Background
Methodology
Variables of the study
Statistical models
Zero-inflated Poisson regression models
Bayesian inference
Bayesian ZIP regression models
The Gibbs sampling algorithm
Convergence of the algorithm
Results
No_ANC visits | Count | Percent | Cumulative percent |
---|---|---|---|
0 | 136 | 37.0 | 37.00 |
1 | 43 | 11.7 | 48.60 |
2 | 35 | 9.5 | 58.20 |
3 | 71 | 19.5 | 77.40 |
4 | 40 | 10.9 | 88.30 |
5 | 18 | 4.9 | 93.20 |
6 | 14 | 3.8 | 97.00 |
7 | 7 | 1.9 | 98.90 |
8 | 2 | 0.5 | 99.50 |
9 | 1 | 0.3 | 99.70 |
10 | 1 | 0.3 | 100.00 |
Test for over dispersion
Models | Df | Value | Value/Df |
---|---|---|---|
Deviance | |||
Poisson | 362 | 845.7467 | 2.3363 |
NegBin | 362 | 333.0707 | 0.9201 |
Pearson | |||
Poisson | 362 | 950.9179 | 2.6268 |
NegBin | 362 | 324.9572 | 0.8977 |
M1 | M2 | V-statistic (p-value) | Model | Best model |
---|---|---|---|---|
ZIP | P | 7.385 (7.65e−14) | M1 > M2 | ZIP |
ZIP | NB | 4.117 (1.92e−05) | M1 > M2 | ZIP |
ZINB | P | 7.276 (1.71e−13) | M1 > M2 | ZINB |
ZINB | NB | 4.43 (4.69e−06) | M1 > M2 | ZINB |
P vs. NB H0: k = 0 vs. H1: k > 0 | ZIP VS. ZINB H0: k = 0 vs. H1: k > 0 | |||
LRT: 203.4174 | LRT: 0.3168 | |||
Best modeling: NB p = 0.000 | Best model: ZIP p = 0.574 |
Model selection criteria
Criteria | P | NB | ZIP | ZINB |
---|---|---|---|---|
− 2Log | 1290.835 | 1087.417 | 1017.381 | 1017.698 |
AIC | 1304.835 | 1103.417 | 1045.698 | 1047.381 |
BIC | 1332.191 | 1134.682 | 1100.411 | 1106.003 |
Parameter estimates and interpretation
Interpretation (zero-inflated model)
Parameters | Zero-inflated poisson | |
---|---|---|
Poisson Estim. (S.E) | Logit Estim. (S.E) | |
Intercept | 1.2842** (0.2059540) | 0.9996** (0.6643) |
Sign of pregnancy (reference-no) | ||
Sign1 | 0.22744** (0.1634150) | − 0.8967 (0.5979) |
Utilization of media (reference-no use of media) | ||
Media1 | 0.1195** (0.1126641) | − 0.5212 (0.2495) |
Mothers education (reference-no education) | ||
M.educ1 | − 0.1297 (0.1311842) | 0.1314** (0.3061) |
Wealth index (reference-poor) | ||
WI2 | 0.00085** (0.141523) | − 0.372** (0.2914) |
WI3 | 0.28494** (0.128498) | − 0.6181** (0.293) |
Area of residence (reference-urban) | ||
Resid2 | − 0.1652** (0.111293) | 0.4702** (0.276) |
Interpretation (count model)
Bayesian zero inflated regression analysis
Time series plot
Density plot
Autocorrelation plot
Gelman–Rubin statistics
Assessing accuracy of Bayesian ZIP model fitting
Parameters | Mean (\(\hat{\upbeta }\)) | Sd | MC error | Median | HPD credible intervals | |
---|---|---|---|---|---|---|
Lower (2.5%) | Upper (97.5%) | |||||
Count model coefficients | ||||||
β1 (Intercept) | 1.011 | 0.1795 | 0.001676 | 1.014 | 0.6536 | 1.358 |
Sign of pregnancy (reference-no) | ||||||
β2 (Sign1) | − 0.4264 | 0.1555 | 0.001374 | − 0.429 | − 0.722 | − 0.12 |
Utilization of media (reference-no use of media) | ||||||
β3 (Media1) | − 0.4594 | 0.1013 | 3.44E−4 | − 0.459 | − 0.658 | − 0.260 |
Mothers’ education (reference -no education) | ||||||
β4 (M.educ1) | 0.257 | 0.1074 | 5.37E−4 | 0.257 | 0.046 | 0.4664 |
Wealth index (reference-poor) | ||||||
β5 (WI2) | − 0.6421 | 0.1134 | 4.49E−4 | − 0.642 | − 0.864 | − 0.42 |
β6 (WI3) | − 0.2698 | 0.1181 | 4.47E−4 | − 0.269 | − 0.502 | − 0.039 |
Area of residence (reference-urban) | ||||||
β7 (Resid2) | 0.3495 | 0.09945 | 3.65E−4 | 0.35 | 0.153 | 0.543 |
Zero-inflation coefficients | ||||||
α1 (Intercept) | 0.755 | 0.196 | 0.0042 | 0.7596 | 0.361 | 1.126 |
Sign of pregnancy (reference-no) | ||||||
α2 (Sign1) | − 0.227 | 0.172 | 0.0037 | − 0.23 | − 0.548 | 0.1259 |
Utilization of media (reference-no use of media) | ||||||
α3 (Media1) | − 0.335 | 0.130 | 0.0022 | − 0.34 | − 0.585 | − 0.082 |
Mothers’ education (reference-no education) | ||||||
α4 (M.educ1) | − 0.608 | 0.148 | 0.003 | − 0.6046 | − 0.9153 | − 0.330 |
Wealth index (reference-poor) | ||||||
α5 (WI2) | − 0.517 | 0.137 | 0.002 | − 0.52 | − 0.787 | − 0.25 |
α6 (WI3) | 0.04589 | 0.181 | 0.004 | 0.03645 | − 0.277 | 0.4431 |
Area of residence (reference-urban) | ||||||
α7 (Resid2) | 0.124 | 0.1292 | 0.002307 | 0.2392 | 0.116 | 0.3623 |
Model comparison
Variable (coefficients) | BZIP | CZIP | SE comparison | ||
---|---|---|---|---|---|
Mean (\(\hat{\beta }\)) | SEβ |
\(\hat{\beta }\)
| SEC | ||
Count model coefficients | |||||
β1 (Intercept) | 1.011 | 0.00936 | 1.2842217 | 0.2059540 | SEB < SEC |
Sign of pregnancy (reference-no) | |||||
β2 (Sign1) | − 0.4264 | 0.008106 | − 0.2274489 | 0.1634150 | SEB < SEC |
Utilization of media (reference-no use of media) | |||||
β3 (Media1) | − 0.4594 | 0.00528 | − 0.1195001 | 0.1126641 | SEB < SEC |
Mothers’ education (reference-no education) | |||||
β4 (M.educ1)) | 0.257 | 0.005599 | 0.1297838 | 0.1311842 | SEB < SEC |
Wealth index (reference-poor) | |||||
β5 (WI2) | − 0.6421 | 0.0059115 | − 0.0008455 | 0.1415231 | SEB < SEC |
β6 (WI3) | − 0.2698 | 0.0061565 | − 0.2849420 | 0.1284985 | SEB < SEC |
Area of residence (reference-urban) | |||||
β7 (Resid2) | 0.3495 | 0.005184 | − 0.1651500 | 0.1112927 | SEB < SEC |
Zero-inflation coefficients | |||||
α1 (Intercept) | 0.755 | 0.01022 | − 0.9996 | 0.6643 | SEB < SEC |
Sign of pregnancy (reference-no) | |||||
α2 (Sign1) | − 0.227 | 0.008966 | 0.8967 | 0.5979 | SEB < SEC |
Utilization of media (reference-no use of Media) | |||||
α3 (M.educ1) | − 0.335 | 0.0067768 | 0.5212 | 0.2495 | SEB < SEC |
Mothers’ education (reference-no education) | |||||
α4 (M.educ1) | − 0.608 | 0.0077152 | − 0.1314 | 0.3061 | SEB < SEC |
Wealth index (reference-poor) | |||||
α5 (WI2) | − 0.517 | 0.0071417 | − 0.3718 | 0.2914 | SEB < SEC |
α6 (WI3) | 0.04589 | 0.009435 | − 0.6181 | 0.2932 | SEB < SEC |
Area of residence (reference-urban) | |||||
α7 (Resid2) | 0.124 | 0.0067351 | 0.4702 | 0.2758 | SEB < SEC |