Modeling of Infant Mortality Rate in East Java Province Using Mixed

Geographically Weighted Regression Approach for Improving

Quality of Health Services

Ninda Ayu Puspitasari

, Nadia Murbarani

, Nopiyanti

, Sartika Aprilia

, Nur Chamidah

Student of Program Study of Statistics, Department of Mathematics, Universitas Airlangga, Surabaya, Indonesia

Department of Mathematics, Faculty of Sciences and Technology, Universitas Airlangga, Surabaya, Indonesia

Keywords: East Java Province , Infant Mortality Rate, Mixed Geographically Weighted Regression

Abstract: Infant mortality is defined as the death of a baby aged less than one year old. Sustainable Development

Goals (SDG) program is a sustainable development program in which there are 17 goals and 169

measurable targets with specified deadlines. One of the targets to be achieved by the year 2030 is to be able

to reduce infant mortality at least up to 12 every 1,000 live births. Infant Mortality Rate in East Java

Province still shows a high number of 5,196 babies die every year. It shows that as many as 13 babies die

every day. The mixed geographically weighted regression (MGWR) model is a combination between global

regression and local regression models where some predictor variables affect globally and the others affect

locally to the response. This study aims to select the best model based on the smallest AICc (Akaike

Information Criterion corrected) value using fixed Gaussian weighted. The variable that affect globally is

percentage of pregnant mothers visit. While other predictor variables that affect locally are percentage of

Integrated Health Services (Posyandu), percentage of number of households with decent sanitation, and

percentage of low birth weight infants.

1 INTRODUCTION

Infant mortality is the death of a baby aged less than

one year old. Infant mortality is measured as the

infant mortality rate, which is the number of child

deaths under one year per 1000 births in one year

(Central Bureau of Statistics, 2012). SDGs is a

sustainable development program in which there are

17 goals with 169 measurable targets with specified

deadlines. SDGs is a world development agenda

aimed at human and planetary welfare. One of the

goals of SDGs is good health, which ensures a

healthy life and promotes well-being for all people

of all ages. The goal has 13 targets, one of which is

by 2030 ending preventable infant and toddler

deaths with all countries trying to reduce infant

mortality by at least 12 per 1,000 live births (Annisa,

2013). The condition of Infant Mortality Rate (IMR)

and Neonatal Mortality Rate in East Java Province is

relatively small, however, the absolute mortality rate

still shows a high number of 5,196 toddlers per year.

It shows that as many as 13 babies died and 14

toddlers die every day. The Mixed Geographically

Weighted Regression (MGWR) model is a

combination model of global regression with Global

Weighted Regression (GWR) considering the

situation where some predictor variables affecting

the response are global and other predictor variables

are localized according to the location of the data

observation (Asih et al, 2013).

2 LITERATURE REVIEW

2.1. Infant Mortality Rate

Infant Mortality Rate (IMR) describes the number of

infant mortality of less than one year per 1000 live

births in a given year. IMR is one indicator of health

development successes that has been declared in

National Health System and even used as a central

indicator of success of health development in

Indonesia (Azizah, 2013). Besides, IMR also reflects

the level of maternal health, environmental health,

and general level of socio-economic development of

the community because the IMR is very sensitive to

Puspitasari, N., Murbani, N., Nopriyanti, ., Aprilia, S. and Chamidah, N.

Modeling of Infant Mortality Rate in East Java Province Using Mixed Geographically Weighted Regression Approach for Improving Quality of Health Services.

DOI: 10.5220/0007546105150519

In Proceedings of the 2nd International Conference Postgraduate School (ICPS 2018), pages 515-519

ISBN: 978-989-758-348-3

515

changes in the level of health and welfare of the

community.

2.2. Mixed Geographically Weighted

Regression Model

Mixed Geographically Weighted Regression

(MGWR) is a combination of global linear

regression model with GWR model. Thus, the

MGWR model will produce parameter estimators

that are partly global and some others are localized

according to the location of observation

(Fotheringham et al 2002). The parameter estimation

on MGWR model can be done by WLS (Weighted

LeastSquare) method as in GWR model (May et al,

2004). The general MGWR model can be written in

the form of:

…………………………………………………………(1)

Estimation of MGWR model parameters with

Weighted Least Square (WLS) approach. Estimation

of MGWR model parameters is as follows:

…………………..(2)

given that is the global predictor variable matrix,

is the local predictor variable matrix, β_g is the

global predictor variable parameter vector and

is the local predictor variable parameter

matrix.

2.3. Test The Suitable of Model MGWR

Test the suitability of the MGWR model is aimed to

find out which model is suitable or not. The

hypothesis is as follows:

…………………………….(3)

Sustainability test of the MGWR model is aimed to

find out which model is suitable or not. The

hypothesis is as follows:

…………………(4)

2.4. Concurrent Test of Global

Parameter

The simultaneous hypothesis test is intended to

know the significance of predictor variables in the

MGWR model simultaneously on the parameter of

global predictor variable . The

collision hypothesis in this test is:

……………..(5)

Statistical test used in the simultaneous test of global

parameters is as follows:

……. (6)

2.5. Concurrent Test of Local

Parameters

In the simultaneous test, this local parameter uses

the following hypothesis:

…………………………………………………..(7)

statistical test used in the simultaneous test of local

parameters is as follows:

…………..(8)

2.6. Partial Test of Global Parameters

In partial test, this local parameter uses hypothesis as

follows:

………………………………………(9)

statistical test used in the partial test of this global

parameter is:

…………………………….............. (10)

2.7. Partial Test of Local Parameters

The hypothesis in this local partial test is as follows:

………………………….…(11)

statistical test and partial test of local parameters can

be calculated using the following formula:

………………………………………..(12)

ICPS 2018 - 2nd International Conference Postgraduate School

516

3 MATERIAL AND METHODS

3.1. Source of Data

The data used in this study is secondary data

obtained from the publication Health Profile of East

Java Province 2016. The observation unit used is 38

administrative areas in East Java Province consisting

of 29 districts and 9 cities.

3.2. Research Variable

Variables used in this study include 8 variables

consisting of one response variable and 7 predictor

variables as follows:

Infant Mortality Rate

Percentage of Infants Gaining Exclusive

Breast Milk

Percentage of Integrated Health Services

(Posyandu)

Percentage of Pregnant Mothers Visit

Percentage of Infants Gaining Health

Services

Percentage of Households Gaining Clean

Drinking Water

Percentage of Number of Households with

Decent Sanitation

Percentage of Low Birth Weight Infants

4 RESULT AND DISCUSSION

4.1 Modeling of Infant Mortality Rate

in East Java with MGWR

4.1.1 Classic Assumption Test

Classic assumption test consists of 4 subjects

namely normality testing, multicollinearity

testing, heterogeneity testing, and spatial

dependency testing.

Based on the results obtained, the data used

meet the classical assumption

4.1.2 Geographically Weighted Regression

Modeling (GWR) Modeling

The selection of the kernel function weights

used was conducted by doing a comparison of

the smallest AICc values based on the four

kernel function weights (Fixed Gaussian, Fixed

Bisquare, Adaptive Gaussian and Adaptive

Bisquare) to obtain the best weights. The best

weights were used to estimate the parameters in

each regency / city in East Java Province.

Table 1 : Value of AICc and R2 GWR model

Kernel

Weighted

Funciton

Minimum

AICc

Fixed Gaussian

0,47061

256,523715

Based on Table 4.1, the best kernel-

weighted function is Fixed Gaussian which has

the smallest AICc value that is 256,523715 so

that Fixed Gaussian kernel weighting function

was used to estimate the best GWR model in

this research.

4.1.3 Mixed Geographically weighted

Regression (MGWR) Modeling

The determination of the kernel function

weights is do the smallest Minimum AICc

value comparison based on the three kernel

functional weights that are Fixed Gaussian,

Fixed Bisquare, and Adaptive Bisquare to

obtain the best functional weights.

Tabel 2 : Value of AICc dan R

MGWR model

Kernel Weighted

Function

Minimum

AICc

Fixed Gaussian

0,572701

254,705810

Based on Table 4.2 above, it can be seen

that the best Kernel functional weights is Fixed

Gaussian because it has the smallest minimum

AICc value. It is equal to 254,705810, with R2

equals to 57,27%.

After obtaining the best Kernel weighted

functionality on the GWR model and the

MGWR model, the next step was to compare

the best model of both models from the

minimal AICc value.

Table 3 : Comparison of AICc value GWR and

MGWR model

Model

AICc minimum

GWR

256,523715

MGWR

254,705810

Modeling of Infant Mortality Rate in East Java Province Using Mixed Geographically Weighted Regression Approach for Improving

Quality of Health Services

517

Based on Table 4.5, the AICc value of the

MGWR model is smaller than the AICc GWR

model value of 254,705810. Thus, the MGWR

model is the most appropriate for modeling

infant mortality rate in East Java. Based on

testing using GWR 4.0 software obtained the

test results of conformity MGWR model.

Table 4: MGWR conformity model test results

Table 4.4 shows that the F value of 6.3688

> F _ ((30,27,710; 0,05)) is 1.88. Then, the

decision taken was Reject so that it can be

concluded that the obtained MGWR spatial

regression model is appropriate. Once the most

appropriate model was obtained, the next step

was to examine the global parameter

significance using GWR 4.0. software.

Table 5 : Global parameter estimation results

Variable

Estimation

Standard

Residual

-1,533768

0,69718

2,19996

Based on Table 4.5, the global parameter

X_3 has significant effect on infant mortality

rate in East Java since the value of

│t_countage = big | -2,19996 | > 2,04227.

Local parameter testing of the spatial

regression MGWR model is partially

performed at each i-location. This test was

conducted to determine the regression

parameters that affect infant mortality rate in

each district/city in East Java. For example, we

will analyze the estimation model in areas with

the highest infant mortality rate namely

Probolinggo and the lowest infant mortality

rate, Situbondo. The MGWR model for

Probolinggo City is:

MGWR model for Situbondo Regency are:

5 CONCLUSION

Based on the analysis and discussion that has been

performed, the conclusions as follows:

1. The best model obtained for Infant

Mortality Rate in East Java 2016 is Mixed

Geographically Weighted Regression

Model (MGWR) with Gaussian Kernel

weighted function. The MGWR model can

explain the diversity of response variables

of 57.27% with an AICc value of

254,705810.

2. Globally affecting factors of Infant

Mortality Rate in East Java Province is the

Percentage of Pregnant Mothers Visit.

While the factors that influence locally is

the Percentage of Integrated Health

Services (Posyandu), Percentage of

Number of Households with Decent

Sanitation and Percentage of Low Birth

Weight Infants.

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Modeling of Infant Mortality Rate in East Java Province Using Mixed Geographically Weighted Regression Approach for Improving

Quality of Health Services

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