1 Introduction
2 Methods
2.1 Sources of Data and Variables in the Model
Dependent variable | Description |
---|---|
ANC | Number of ANC visits |
Independent variables | Catagories |
---|---|
Age | 1 = 15–24, 2 = 25–34, 3 = 35–49 |
Wealth Index | 1 = Poor, 2 = Middle, 3 = Rich |
Residence | 0 = Urban, 1 = Rural |
Exposure to media | 0 = No, 1 = Yes |
Marital Status | 0 = Married, 1 = Single |
Employment status | 0 = No, 1 = Yes |
Religion | 1 = Orthodox, 2 = Catholic, 3 = Protestant, 4 = Muslim, 5 = Traditional |
Mother education | 1 = No education, 2 = Primary, 3 = Secondary, 4 = Higher |
Partner education | 1 = No education, 2 = Primary, 3 = Secondary, 4 = Higher |
2.2 Statistical Models
2.2.1 Poisson Regression Model
2.2.2 Negative Binomial Regression Model
2.2.3 Zero-Inflated Models
2.2.4 Zero-Inflated Poisson (ZIP) Regression Model
2.2.5 Zero-Inflated Negative Binomial (ZINB) Regression Model
2.2.6 Hurdle Regression Models
2.2.7 Hurdle Poisson (HP) Regression Model
2.2.8 Hurdle NB Regressions Model
2.2.9 Voung Test
3 Results
3.1 Exploratory Analysis of ANC Visits
3.1.1 Why it is Important to Model Zero Counts and Positive Counts Separately
Number of visits | Frequency | Percentage |
---|---|---|
0 | 2240 | 34.7 |
1 | 313 | 4.9 |
2 | 522 | 8.1 |
3 | 1073 | 16.6 |
4 | 1014 | 15.7 |
5 | 551 | 8.5 |
6 | 353 | 5.5 |
7 | 171 | 2.7 |
8 | 89 | 1.4 |
9 | 51 | 0.8 |
10 | 35 | 0.5 |
11 | 8 | 0.1 |
12 | 8 | 0.1 |
13 | 6 | 0.1 |
14 | 2 | 0.0 |
15 | 4 | 0.1 |
16 | 1 | 0.0 |
20 | 9 | 0.1 |
Total | 6450 | 100 |
Variables | Categories | Number | Percentage |
---|---|---|---|
Mothers age | |||
15–24 | 1622 | 15.1 | |
25–34 | 3203 | 49.7 | |
35–49 | 1625 | 25.2 | |
Mothers religion | |||
Orthodox | 2062 | 32.0 | |
Catholic | 45 | 0.7 | |
Protestant | 1225 | 19.0 | |
Muslim | 3055 | 47.4 | |
Traditional | 63 | 1.0 | |
Wealth Index | |||
Poor | 3270 | 50.7 | |
Middle | 932 | 14.4 | |
Rich | 2248 | 34.9 | |
Mothers education level | |||
No education | 3971 | 61.6 | |
Primary | 1713 | 26.6 | |
Secondary | 495 | 7.7 | |
Higher | 271 | 4.2 | |
Employment status | |||
No | 1426 | 71.8 | |
Yes | 1822 | 28.2 | |
Partner education level | |||
No education | 3062 | 47.5 | |
Primary | 2126 | 33.0 | |
Secondary | 723 | 11.2 | |
Higher | 539 | 8.4 | |
Marital status | |||
Married | 6369 | 98.7 | |
Single | 81 | 1.3 | |
Exposure to media | |||
No | 4658 | 72.2 | |
Yes | 1792 | 27.8 |
3.2 Simulation Study
3.2.1 The Simulation Experiment on Zero-Inflated Count Data Generated from Zero-Inflated Poisson Model
Models | ZIP | ZINB | Hurdle | Poisson | Negative binomial | |||||
---|---|---|---|---|---|---|---|---|---|---|
Covariates for positive counts | Estimates | S.E. | Estimates | S.E. | Estimates | S.E. | Estimates | S.E. | Estimates | S.E. |
Intercept | 1.269\(***\) | 0.036 | 1.269\(***\) | 0.036 | 1.269\(***\) | 0.036 | 0.793\(***\) | 0.035 | 0.792\(***\) | 0.055 |
Marital status (Ref = Married) | ||||||||||
Single | 0.085 | 0.064 | 0.085 | 0.064 | 0.085 | 0.064 | \(-\) 0.004\(***\) | 0.063 | 0.009 | 0.104 |
Exposer to media(Ref = No) | ||||||||||
Yes | 0.052\(**\) | 0.017 | 0.052\(**\) | 0.017 | 0.052\(**\) | 0.017 | 0.045\(**\) | 0.017 | 0.042 | 0.028 |
Employment status(Ref = No) | ||||||||||
Yes | \(-\) 0.002 | 0.018 | \(-\) 0.002 | 0.018 | \(-\) 0.001 | 0.018 | 0.023 | 0.017 | 0.041 | 0.027 |
Age(Ref = 15\(-\) 24) | ||||||||||
25\(-\) 34 | 0.076\(***\) | 0.020 | 0.076\(***\) | 0.020 | 0.077\(***\) | 0.020 | 0.068\(***\) | 0.019 | 0.075\(*\) | 0.030 |
35\(-\) 49 | 0.089\(***\) | 0.025 | 0.089\(***\) | 0.025 | 0.090\(***\) | 0.025 | \(-\) 0.001 | 0.023 | \(-\) 0.025 | 0.036 |
Residence(Ref = Urban) | ||||||||||
Rural | \(-\) 0.174\(***\) | 0.023 | \(-\) 0.174\(***\) | 0.023 | \(-\) 0.175\(***\) | 0.023 | \(-\) 0.296\(***\) | 0.022 | \(-\) 0.296\(***\) | 0.037 |
Wealth index(Ref = Poor) | ||||||||||
Middle | 0.070\(**\) | 0.026 | 0.070\(**\) | 0.026 | 0.072\(**\) | 0.026 | 0.285\(***\) | 0.025 | 0.294\(***\) | 0.037 |
Rich | 0.123\(***\) | 0.023 | 0.123\(***\) | 0.023 | 0.123\(***\) | 0.023 | 0.350\(***\) | 0.023 | 0.360\(***\) | 0.035 |
Partner education(Ref = No education) | ||||||||||
Primary | 0.069\(**\) | 0.021 | 0.069\(**\) | 0.021 | 0.069\(**\) | 0.021 | 0.236\(***\) | 0.020 | 0.238\(***\) | 0.030 |
Secondary | 0.111\(***\) | 0.029 | 0.111\(***\) | 0.029 | 0.110\(***\) | 0.029 | 0.284\(***\) | 0.028 | 0.288\(***\) | 0.045 |
Higher | 0.142\(***\) | 0.034 | 0.142\(***\) | 0.034 | 0.141\(***\) | 0.034 | 0.292\(***\) | 0.033 | 0.288\(***\) | 0.055 |
Religion(Ref = Orthodox) | ||||||||||
Catholic | \(-\) 0.172 | 0.103 | \(-\) 0.172 | 0.103 | \(-\) 0.173 | 0.104 | \(-\) 0.451\(***\) | 0.099 | \(-\) 0.521\(***\) | 0.151 |
protestant | \(-\) 0.110\(***\) | 0.023 | \(-\) 0.110\(***\) | 0.023 | \(-\) 0.109\(***\) | 0.023 | \(-\) 0.273\(***\) | 0.022 | \(-\) 0.292\(***\) | 0.035 |
Muslim | \(-\) 0.096\(***\) | 0.018 | \(-\) 0.096\(***\) | 0.018 | \(-\) 0.096\(***\) | 0.018 | \(-\) 0.226\(***\) | 0.018 | \(-\) 0.245\(***\) | 0.028 |
Traditional | \(-\) 0.215 | 0.166 | \(-\) 0.215 | 0.166 | \(-\) 0.214 | 0.165 | \(-\) 1.038\(***\) | 0.150 | \(-\) 1.079\(***\) | 0.179 |
Education level(Ref = No education) | ||||||||||
Primary | 0.090\(***\) | 0.021 | 0.090\(***\) | 0.021 | 0.090\(***\) | 0.021 | 0.266\(***\) | 0.020 | 0.278\(***\) | 0.032 |
Secondary | 0.130\(***\) | 0.031 | 0.130\(***\) | 0.031 | 0.130\(***\) | 0.031 | 0.290\(***\) | 0.031 | 0.303\(***\) | 0.052 |
Higher | 0.150\(***\) | 0.040 | 0.150\(***\) | 0.040 | 0.149\(***\) | 0.040 | 0.314\(***\) | 0.039 | 0.304\(***\) | 0.070 |
Log(theta) | 1.280\(***\) | (0.791) | ||||||||
AIC | 23422.600 | 23424.600 | 23425.930 | 27637.720 | 26061.690 | |||||
Log likelihood | \(-\) 11673.300 | \(-\) 11673.300 | \(-\) 11672.960 | \(-\) 13799.860 | \(-\) 13010.850 | |||||
Num. obs | 6450 | 6450 | 6450 | 6450 | 6450 | |||||
BIC | 27766.380 | 26197.130 | ||||||||
Deviance | 14354 | 8145.600 |
Models | ZIP | ZINB | Hurdle | ||||
---|---|---|---|---|---|---|---|
Covariates for zero count | Categories | Estimates | S.E. | Estimates | S.E. | Estimates | S.E. |
Intercept | \(-\) 1.450\(*\) \(*\) \(*\) | 0.175 | \(-\) 1.450\(*\) \(*\) \(*\) | 0.175 | 1.836\(*\) | 0.814 | |
Marital status(Ref = Married) | |||||||
Single | 0.398 | 0.293 | 0.398 | 0.293 | \(-\) 0.398 | 0.337 | |
Exposer to media(Ref = No) | |||||||
Yes | \(-\) 0.045 | 0.079 | \(-\) 0.045 | 0.079 | 0.084 | 0.096 | |
Employment status(Ref = No) | |||||||
Yes | \(-\) 0.157\(*\) | 0.074 | \(-\) 0.157\(*\) | 0.074 | 0.180 | 0.098 | |
Age(Ref = 15\(-\) 24) | |||||||
25\(-\) 34 | \(-\) 0.016 | 0.082 | \(-\) 0.016\(*\) \(*\) \(*\) | 0.082 | 0.056 | 0.092 | |
35\(-\) 49 | 0.302\(*\) \(*\) | 0.092 | 0.302\(*\) \(*\) | 0.092 | \(-\) 0.297\(*\) | 0.118 | |
Residence(Ref = Urban) | |||||||
Rural | 1.105\(*\) \(*\) \(*\) | 0.141 | 1.105\(*\) \(*\) \(*\) | 0.141 | \(-\) 1.394\(*\) \(*\) | 0.493 | |
Wealth index(Poor) | |||||||
Middle | \(-\) 0.564\(*\) \(*\) \(*\) | 0.090 | \(-\) 0.564\(*\) \(*\) \(*\) | 0.090 | 0.653\(*\) \(*\) \(*\) | 0.184 | |
Rich | \(-\) 0.712\(*\) \(*\) \(*\) | 0.092 | \(-\) 0.712\(*\) \(*\) \(*\) | 0.092 | 0.854\(*\) \(*\) \(*\) | 0.240 | |
Partner education(Ref = No education) | |||||||
Primary | \(-\) 0.513\(*\) \(*\) \(*\) | 0.074 | \(-\) 0.513\(*\) \(*\) \(*\) | 0.074 | 0.592\(*\) \(*\) \(*\) | 0.148 | |
Secondary | \(-\) 0.751\(*\) \(*\) \(*\) | 0.145 | \(-\) 0.751\(*\) \(*\) \(*\) | 0.145 | 0.888\(*\) \(*\) \(*\) | 0.268 | |
Higher | \(-\) 0.314 | 0.183 | \(-\) 0.314 | 0.183 | 0.392 | 0.219 | |
Religion(Ref = Orthodox) | |||||||
Catholic | 1.416\(*\) \(*\) \(*\) | 0.363 | 1.416\(*\) \(*\) \(*\) | 0.363 | \(-\) 1.669\(*\) \(*\) | 0.575 | |
Protestant | 0.876\(*\) \(*\) \(*\) | 0.096 | 0.876\(*\) \(*\) \(*\) | 0.096 | \(-\) 1.025\(*\) \(*\) \(*\) | 0.261 | |
Muslim | 0.642\(*\) \(*\) \(*\) | 0.076 | 0.642\(*\) \(*\) \(*\) | 0.076 | \(-\) 0.759\(*\) \(*\) \(*\) | 0.199 | |
Traditional | 1.760\(*\) \(*\) \(*\) | 0.327 | 1.760\(*\) \(*\) \(*\) | 0.327 | \(-\) 1.967\(*\) \(*\) \(*\) | 0.462 | |
Education level(Ref = No education) | |||||||
Primary | \(-\) 0.722\(*\) \(*\) \(*\) | 0.086 | \(-\) 0.722\(*\) \(*\) \(*\) | 0.086 | 0.856\(*\) \(*\) \(*\) | 0.247 | |
Secondary | \(-\) 1.048\(*\) \(*\) \(*\) | 0.204 | \(-\) 1.048\(*\) \(*\) \(*\) | 0.204 | 1.281\(*\) \(*\) | 0.458 | |
Higher | \(-\) 2.384\(*\) \(*\) \(*\) | 0.622 | \(-\) 2.384\(*\) \(*\) \(*\) | 0.622 | 2.949\(*\) | 1.334 | |
Log(theta) | 6.542 | 5.234 | \(-\) 3.369\(*\) \(*\) \(*\) | 0.444 |
3.3 Parameter Estimates and Interpretation
3.4 Model Comparison
ZIP | ZINB | Hurdle | Poisson | NB | Best model | |
---|---|---|---|---|---|---|
ZIP | 0.479 | 0.359 | 0.000*** | 0.000*** | Hurdle | |
ZIBP | 0.359 | 0.000*** | 0.000*** | Hurdle | ||
Hurdle | 0.000*** | 0.000*** | Hurdle | |||
Poisson | 0.000*** | NB | ||||
NB | Hurdle |
3.5 Hurdle Model Parameter Estimate
Estimate | S.E. | z value | Pr(\(>|z|\)) | ||
---|---|---|---|---|---|
Count model coefficients (truncated negbin with log link) | |||||
Intercept | 1.269 | 0.036 | 34.545 | < 2e-16 | \(***\) |
Residence (Ref = Urban) | |||||
Rural | \(-\) 0.175 | 0.023 | \(-\) 7.542 | 4.63e-14 | \(***\) |
Marital status (Ref = Married) | |||||
Single | 0.085 | 0.064 | 1.324 | 0.185 | |
Exposer to media (Ref = No) | |||||
Yes | 0.052 | 0.017 | 2.900 | 0.003 | \(**\) |
Employment status (Ref = No) | |||||
Yes | \(-\) 0.001 | 0.018 | \(-\) 0.090 | 0.927 | |
Age (Ref = 15\(-\) 24) | |||||
25\(-\) 34 | 0.077 | 0.020 | 3.776 | 0.000 | \(***\) |
35\(-\) 49 | 0.090 | 0.025 | 3.604 | 0.000 | \(***\) |
Wealth index (Ref = Poor) | |||||
Middle | 0.072 | 0.026 | 2.731 | 0.006 | \(**\) |
Rich | 0.123 | 0.023 | 5.191 | 2.10e-07 | \(***\) |
Partner education (Ref = No education) | |||||
Primary | 0.069 | 0.021 | 3.209 | 0.001 | \(**\) |
Secondary | 0.110 | 0.029 | 3.790 | 0.000 | \(***\) |
Higher | 0.141 | 0.034 | 4.113 | 3.90e-05 | \(***\) |
Religion (Ref = Orthodox) | |||||
Catholic | \(-\) 0.173 | 0.104 | \(-\) 1.669 | 0.095 | |
protestant | \(-\) 0.109 | 0.023 | \(-\) 4.647 | 3.37e-06 | \(***\) |
Muslim | \(-\) 0.096 | 0.018 | \(-\) 5.157 | 2.51e-07 | \(***\) |
Traditional | \(-\) 0.214 | 0.165 | \(-\) 1.296 | 0.194 | |
Education level (Ref = No education) | |||||
Primary | 0.091 | 0.021 | 4.212 | 2.53e-05 | \(***\) |
Secondary | 0.130 | 0.031 | 4.096 | 4.21e-05 | \(***\) |
Higher | 0.149 | 0.040 | 3.712 | 0.000 | \(***\) |
Log(theta) | 1.280 | 0.791 | 6.670 | 0.000 | \(***\) |
Zero hurdle model coefficient (censored negative binomial with log link) | |||||
Intercept | 1.836 | 0.814 | 2.254 | 0.024 | \(*\) |
Residence (Ref = Urban) | |||||
Rural | \(-\) 1.394 | 0.493 | \(-\) 2.825 | 0.004 | \(**\) |
Marital status (Ref = Married) | |||||
Single | \(-\) 0.398 | 0.337 | \(-\) 1.181 | 0.237 | |
Exposer to media (Ref = No) | |||||
Yes | 0.084 | 0.096 | 0.879 | 0.379 | |
Employment status (Ref = No) | |||||
Yes | 0.180 | 0.098 | 1.826 | 0.067 | |
Age (Ref = 15\(-\) 24) | |||||
25\(-\) 34 | 0.056 | 0.092 | 0.609 | 0.542 | |
35\(-\)49 | \(-\) 0.297 | 0.118 | \(-\) 2.515 | 0.011 | \(*\) |
Wealth index (Ref = Poor) | |||||
Middle | 0.653 | 0.184 | 3.540 | 0.000 | \(***\) |
Rich | 0.854 | 0.240 | 3.545 | 0.000 | \(***\) |
Partner education (Ref = No education) | |||||
Primary | 0.592 | 0.148 | 3.980 | 6.89e-05 | \(***\) |
Secondary | 0.888 | 0.268 | 3.316 | 0.000 | \(***\) |
Higher | 0.392 | 0.219 | 1.791 | 0.073 | |
Religion (Ref = Orthodox) | |||||
Catholic | \(-\) 1.669 | 0.575 | \(-\) 2.900 | 0.003 | \(**\) |
Protestant | \(-\) 1.025 | 0.261 | \(-\) 3.918 | 8.93e-05 | \(***\) |
Muslim | \(-\) 0.759 | 0.199 | \(-\) 3.813 | 0.000 | \(***\) |
Traditional | \(-\) 1.967 | 0.462 | \(-\) 4.250 | 2.14e-05 | \(***\) |
Education level (Ref = No education) | |||||
Primary | 0.856 | 0.247 | 3.466 | 0.000 | \(***\) |
Secondary | 1.281 | 0.458 | 2.796 | 0.005 | \(**\) |
Higher | 2.949 | 1.334 | 2.210 | 0.027 | \(*\) |
Log(theta) | \(-\) 3.369 | 0.4442 | \(-\) 12.831 | 0.000 | \(***\) |