Journal of Probability and Statistics

Research Article

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

Table 7

Posterior mean, standard deviation, and 95% credible intervals of marginal effects of covariates on probability of smoking and chewing tobacco (BOP model).
VariableProbabilityMeanSt. dev.2.50%Median97.50%
AgeAll zeros, 𝑦 1 = 0 0.0368 0.0038 0.0288 0.0369 0.0438
𝑦 1 = 1 −0.0004 0.0003 −0.0009 −0.0004 0.0002
𝑦 1 = 2 −0.0073 0.0010 −0.0093 −0.0073 −0.0054
𝑦 1 = 3 −0.0292 0.0029 −0.0345 −0.0292 −0.0230
All zeros, 𝑦 2 = 0 0.0213 0.0043 0.0125 0.0215 0.0298
𝑦 2 = 1 −0.0056 0.0013 −0.0082 −0.0057 −0.0031
𝑦 2 = 2 −0.0030 0.0008 −0.0047 −0.0030 −0.0014
EducationAll zeros, 𝑦 1 = 0 −0.0342 0.0236 −0.0803 −0.0340 0.0126
𝑦 1 = 1 0.0038 0.0025 −0.0011 0.0039 0.0086
𝑦 1 = 2 0.0130 0.0084 −0.0039 0.0129 0.0293
𝑦 1 = 3 0.0174 0.0128 −0.0076 0.0172 0.0428
All zeros, 𝑦 2 = 0 0.0322 0.0156 0.0002 0.0326 0.0616
𝑦 2 = 1 −0.0150 0.0077 −0.0296 −0.0151 0.0009
𝑦 2 = 2 −0.0201 0.0113 −0.0418 −0.0203 0.0024
IncomeAll zeros, 𝑦 1 = 0 −0.0001 0.0004 −0.0009 −0.0001 0.0007
𝑦 1 = 1 0.0000 0.0000 −0.0001 0.0000 0.0001
𝑦 1 = 2 0.0000 0.0001 −0.0002 0.0000 0.0002
𝑦 1 = 3 0.0000 0.0002 −0.0004 0.0000 0.0005
All zeros, 𝑦 2 = 0 −0.0003 0.0005 −0.0012 −0.0003 0.0007
𝑦 2 = 1 0.0001 0.0002 −0.0002 0.0001 0.0004
𝑦 2 = 2 0.0001 0.0002 −0.0002 0.0001 0.0004
MaleAll zeros, 𝑦 1 = 0 −0.3824 0.0121 −0.4064 −0.3826 −0.3586
𝑦 1 = 1 0.0641 0.0040 0.0567 0.0640 0.0722
𝑦 1 = 2 0.1540 0.0065 0.1416 0.1540 0.1667
𝑦 1 = 3 0.1643 0.0083 0.1487 0.1641 0.1807
All zeros, 𝑦 2 = 0 0.0721 0.0123 0.0481 0.0721 0.0962
𝑦 2 = 1 0.0500 0.0032 0.0438 0.0500 0.0565
𝑦 2 = 2 −0.1222 0.0108 −0.1430 −0.1220 −0.1014
MarriedAll zeros, 𝑦 1 = 0 −0.0416 0.0124 −0.0666 −0.0415 −0.0174
𝑦 1 = 1 0.0039 0.0013 0.0015 0.0038 0.0067
𝑦 1 = 2 0.0131 0.0042 0.0053 0.0130 0.0218
𝑦 1 = 3 0.0246 0.0070 0.0106 0.0247 0.0385
All zeros, 𝑦 2 = 0 0.0018 0.0118 −0.0207 0.0018 0.0254
𝑦 2 = 1 0.0622 0.0031 0.0563 0.0622 0.0685
𝑦 2 = 2 −0.0640 0.0114 −0.0873 −0.0640 −0.0420
MuslimAll zeros, 𝑦 1 = 0 0.0154 0.0092 −0.0029 0.0154 0.0331
𝑦 1 = 1 −0.0013 0.0008 −0.0028 −0.0013 0.0002
𝑦 1 = 2 −0.0044 0.0026 −0.0093 −0.0044 0.0008
𝑦 1 = 3 −0.0097 0.0058 −0.0211 −0.0097 0.0018
All zeros, 𝑦 2 = 0 0.0126 0.0093 −0.0051 0.0125 0.0313
𝑦 2 = 1 0.0613 0.0031 0.0555 0.0613 0.0675
𝑦 2 = 2 −0.0739 0.0091 −0.0922 −0.0739 −0.0562
Father useAll zeros, 𝑦 1 = 0 0.7604 0.0042 0.7521 0.7604 0.7684
𝑦 1 = 1 0.0477 0.0027 0.0426 0.0477 0.0531
𝑦 1 = 2 0.0982 0.0035 0.0915 0.0982 0.1051
𝑦 1 = 3 0.0937 0.0032 0.0874 0.0936 0.1000
All zeros, 𝑦 2 = 0 0.8713 0.0039 0.8635 0.8713 0.8789
𝑦 2 = 1 0.0623 0.0030 0.0566 0.0623 0.0684
𝑦 2 = 2 0.0664 0.0030 0.0607 0.0664 0.0724
Mother useAll zeros, 𝑦 1 = 0 0.7604 0.0042 0.7521 0.7604 0.7684
𝑦 1 = 1 0.0477 0.0027 0.0426 0.0477 0.0531
𝑦 1 = 2 0.0982 0.0035 0.0915 0.0982 0.1051
𝑦 1 = 3 0.0937 0.0032 0.0874 0.0936 0.1000
All zeros, 𝑦 2 = 0 0.8713 0.0039 0.8635 0.8713 0.8789
𝑦 2 = 1 0.0623 0.0030 0.0566 0.0623 0.0684
𝑦 2 = 2 0.0664 0.0030 0.0607 0.0664 0.0724
RegionAll zeros, 𝑦 1 = 0 −0.0075 0.0079 −0.0229 −0.0075 0.0080
𝑦 1 = 1 0.0006 0.0007 −0.0007 0.0006 0.0020
𝑦 1 = 2 0.0022 0.0023 −0.0023 0.0022 0.0067
𝑦 1 = 3 0.0047 0.0049 −0.0050 0.0047 0.0144
All zeros, 𝑦 2 = 0 −0.0691 0.0078 −0.0846 −0.0691 −0.0539
𝑦 2 = 1 0.0756 0.0038 0.0684 0.0755 0.0832
𝑦 2 = 2 −0.0065 0.0070 −0.0200 −0.0065 0.0072
UrbanAll zeros, 𝑦 1 = 0 0.0167 0.0087 −0.0003 0.0167 0.0339
𝑦 1 = 1 −0.0014 0.0008 −0.0030 −0.0014 0.0000
𝑦 1 = 2 −0.0049 0.0026 −0.0100 −0.0049 0.0001
𝑦 1 = 3 −0.0104 0.0054 −0.0210 −0.0104 0.0002
All zeros, 𝑦 2 = 0 0.0130 0.0088 −0.0041 0.0129 0.0303
𝑦 2 = 1 0.0592 0.0036 0.0524 0.0591 0.0664
𝑦 2 = 2 −0.0721 0.0074 −0.0866 −0.0721 −0.0576
AgriserviceAll zeros, 𝑦 1 = 0 0.0218 0.0088 0.0043 0.0219 0.0390
𝑦 1 = 1 −0.0018 0.0007 −0.0032 −0.0018 −0.0004
𝑦 1 = 2 −0.0062 0.0025 −0.0110 −0.0062 −0.0013
𝑦 1 = 3 −0.0138 0.0057 −0.0250 −0.0139 −0.0027
All zeros, 𝑦 2 = 0 −0.0127 0.0119 −0.0366 −0.0127 0.0106
𝑦 2 = 1 0.0656 0.0043 0.0572 0.0655 0.0742
𝑦 2 = 2 −0.0528 0.0094 −0.0711 −0.0529 −0.0338
Self employedAll zeros, 𝑦 1 = 0 0.0277 0.0162 −0.0039 0.0277 0.0592
𝑦 1 = 1 −0.0028 0.0018 −0.0065 −0.0027 0.0003
𝑦 1 = 2 −0.0087 0.0053 −0.0194 −0.0086 0.0012
𝑦 1 = 3 −0.0163 0.0093 −0.0335 −0.0165 0.0025
All zeros, 𝑦 2 = 0 −0.0290 0.0144 −0.0578 −0.0286 −0.0017
𝑦 2 = 1 0.0686 0.0046 0.0600 0.0685 0.0779
𝑦 2 = 2 −0.0396 0.0116 −0.0617 −0.0398 −0.0162
StudentAll zeros, 𝑦 1 = 0 0.1287 0.0155 0.0980 0.1286 0.1588
𝑦 1 = 1 −0.0173 0.0030 −0.0235 −0.0171 −0.0118
𝑦 1 = 2 −0.0475 0.0069 −0.0614 −0.0475 −0.0343
𝑦 1 = 3 −0.0639 0.0063 −0.0758 −0.0640 −0.0510
All zeros, 𝑦 2 = 0 0.0855 0.0151 0.0531 0.0866 0.1117
𝑦 2 = 1 0.0278 0.0071 0.0154 0.0274 0.0428
𝑦 2 = 2 −0.1133 0.0088 −0.1288 −0.1140 −0.0944