## 3 Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **Mean** &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & **Minimum** & **Maximum** & **VIF** \\ \hline The percentage of active integrated service & & & & & \\ post (\(X_{1}\)) & 80.95 & 14.91 & 31.00 & 98.00 & 1.871 \\ \hline The percentage of active family planning & & & & & \\ participants (\(X_{2}\)) & 75.40 & 3.39 & 67.03 & 82.97 & 1.186 \\ \hline The percentage of the population with & & & & & \\ BPJS health insurance (\(X_{3}\)) & 50.47 & 10.70 & 32.83 & 74.87 & 1.998 \\ \hline Education index (\(X_{4}\)) & 0.628 & 0.075 & 0.490 & 0.770 & 2.999 \\ \hline The percentage of household that has & & & & & \\ improved sanitation (\(X_{5}\)) & 72.20 & 18.87 & 25.51 & 97.43 & 3.104 \\ \hline The number of live birth (\(q_{1}\)) & 15,240 & 10,370 & 2012 & 44,378 & \\ \hline The number of under-5 population (\(q_{2}\)) & 14,787 & 10,008 & 2079 & 41,646 & \\ \hline The number of pregnant women (\(q_{3}\)) & 59,252 & 39,641 & 8013 & 168,060 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary statistics of predictor variables and exposure variables. Figure 3: Distribution of the number of maternal deaths in East Java in 2019. Figure 2: Distribution of the number of under-5 deaths in East Java in 2019. The higher the value of the education index, the better the quality of education and society, which will consequently improve the quality of life. As for the environment variables, there was a large gap in the percentage of households with improved sanitation, with the minimum percentage being 25.25%. This means that there are still many households with inadequate sanitation. Furthermore, a multicollinearity test, which assumes that there is no relationship among predictor variables (mutually independent), was carried out as a requirement for the regression analysis. In this study, the variance inflation factor (VIF) criteria was used to identify multicollinearity among predictor variables. The last column in Table 2 shows that the VIF value of all of the predictor variables is lower than ten (VIF \(<\) 10). Thus, there are no multicollinearity issues among the predictor variables. An initial examination of the relationship between the response and the predictor variables is important because it relates to the initial description of the relationships between variables found in the modeling. Based on Figure 4, the relationship between the predictor variable and the response variable seems non-linear. Log(\(Y_{1}/q_{1}\)) has the strongest correlation with \(X_{3}\) (\(-\)0.23). Meanwhile, log(\(Y_{2}/q_{2}\)) has the strongest correlation with \(X_{1}\) (\(-\)0.36) and log(\(Y_{3}/q_{3}\)) has the strongest correlation with \(X_{2}\) (\(-\)0.29). Several assumptions must be met before carrying out GWMPIGR modelling. Specifically, the response variable is not Poisson distributed, and there is spatial heterogeneity. Testing the distribution of the response variables was carried out using the Crockett test, and it was found that the response variables did not have a trivariate Poisson distribution (because there were three responses). This result is also supported by the issue of overdispersion on the response variables. The methods used to test the overdispersion are deviance per degree of freedom (deviance/df) and the Lagrange multiplier (LM) test, the test results of which are shown in Table 2.  
Overdispersion exists if the value of deviance/df is greater than one and the LM method produces a value of \(\chi^{2}>Z_{\pi}\) or a \(p\)-value of \(<\)\(\alpha\). Based on Table 3, there are cases of overdispersion on the response variable. Therefore, the GWMPIGR model can be used  
Figure 4: The matrix plot of the response variable and predictor variables. to model data on the number of infant, under-5 and maternal deaths in East Java in 2019.