A Comparison of Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Models with and without Exposure Variables
Abstract
:1. Introduction
2. Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Type II (BZIPIGR)
2.1. BZIPIGR Type II Model with Exposure Variables
2.2. BZIPIGR Type II Model without Exposure Variable
2.3. Parameter Estimation of BZIPIGR Type II Model
- Step 1.
- Determine the initial value of each parameter of the BZIPIGR type II model . The initial values of model parameters are obtained from the regression model parameter values using OLS, whereas the dispersion parameter is obtained from the variance of the PIG distribution.
- Step 2.
- Define gradient vector
- Step 3.
- Determine the Hessian matrix (H*) for the BHHH algorithm
- Step 4.
- Start the BHHH iteration using the following formula:The iteration of the BHHH algorithm starts at m = 0 and stops if where is a small positive close to 0.
2.4. Hypothesis Testing of the BZIPIGR Type II Model
- Partial test of parameter λhj
- Partial test of parameter αhj
- Partial test of parameter τ
3. Application
3.1. Modeling the Number of Maternal and Early Neonatal Mortalities Using the BZIPIGR Type II Model Involving Exposure Variables
3.2. Modeling the Number of Maternal and Early Neonatal Mortalities Using the BZIPIGR Type II Model without Exposure Variables
3.3. Comparison of the BZIPIGR Type II Model with and without Exposure Variables
4. Discussion
- Regression model for the number of maternal mortalities:
- Regression model for the number of early neonatal mortalities:
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
References
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Variable (n = 75) | Mean | SD | Coefficient of Variance | Min | Max |
---|---|---|---|---|---|
Number of maternal mortalities (Y1) | 0.59 | 1.02 | 172.95 | 0 | 6 |
Number of early neonatal mortalities (Y2) | 0.53 | 1.14 | 214.3 | 0 | 8 |
Percentage of visits by pregnant women (X1) | 91.39 | 8.14 | 8.91 | 68.36 | 100 |
Percentage of pregnant women who received Fe3 tablets (X2) | 82.31 | 24.83 | 30.16 | 15.31 | 127.76 |
Percentage of births assisted by health workers (X3) | 91.1 | 9.15 | 10.05 | 49.34 | 100 |
Percentage of mother who attended at least three postpartum maternal visits (X4) | 76.54 | 19.34 | 25.26 | 39.45 | 100 |
Percentage of active integrated service posts (X5) | 73.44 | 35.71 | 48.63 | 0 | 100 |
Percentage of obstetric complications (X6) | 72.03 | 29.09 | 40.39 | 7.27 | 128.31 |
Variable | % of Zero Value | Dh | df | Dh/df |
---|---|---|---|---|
Number of maternal mortalities (Y1) | 61.33 | 88.637 | 68 | 1.303 |
Number of early neonatal mortalities (Y2) | 68 | 99.099 | 68 | 1.457 |
Parameter | Estimate | Standard Error | Z | p-Value |
---|---|---|---|---|
Number of maternal mortalities (Y1) | ||||
−7.308 | 0.002 | −3785.456 | p < 0.05 | |
0.005 | 0.002 | 2.860 | p < 0.05 | |
−0.006 | 0.0003 | −20.465 | p < 0.05 | |
0.043 | 0.002 | 27.838 | p < 0.05 | |
−0.018 | 0.0003 | −56.475 | p < 0.05 | |
−0.002 | 0.0003 | −7.979 | p < 0.05 | |
0.005 | 0.0001 | 25.392 | p < 0.05 | |
−5.031 | 0.0004 | −11,937.814 | p < 0.05 | |
0.157 | 0.013 | 2.159 | p < 0.05 | |
−0.004 | 0.003 | −1.539 | p > 0.05 | |
−0.101 | 0.013 | −7.535 | p < 0.05 | |
0.013 | 0.003 | 4.272 | p < 0.05 | |
0.006 | 0.002 | 2.793 | p < 0.05 | |
0.009 | 0.002 | 4.985 | p < 0.05 | |
Number of early neonatal mortalities (Y2) | ||||
−3.532 | 0.0438 | −80.570 | p < 0.05 | |
−0.036 | 0.0013 | −28.411 | p < 0.05 | |
0.066 | 0.0010 | 65.948 | p < 0.05 | |
−0.117 | 0.0018 | −64.065 | p < 0.05 | |
0.064 | 0.0013 | 48.034 | p < 0.05 | |
0.007 | 0.0004 | 18.887 | p < 0.05 | |
0.008 | 0.0005 | 16.890 | p < 0.05 | |
−10.340 | 0.005 | −1945.105 | p < 0.05 | |
0.143 | 0.007 | 21.030 | p < 0.05 | |
−0.017 | 0.003 | −4.686 | p < 0.05 | |
0.144 | 0.006 | 26.107 | p < 0.05 | |
−0.116 | 0.002 | −46.762 | p < 0.05 | |
−0.009 | 0.003 | −3.670 | p < 0.05 | |
−0.016 | 0.004 | −3.977 | p < 0.05 |
Parameter | Estimate | Standard Error | Z | p-Value |
---|---|---|---|---|
Number of maternal mortalities (Y1) | ||||
−11.274 | 0.119 | −94.127 | p < 0.05 | |
−0.113 | 0.026 | −4.312 | p < 0.05 | |
0.047 | 0.008 | 5.948 | p < 0.05 | |
0.229 | 0.027 | 8.438 | p < 0.05 | |
−0.037 | 0.005 | −7.323 | p < 0.05 | |
−0.077 | 0.008 | −11.437 | p < 0.05 | |
0.055 | 0.005 | 12.159 | p < 0.05 | |
−12.243 | 0.538 | −22.760 | p < 0.05 | |
0.109 | 0.009 | 11.254 | p < 0.05 | |
0.096 | 0.003 | 35.748 | p < 0.05 | |
−0.138 | 0.009 | −14.912 | p < 0.05 | |
0.073 | 0.004 | 18.467 | p < 0.05 | |
−0.084 | 0.003 | −30.094 | p < 0.05 | |
0.087 | 0.003 | 26.189 | p < 0.05 | |
Number of early neonatal mortalities (Y2) | ||||
−4.917 | 0.296 | −16.627 | p < 0.05 | |
0.054 | 0.036 | 1.485 | p > 0.05 | |
−0.009 | 0.023 | −0.421 | p > 0.05 | |
−0.046 | 0.037 | −1.231 | p > 0.05 | |
0.020 | 0.031 | 0.655 | p > 0.05 | |
−0.013 | 0.005 | −2.713 | p < 0.05 | |
0.051 | 0.005 | 10.056 | p < 0.05 | |
3.252 | 0.396 | 8.218 | p < 0.05 | |
−0.159 | 0.023 | −6.904 | p < 0.05 | |
−0.059 | 0.013 | −4.626 | p < 0.05 | |
0.383 | 0.035 | 10.827 | p < 0.05 | |
−0.235 | 0.026 | −9.089 | p < 0.05 | |
−0.021 | 0.003 | −6.562 | p < 0.05 | |
0.048 | 0.004 | 12.068 | p < 0.05 |
BZIPIGR Type II Model | SSE | RMSE |
---|---|---|
Model with exposure variables | 218.8805 | 1.7811 |
Model without exposure variables | 620.6658 | 2.9992 |
N | BZIPIGR Type II Model | SSE | RMSE |
---|---|---|---|
N = 75 | Model with exposure variables | 314.7814 | 2.1359 |
Model without exposure variables | 369.6821 | 2.3147 | |
N = 100 | Model with exposure variables | 584.6494 | 2.9109 |
Model without exposure variables | 4241.603 | 7.8404 |
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Ermawati, E.; Purhadi, P.; Rahayu, S.P. A Comparison of Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Models with and without Exposure Variables. Symmetry 2022, 14, 277. https://doi.org/10.3390/sym14020277
Ermawati E, Purhadi P, Rahayu SP. A Comparison of Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Models with and without Exposure Variables. Symmetry. 2022; 14(2):277. https://doi.org/10.3390/sym14020277
Chicago/Turabian StyleErmawati, Ermawati, Purhadi Purhadi, and Santi Puteri Rahayu. 2022. "A Comparison of Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Models with and without Exposure Variables" Symmetry 14, no. 2: 277. https://doi.org/10.3390/sym14020277
APA StyleErmawati, E., Purhadi, P., & Rahayu, S. P. (2022). A Comparison of Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Models with and without Exposure Variables. Symmetry, 14(2), 277. https://doi.org/10.3390/sym14020277