (1.123, 1.766) 4.195
\({\upbeta }_{3}\) − 0.161 0.073 (− 0.304, − 0.021) 0.851 \({\upgamma }_{3}\) − 0.709 0.141 (− 0.992, − 0.433) 0.492
\({\upbeta }_{4}\) − 0.035 0.050 (− 0.133, 0.064) 0.966 \({\upgamma }_{4}\) 0.369 0.102 (0.174, 0.573) 1.446
\({\upbeta }_{5}\) 0.133 0.089 (− 0.041, 0.305) 1.142 \({\upgamma }_{5}\) − 0.518 0.149 (− 0.812, − 0.223) 0.596
\({\upbeta }_{6}\) 0.223 0.078 (0.075, 0.376) 1.25 \({\upgamma }_{6}\) − 0.099 0.138 (− 0.366, 0.179) 0.906
\({\upbeta }_{7}\) 0.056 0.067 (− 0.077, 0.188) 1.058 \({\upgamma }_{7}\) − 0.250 0.134 (− 0.515, 0.007) 0.779
\({\upbeta }_{8}\) − 0.068 0.070 (− 0.206, 0.064) 0.934 \({\upgamma }_{8}\) − 0.313 0.131 (− 0.569, − 0.057) 0.731
\({\upbeta }_{9}\) − 0.080 0.069 (− 0.217, 0.054) 0.923 \({\upgamma }_{9}\) − 0.887 0.137 (− 1.162, − 0.624) 0.412
\({\upbeta }_{10}\) 0.027 0.094 (− 0.156, 0.209) 1.027 \({\upgamma }_{10}\) − 0.371 0.181 (− 0.731, − 0.018) 0.69
\({\upbeta }_{11}\) 0.105 0.082 (− 0.050, 0.271) 1.111 \({\upgamma }_{11}\) − 0.249 0.151 (− 0.547,0.045) 0.780
\({\upbeta }_{12}\) 0.221 0.065 (0.096, 0.349) 1.247 \({\upgamma }_{12}\) 2.121 0.112 (1.908,2.345) 8.339
\({\upbeta }_{13}\) 0.149 0.065 (0.025, 0.279) 1.161 \({\upgamma }_{13}\) − 0.383 0.128 (− 0.629, − 0.120) 0.682
\({\upbeta }_{14}\) 0.005 0.047 (− 0.088, 0.098) 1.005 \({\upgamma }_{14}\) − 0.227 0.095 (− 0.410, − 0.041) 0.797
Para Bayesian zero-inflated negative binomial (BZINB)
Posterior count model coefficients Para Posterior zero-inflation model coefficients
Mean SD HPD of 95% CrI OR Mean SD HPD of 95% CrI OR
\(\varnothing \) 0.029 0.016 (0.003, 0.065) 1.029 \({\upgamma }_{0}\) 3.210 0.302 (2.570, 3.799) 24.78
\({\upbeta }_{0}\) 0.901 0.163 (0.588, 1.215) 2.462 \({\upgamma }_{1}\) − 1.021 0.156 (− 1.339, − 0.725) 0.360
\({\upbeta }_{1}\) 0.019 0.087 (− 0.154, 0.185) 1.019 \({\upgamma }_{2}\) − 1.426 0.165 (− 1.767, − 1.110) 0.240
\({\upbeta }_{2}\) 0.083 0.088 (− 0.092, 0.251) 1.087 \({\upgamma }_{3}\) 0.697 0.136 (0.431, 0.965) 2.008
\({\upbeta }_{3}\) − 0.170 0.075 (− 0.321, − 0.029) 0.844 \({\upgamma }_{4}\) − 0.378 0.103 (− 0.577, − 0.173) 0.685
\({\upbeta }_{4}\) − 0.036 0.051 (− 0.135, 0.066) 0.965 \({\upgamma }_{5}\) 0.529 0.152 (0.238, 0.828) 1.697
\({\upbeta }_{5}\) 0.122 0.092 (− 0.053, 0.306) 1.13 \({\upgamma }_{6}\) 0.121 0.143 (− 0.148, 0.408) 1.129
\({\upbeta }_{6}\) 0.213 0.082 (0.059, 0.376) 1.237 \({\upgamma }_{7}\) 0.254 0.132 (− 0.007, 0.514) 1.289
\({\upbeta }_{7}\) 0.053 0.068 (− 0.080, 0.186) 1.054 \({\upgamma }_{8}\) 0.306 0.130 (0.053, 0.563) 1.358
\({\upbeta }_{8}\) − 0.075 0.069 (− 0.212, 0.059) 0.928 \({\upgamma }_{9}\) 0.889 0.133 (0.625, 1.152) 2.433
\({\upbeta }_{9}\) − 0.088 0.072 (− 0.233, 0.052) 0.916 \({\upgamma }_{10}\) 0.360 0.191 (− 0.003, 0.748) 1.433
\({\upbeta }_{10}\) 0.011 0.096 (− 0.175, 0.200) 1.011 \({\upgamma }_{11}\) 0.251 0.156 (− 0.050, 0.560) 1.285
\({\upbeta }_{11}\) 0.098 0.082 (− 0.063, 0.261) 1.103 \({\upgamma }_{12}\) − 2.096 0.113 (− 2.315, − 1.875) 0.123
\({\upbeta }_{12}\) 0.221 0.065 (0.098, 0.353) 1.247 \({\upgamma }_{13}\) 0.406 0.127 (0.151, 0.651) 1.501
\({\upbeta }_{13}\) 0.152 0.071 (0.016, 0.293) 1.164 \({\upgamma }_{14}\) 0.231 0.094 (0.050, 0.413) 1.26
\({\upbeta }_{14}\) 0.004 0.047 (-0.088, 0.098) 1.004      
  1. Intercept(\({\beta }_{0}\)); age: 25–34 (\({\beta }_{1} \& {\gamma }_{1}\)), =  > 35 (\({\beta }_{2} \& {\gamma }_{2}\)); Rural (\({\beta }_{3} \& {\gamma }_{3}\)); education level(\({\beta }_{4} \& {\gamma }_{4}\)); Religion: Orthodox(\({\beta }_{5} \& {\gamma }_{5}\)), Muslim \({(\beta }_{6} \& {\gamma }_{6})\); Internet \({(\beta }_{7} \& {\gamma }_{7})\); wealth index: Middle(\({\beta }_{8}\&{\gamma }_{8}\)), Rich (\({\beta }_{9}\&{\gamma }_{9}\)); marital status: single(\({\beta }_{10}\&{\gamma }_{10}\)), married(\({\beta }_{11}\&{\gamma }_{11}\)); chewed chat(\({\beta }_{12}\&{\gamma }_{12}\));Occupation(\({\beta }_{13}\&{\gamma }_{13}\)) and media (\({\beta }_{14}\&{\gamma }_{14}\)),\(\varnothing \) is dispersion parameter