| Characteristic | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| OR (95% CI)1 | p-value | OR (95% CI)1 | p-value | OR (95% CI)1 | p-value | OR (95% CI)1 | p-value | OR (95% CI)1 | p-value | |
| ngender | 0.083 | 0.13 | 0.046 | 0.14 | 0.015 | |||||
| 0 | — | — | — | — | — | |||||
| 1 | 1.23 (0.97, 1.57) | 1.21 (0.95, 1.55) | 1.29 (1.00, 1.67) | 1.22 (0.93, 1.59) | 1.41 (1.07, 1.85) | |||||
| nmarital | >0.9 | 0.7 | 0.3 | 0.092 | 0.2 | |||||
| 0 | — | — | — | — | — | |||||
| 1 | 1.02 (0.79, 1.31) | 0.94 (0.73, 1.23) | 0.86 (0.65, 1.12) | 0.78 (0.59, 1.04) | 0.82 (0.61, 1.10) | |||||
| religiosity | 1.48 (1.31, 1.68) | <0.001 | 1.45 (1.28, 1.65) | <0.001 | 1.09 (0.95, 1.25) | 0.2 | 1.04 (0.90, 1.20) | 0.6 | 1.08 (0.94, 1.26) | 0.3 |
| nrace | >0.9 | 0.13 | 0.13 | 0.7 | 0.4 | |||||
| 0 | — | — | — | — | — | |||||
| 1 | 1.01 (0.78, 1.33) | 0.81 (0.61, 1.07) | 0.80 (0.60, 1.06) | 1.06 (0.79, 1.43) | 0.87 (0.64, 1.19) | |||||
| nage | 0.73 (0.64, 0.84) | <0.001 | 0.77 (0.66, 0.89) | <0.001 | 0.72 (0.62, 0.84) | <0.001 | 0.77 (0.65, 0.90) | 0.001 | 0.70 (0.59, 0.83) | <0.001 |
| nincome | 0.91 (0.86, 0.97) | 0.002 | 0.92 (0.86, 0.98) | 0.006 | 0.95 (0.89, 1.02) | 0.14 | 0.97 (0.91, 1.04) | 0.3 | 0.94 (0.88, 1.01) | 0.093 |
| nemploy | <0.001 | <0.001 | 0.003 | 0.016 | 0.041 | |||||
| 0 | — | — | — | — | — | |||||
| 1 | 1.82 (1.39, 2.39) | 1.70 (1.29, 2.25) | 1.53 (1.15, 2.04) | 1.44 (1.07, 1.93) | 1.37 (1.01, 1.86) | |||||
| neduc | 0.53 (0.46, 0.61) | <0.001 | 0.57 (0.49, 0.66) | <0.001 | 0.66 (0.57, 0.77) | <0.001 | 0.71 (0.61, 0.83) | <0.001 | 0.67 (0.57, 0.79) | <0.001 |
| onlinesocialnews | 0.99 (0.95, 1.04) | 0.7 | 0.97 (0.93, 1.02) | 0.2 | 0.96 (0.92, 1.01) | 0.14 | 1.00 (0.95, 1.05) | >0.9 | ||
| natnewspaper | 0.79 (0.73, 0.86) | <0.001 | 0.88 (0.81, 0.96) | 0.003 | 0.91 (0.83, 1.00) | 0.047 | 0.93 (0.84, 1.02) | 0.11 | ||
| nattvnews | 0.86 (0.79, 0.95) | 0.002 | 0.93 (0.85, 1.02) | 0.14 | 0.94 (0.85, 1.04) | 0.2 | 0.99 (0.89, 1.10) | 0.9 | ||
| locnewspaper | 1.06 (0.98, 1.15) | 0.13 | 1.06 (0.98, 1.15) | 0.2 | 1.06 (0.98, 1.16) | 0.15 | 1.07 (0.98, 1.17) | 0.11 | ||
| loctvnews | 0.96 (0.87, 1.06) | 0.4 | 0.94 (0.86, 1.04) | 0.3 | 0.94 (0.85, 1.04) | 0.3 | 0.98 (0.88, 1.09) | 0.7 | ||
| chipcovid | 2.44 (2.04, 2.93) | <0.001 | 1.62 (1.34, 1.98) | <0.001 | 1.51 (1.24, 1.85) | <0.001 | ||||
| politview | 1.42 (1.29, 1.56) | <0.001 | 1.38 (1.25, 1.53) | <0.001 | 1.25 (1.13, 1.39) | <0.001 | ||||
| safetyvac | 2.29 (1.91, 2.75) | <0.001 | 2.52 (2.09, 3.05) | <0.001 | ||||||
| sideeffect | 1.72 (1.41, 2.10) | <0.001 | 1.77 (1.44, 2.19) | <0.001 | ||||||
| effectivevac | 0.41 (0.32, 0.53) | <0.001 | 0.57 (0.43, 0.76) | <0.001 | ||||||
| worrycovid | 0.97 (0.94, 0.99) | <0.001 | ||||||||
| fearlovedcovid | 0.57 (0.49, 0.66) | <0.001 | ||||||||
| familyhealth | 0.88 (0.69, 1.12) | 0.3 | ||||||||
| communhealth | 0.62 (0.49, 0.77) | <0.001 | ||||||||
| 1 OR = Odds Ratio | ||||||||||
Model Overview
Ordinal Logistic Model
We are modeling \(\frac{P(Y \leq j)}{P(Y > j)} \equiv \operatorname{logit}(P(Y \leq j)); \quad j \in (1,2,3)\). The outcome is on a Likert-like scale and represents the answer to “When a safe and effective coronavirus (COVID-19) vaccine becomes available, I will get it as soon as possible (1=Strongly Disagree, 4=Strongly Agree).”
Hierarchical setup
Single-stage setup
| Characteristic | OR (95% CI)1 | p-value |
|---|---|---|
| worrycovid | 0.97 (0.94, 0.99) | <0.001 |
| fearlovedcovid | 0.57 (0.49, 0.66) | <0.001 |
| familyhealth | 0.88 (0.69, 1.12) | 0.3 |
| communhealth | 0.62 (0.49, 0.77) | <0.001 |
| safetyvac | 2.52 (2.09, 3.05) | <0.001 |
| sideeffect | 1.77 (1.44, 2.19) | <0.001 |
| effectivevac | 0.57 (0.43, 0.76) | <0.001 |
| chipcovid | 1.51 (1.24, 1.85) | <0.001 |
| politview | 1.25 (1.13, 1.39) | <0.001 |
| onlinesocialnews | 1.00 (0.95, 1.05) | >0.9 |
| natnewspaper | 0.93 (0.84, 1.02) | 0.11 |
| nattvnews | 0.99 (0.89, 1.10) | 0.9 |
| locnewspaper | 1.07 (0.98, 1.17) | 0.11 |
| loctvnews | 0.98 (0.88, 1.09) | 0.7 |
| ngender | 0.015 | |
| 0 | — | |
| 1 | 1.41 (1.07, 1.85) | |
| nmarital | 0.2 | |
| 0 | — | |
| 1 | 0.82 (0.61, 1.10) | |
| religiosity | 1.08 (0.94, 1.26) | 0.3 |
| nrace | 0.4 | |
| 0 | — | |
| 1 | 0.87 (0.64, 1.19) | |
| nage | 0.70 (0.59, 0.83) | <0.001 |
| nincome | 0.94 (0.88, 1.01) | 0.093 |
| nemploy | 0.041 | |
| 0 | — | |
| 1 | 1.37 (1.01, 1.86) | |
| neduc | 0.67 (0.57, 0.79) | <0.001 |
| 1 OR = Odds Ratio | ||
Bayesian Monotonic Regression
The effect of the linear predictor on the outcome is expressed as
\[ \eta_n = b \cdot D \sum_{i \in x_n} \zeta_i \]
Where \(b\) is the size and direction of the monotonic effect, \(D\) is the number of categories in \(x_n\) minus one (i.e., same as \(\operatorname{dom}(i)\)), and \(\zeta_i \in [0,1]\) is a simplex that scales \(b\) between levels of \(x_n\). The upcoming model was fit using non-informative priors, four chains with 4,000 iterations each, where the first half of the samples from each chain were discarded.
For comparison sake, a non-monotonic ordinal regression model was fit using the similar non-informative priors and sampler settings. Both the Bayes Factor and the LOO-CV approach found the monotonic effects model to be superior to the non-monotonic effects model in the Bayesian framework.
Family: cumulative
Links: mu = logit; disc = identity
Formula: ordered(Covidhesit) ~ worrycovid + ngender + nmarital + nrace + nemploy + nregion + mo(fearlovedcovid) + mo(familyhealth) + mo(communhealth) + mo(safetyvac) + mo(sideeffect) + mo(effectivevac) + mo(chipcovid) + mo(politview) + mo(onlinesocialnews) + mo(natnewspaper) + mo(nattvnews) + mo(locnewspaper) + mo(loctvnews) + mo(religiosity) + mo(nage) + mo(nincome) + mo(neduc)
Data: chapman_21_cont (Number of observations: 991)
Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 4000
Regression Coefficients:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept[1] -3.70 0.73 -5.22 -2.37 1.00 2187 2543
Intercept[2] -1.60 0.73 -3.10 -0.25 1.00 2227 2415
Intercept[3] 0.56 0.71 -0.88 1.86 1.00 2315 2523
worrycovid -0.04 0.01 -0.06 -0.02 1.00 4133 2787
ngender1 0.29 0.14 0.00 0.57 1.00 4208 2898
nmarital1 -0.30 0.15 -0.61 -0.02 1.00 3542 2650
nrace1 -0.18 0.16 -0.51 0.15 1.00 2757 2711
nemploy1 0.17 0.17 -0.16 0.50 1.00 2988 2986
nregion2 0.22 0.21 -0.20 0.64 1.00 2905 2863
nregion3 0.08 0.19 -0.29 0.45 1.00 2576 2737
nregion4 -0.32 0.21 -0.73 0.11 1.00 2729 2922
mofearlovedcovid -0.67 0.09 -0.85 -0.50 1.00 3647 3211
mofamilyhealth -0.17 0.13 -0.44 0.07 1.00 2724 2894
mocommunhealth -0.44 0.14 -0.75 -0.21 1.00 2539 2335
mosafetyvac 0.90 0.11 0.69 1.11 1.00 2881 3339
mosideeffect 0.52 0.14 0.29 0.83 1.00 2048 2481
moeffectivevac -0.55 0.21 -1.03 -0.21 1.00 2134 1993
mochipcovid 0.34 0.10 0.16 0.54 1.00 3339 2791
mopolitview 0.29 0.08 0.15 0.45 1.00 2401 2970
moonlinesocialnews -0.00 0.03 -0.06 0.05 1.00 3632 2853
monatnewspaper -0.09 0.06 -0.20 0.02 1.00 3010 3101
monattvnews -0.01 0.06 -0.12 0.11 1.00 2498 2965
molocnewspaper 0.07 0.04 -0.02 0.16 1.00 2884 2894
moloctvnews -0.02 0.06 -0.13 0.09 1.00 2589 2873
moreligiosity 0.10 0.09 -0.08 0.26 1.00 2474 3060
monage -0.36 0.08 -0.52 -0.20 1.00 2588 2736
monincome -0.05 0.04 -0.13 0.01 1.00 2519 2752
moneduc -0.39 0.11 -0.63 -0.19 1.00 2205 2922
Monotonic Simplex Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
mofearlovedcovid1[1] 0.54 0.08 0.38 0.69 1.00 3594
mofearlovedcovid1[2] 0.12 0.07 0.01 0.29 1.00 2622
mofearlovedcovid1[3] 0.34 0.08 0.18 0.49 1.00 5539
mofamilyhealth1[1] 0.36 0.23 0.02 0.85 1.00 3765
mofamilyhealth1[2] 0.32 0.22 0.02 0.81 1.00 3976
mofamilyhealth1[3] 0.32 0.21 0.01 0.80 1.00 4135
mocommunhealth1[1] 0.37 0.18 0.03 0.69 1.00 2641
mocommunhealth1[2] 0.12 0.10 0.00 0.39 1.00 2820
mocommunhealth1[3] 0.51 0.17 0.24 0.87 1.00 2826
mosafetyvac1[1] 0.22 0.08 0.06 0.37 1.00 2767
mosafetyvac1[2] 0.33 0.07 0.21 0.48 1.00 2931
mosafetyvac1[3] 0.44 0.07 0.31 0.58 1.00 4485
mosideeffect1[1] 0.30 0.16 0.02 0.60 1.00 1684
mosideeffect1[2] 0.14 0.10 0.01 0.37 1.00 2514
mosideeffect1[3] 0.56 0.15 0.31 0.86 1.00 2414
moeffectivevac1[1] 0.34 0.20 0.03 0.73 1.00 2223
moeffectivevac1[2] 0.34 0.19 0.03 0.72 1.00 3167
moeffectivevac1[3] 0.31 0.16 0.07 0.70 1.00 2961
mochipcovid1[1] 0.46 0.17 0.16 0.83 1.00 2610
mochipcovid1[2] 0.39 0.17 0.04 0.72 1.00 3194
mochipcovid1[3] 0.15 0.12 0.01 0.43 1.00 3311
mopolitview1[1] 0.17 0.11 0.01 0.41 1.00 3200
mopolitview1[2] 0.22 0.11 0.03 0.47 1.00 2434
mopolitview1[3] 0.09 0.08 0.00 0.28 1.00 2530
mopolitview1[4] 0.10 0.08 0.00 0.30 1.00 3315
mopolitview1[5] 0.16 0.10 0.01 0.39 1.00 3668
mopolitview1[6] 0.26 0.14 0.02 0.54 1.00 2801
moonlinesocialnews1[1] 0.11 0.09 0.00 0.35 1.00 3763
moonlinesocialnews1[2] 0.10 0.09 0.00 0.34 1.00 3904
moonlinesocialnews1[3] 0.10 0.09 0.00 0.33 1.00 3466
moonlinesocialnews1[4] 0.10 0.09 0.00 0.33 1.00 4276
moonlinesocialnews1[5] 0.10 0.09 0.00 0.32 1.00 3898
moonlinesocialnews1[6] 0.10 0.09 0.00 0.33 1.00 3157
moonlinesocialnews1[7] 0.10 0.09 0.00 0.33 1.00 4092
moonlinesocialnews1[8] 0.10 0.09 0.00 0.32 1.00 4584
moonlinesocialnews1[9] 0.10 0.09 0.00 0.33 1.00 3721
moonlinesocialnews1[10] 0.11 0.09 0.00 0.35 1.00 4627
monatnewspaper1[1] 0.14 0.13 0.00 0.47 1.00 2829
monatnewspaper1[2] 0.18 0.15 0.01 0.57 1.00 3043
monatnewspaper1[3] 0.14 0.13 0.00 0.50 1.00 3864
monatnewspaper1[4] 0.21 0.16 0.01 0.61 1.00 3876
monatnewspaper1[5] 0.33 0.21 0.02 0.75 1.00 2792
monattvnews1[1] 0.20 0.18 0.00 0.64 1.00 2784
monattvnews1[2] 0.20 0.16 0.01 0.61 1.00 3843
monattvnews1[3] 0.20 0.17 0.01 0.61 1.00 3603
monattvnews1[4] 0.19 0.16 0.01 0.59 1.00 4565
monattvnews1[5] 0.21 0.17 0.01 0.61 1.00 4045
molocnewspaper1[1] 0.25 0.18 0.01 0.64 1.00 3058
molocnewspaper1[2] 0.19 0.16 0.01 0.59 1.00 3723
molocnewspaper1[3] 0.16 0.14 0.00 0.52 1.00 3417
molocnewspaper1[4] 0.24 0.18 0.01 0.65 1.00 3523
molocnewspaper1[5] 0.16 0.14 0.00 0.52 1.00 4591
moloctvnews1[1] 0.21 0.17 0.01 0.61 1.00 3619
moloctvnews1[2] 0.18 0.15 0.01 0.56 1.00 2973
moloctvnews1[3] 0.20 0.16 0.01 0.59 1.00 3772
moloctvnews1[4] 0.19 0.16 0.01 0.58 1.00 3605
moloctvnews1[5] 0.22 0.17 0.01 0.61 1.00 3792
moreligiosity1[1] 0.24 0.20 0.01 0.76 1.00 2986
moreligiosity1[2] 0.24 0.20 0.01 0.75 1.00 3306
moreligiosity1[3] 0.52 0.25 0.03 0.92 1.00 2350
monage1[1] 0.06 0.06 0.00 0.22 1.00 3267
monage1[2] 0.53 0.15 0.23 0.85 1.00 3342
monage1[3] 0.40 0.16 0.09 0.71 1.00 3094
monincome1[1] 0.13 0.11 0.00 0.41 1.00 2876
monincome1[2] 0.13 0.11 0.00 0.40 1.00 3720
monincome1[3] 0.10 0.09 0.00 0.33 1.00 3738
monincome1[4] 0.10 0.09 0.00 0.35 1.00 4439
monincome1[5] 0.12 0.11 0.00 0.39 1.00 4123
monincome1[6] 0.15 0.12 0.00 0.45 1.00 2843
monincome1[7] 0.13 0.11 0.00 0.43 1.00 3978
monincome1[8] 0.13 0.12 0.00 0.42 1.00 3761
moneduc1[1] 0.34 0.17 0.03 0.67 1.00 2353
moneduc1[2] 0.31 0.16 0.04 0.67 1.00 2833
moneduc1[3] 0.34 0.15 0.07 0.68 1.00 3654
Tail_ESS
mofearlovedcovid1[1] 2466
mofearlovedcovid1[2] 1740
mofearlovedcovid1[3] 2951
mofamilyhealth1[1] 1960
mofamilyhealth1[2] 2940
mofamilyhealth1[3] 2583
mocommunhealth1[1] 2260
mocommunhealth1[2] 1954
mocommunhealth1[3] 2651
mosafetyvac1[1] 1472
mosafetyvac1[2] 2712
mosafetyvac1[3] 3251
mosideeffect1[1] 1438
mosideeffect1[2] 1566
mosideeffect1[3] 2652
moeffectivevac1[1] 1940
moeffectivevac1[2] 1919
moeffectivevac1[3] 2221
mochipcovid1[1] 1907
mochipcovid1[2] 1904
mochipcovid1[3] 2208
mopolitview1[1] 2156
mopolitview1[2] 1332
mopolitview1[3] 1511
mopolitview1[4] 1827
mopolitview1[5] 2060
mopolitview1[6] 2146
moonlinesocialnews1[1] 1969
moonlinesocialnews1[2] 1971
moonlinesocialnews1[3] 2046
moonlinesocialnews1[4] 1880
moonlinesocialnews1[5] 2265
moonlinesocialnews1[6] 1805
moonlinesocialnews1[7] 2394
moonlinesocialnews1[8] 2766
moonlinesocialnews1[9] 2576
moonlinesocialnews1[10] 2599
monatnewspaper1[1] 1857
monatnewspaper1[2] 1632
monatnewspaper1[3] 2153
monatnewspaper1[4] 2321
monatnewspaper1[5] 2699
monattvnews1[1] 1683
monattvnews1[2] 1974
monattvnews1[3] 2282
monattvnews1[4] 2809
monattvnews1[5] 3005
molocnewspaper1[1] 1567
molocnewspaper1[2] 2123
molocnewspaper1[3] 1828
molocnewspaper1[4] 2687
molocnewspaper1[5] 2795
moloctvnews1[1] 1740
moloctvnews1[2] 2070
moloctvnews1[3] 2246
moloctvnews1[4] 1973
moloctvnews1[5] 2487
moreligiosity1[1] 2019
moreligiosity1[2] 2251
moreligiosity1[3] 2602
monage1[1] 1537
monage1[2] 2119
monage1[3] 1776
monincome1[1] 1470
monincome1[2] 2064
monincome1[3] 2099
monincome1[4] 2331
monincome1[5] 1921
monincome1[6] 1562
monincome1[7] 2550
monincome1[8] 2285
moneduc1[1] 1931
moneduc1[2] 2155
moneduc1[3] 2267
Further Distributional Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
disc 1.00 0.00 1.00 1.00 NA NA NA
Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 7
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6