Ijmet 10 01_063

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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 01, January 2019, pp. 626–632, Article ID: IJMET_10_01_063
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=01
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
SPATIAL AUTOREGRESSIVE MODEL FOR
MODELING OF HUMAN DEVELOPMENT INDEX
IN EAST JAVA PROVINCE
Wara Pramesti
Faculty of Mathematics and Natural Science, Adi Buana University, Surabaya, Indonesia.
Agus Suharsono
Department of Statistics, FMKSD, Institut Teknologi Sepuluh Nopember, Surabaya,Indonesia
ABSTRACT
The Human Development Index (HDI) is set by the United Nations (UN) as a measure
of human development standards. HDI can also be used as a determinant of a country
including developed and developing countries. HDI is formed based on three basic
dimensions, namely longevity and healthy life, knowledge and decent living standards.
The purpose of this study was to model the HDI with the Spatial Autoregressive Model,
and determine the factors that influence HDI in each district / city in East Java, namely
the average length of school, literacy rates, per capita expenditure, the percentage of
poor people, and school expectations. The results of the analysis show that the average
school years, literacy rates, per capita expenditure, and district / city school expectations
in East Java significantly influence the human development index. The coefficient of
determination is 0.9916, indicating that variations in HDI can be explained by the model
of 99.16%, and 0.84% explained by factors that do not enter the model.
Keywords: Queen Contiguity, Spatial Autoregressive Model, HDI
Cite this Article: Wara Pramesti and Agus Suharsono, Spatial Autoregressive Model for
Modeling of Human Development Index in East Java Province, International Journal of
Mechanical Engineering and Technology, 10(01), 2019, pp.626–632
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&Type=01
1. INTRODUCTION
HDI is an important indicator to measure success in an effort to build the quality of human life
and can determine the ranking or level of development of a region. This HDI is formed based on
3 (three) basic dimensions, namely longevity and healthy life, knowledge and decent living
standards. HDI is set by the United Nations (UN) as a measure of human development standards.
Globally, HDI can also be used as a determinant of a country including developed and developing
countries.
Data from the Central Statistics Agency (BPS) on human development in East Java in 2016
continued to progress marked by continued increase in East Java HDI. In 2016, East Java HDI

Wara Pramesti and Agus Suharsono
reached 69.74, an increase of 0.79 points compared to East Java HDI in 2015 which was only
68.95 (BPS, 2017). HDI figures are presented at the national, provincial and district / city levels.
The presentation of HDI according to the regions allows each province and district / city to know
human development maps both in terms of achievement, position, and inter-regional disparity.
Thus, it is expected that each region will improve development performance (e.g.
Mangkoedihardjo, 2007; Mangkoedihardjo and Triastuti, 2011) by paying attention to the
surrounding area, because the surrounding area will contribute more. This is in accordance with
the laws of geography proposed by Tobler which states "everything is related to everything else,
but things are more related than distant things". Everything is related to one another, but
something closer will be more influential than something far away. Based on the Tobler law, it
can be interpreted that the district / city HDI in East Java which has a close location certainly has
a higher relationship.
Factors that influence the HDI include the average length of school, literacy rates, life
expectancy, the percentage of poor people and school expectations. According to Tobler's law
problems can be examined based on location effects or spatial methods. So to find out the
influence of these factors can be used analysis that includes location effects, namely the spatial
regression analysis approach. Based on data types, spatial modeling can be differentiated into
modeling with point and area approaches. Types of point approaches include Geographically
Weighted Regression (GWR), Geographically Weighted Poisson Regression (GWPR), Space-
Time Autoregressive (STAR), and Generalized Space Time Autoregressive (GSTAR). The types
of area approaches include Spatial Autoregressive Models (SAR), Spatial Error Models (SEM),
Spatial Durbin Models (HR), Conditional Autoregressive Models (CAR), Spatial Autoregressive
Moving Average (SARMA), and Data Panel Regression. However the STAR, GSTAR and VAR
models can only be used to analyze space-time relationship for one variable only. Spatial Vector
Autoregressive developed by (Sumarminingsih. E, 2018) and (Novianto. M. A, 2018 ) is the
model to analyze space-time data which has more than one variable. While the VAR Model is
one form of multivariate time series analysis used to predict if the variables observed are
many and correlate with each other (Suharsono. A, 2018)
The Spatial Autoregresive (SAR) model is a linear regression model which in the response
variable has spatial correlation (Anselin. L, 1988). SAR model is a model that is formed from a
combination of simple linear regression models with spatial lag of independent variables using
cross section data. SAR model is formed if the value of ρ ≠ 1 and λ = 0 (Anselin. L, 1988). In
SAR modeling the fundamental component of the model is the presence of a spatial weighting
matrix. This spatial weighting matrix reflects the relationship between one region and another.
The weighting matrix used is Queen Contiguity. Queen Contigity is a contact concept that gives
the value wij = 1 for areas that intersect the sides and angles of the observed area and the value of
wij = 0 for other regions.
Research on Human Development Index Modeling Using Spatial Panel Fixed Effect,
concluded that the independent variables that significantly influence the Human Development
Index are School Participation Figures and Poverty Percentages in each district / city (Novian. T
and Rita. R, 2016). The study entitled modeling the Human Development Index of East Java
Province Using Ridge Logistic Regression Method, concluded that infant mortality, illiteracy
rates and school enrollment rates affected the human development index (Dwi M.P and Vita R,
2015). The results of the study with the title East Java Human Development Index Modeling with
Spatial Regression Approach, states that per capita income, the percentage of poor people,
average school years have a significant effect on the human development index, both from spatial
autoregressive and spatial error models (Wara. P and Artanti. I, 2018),

Spatial Autoregressive Model for Modeling of Human Development Index in East Java Province
This study aims to determine the factors that influence the HDI using the autoregressive
spatial model. It is expected that the use of this spatial autoregressive model can determine the
factors that influence HDI in each district / city in East Java.
2. METHODOLOGY
The data used are secondary data obtained from (BPS, 2017), which consists of data on Human
Development Index, Average School Length, Literacy Rate, Per Capita Expenditure, Percentage
Poor Population, and School Expectation.
The response variable in this study is HDI. HDI was introduced by the United Nations
Development Program (UNDP) in 1990 and published regularly in the annual Human
Development Report (HDR) report. The HDI explains how residents can access the results of
development in obtaining income, health, education and so on. Variable predictors are 5, namely
1. Average School Duration, which is the number of years of study of residents aged 15
years and over who have been completed in formal education (not including the year
of repeating).
2. Literacy rates, a proportion of the population aged 15 years and over who have the
ability to read and write simple sentences in Latin letters, Arabic letters, and other
letters (such as Javanese, starch, etc.).
3. Per capita expenditure, which is the cost incurred for the consumption of all household
members for a month divided by the number of household members
4. Percentage of Poor Population, which is a population with per capita expenditure per
month below the Poverty Line
5. School Expectation Numbers, are defined as the length of school (in years) expected
by children at a certain age in the future
The first step in the analysis is multiple linear regression modeling, followed by testing
assumptions. Because the assumption of independence or dependence between observations is
not fulfilled, it is continued by providing spatial weighting of Queen Contiguity to find out the
relationship between observation areas seen from the side contact Test spatial dependencies or
relationships between observations that are close to the Morans' test, if the test is significant, then
testing Lagrange Multiplier (LM) to determine the appropriate spatial modeling. If an appropriate
model has been obtained, testing the assumptions of normality, homogeneity of variance and the
last interpretation of the model
3. RESULTS AND DISCUSSION
The first step is Ordinary Least Square (OLS) regression analysis to see whether there is a
tendency for dependency or dependency between observations. The estimation results and
parameter testing are shown in Table 1 below:
Table 1 Results of Parameter Estimation and Testing
Variable Coefficient P Value
Konstanta 23,289 0,00013
X1 1,33956 0,00001
X2 0,15495 0,00471
X3 0,000782147 0,00000
X4 0,0052508 0,89477
X5 1,07615 0,00001
Based on Table 1, all significant variables, except the percentage variable of the poor
population. From the results of the analysis it is known that if X2 (AMH), X3 (PPK), X4 (PPM)

and X5 AHS are considered constant and when X1 (RRLS) increases, the East Java HDI will also
increase, as well as X1 (RLLS), X3 (PPK), X4 (PPM) and X5 (AHS) are considered constant and
X2 (AMH) increases, the East Java HDI will also increase. Likewise with other variables
The coefficient of determination obtained is 0.989, meaning that the ability of the model to
explain the total variation of HDI is 98.9%, and 1.1% is explained by variables that do not enter
the model. Regression model obtained:
54321 07615,10052508,0000782147,015495,01,33956x3,2892ˆ xxxxy +++++=
Test assumptions in regression include testing of residual variance homogeneity,
independence and normality testing of residual models. The test results show that only
independence assumptions are not fulfilled. Breusch-Pagan is used to test the assumption of
homogeneity of variance, and obtained a Breusch-Pagan value of 2.2384 with a probability value
of 0.32654 greater than 0.05, which means that the assumption of a homogeneous variance is
fulfilled. The independence test using Durbin Watson and the DW value obtained at 1.17283 lies
in the interval 0 <1.17283 <1.2614, which means that the independence assumption is not
fulfilled. Normality testing is used Kolmogorov Smirnov Test with a probability value of 0.200
greater than 0.05, then a residual assumption with a normal distribution is fulfilled. Independent
assumptions are not met, then proceed to the spatial regression approach, by testing spatial
dependencies to determine whether or not there are spatial or location influences in the model.
3.2. Spatial Effect Test
The spatial aspects that occur between regions consist of two types, namely spatial dependencies
and spatial heterogeneity. Testing of spatial dependencies is done by the Morans'I test (Lee, J.,
& Wong, D.W.S., 2001). The results of the calculation, obtained an I value of 0.9420 greater than
the Io value, it can be said that the observations form a cluster or group pattern. In Moran's I test,
the probability value of 0.04421 was less than α, it can be concluded that there are spatial
dependencies or interrelationships between regions.
3.3. Test Lagrange Multiplier
The Lagrange Multiplier test is used to test the effects of spatial dependencies (LeSage. J.P.,
1999). The results obtained are used as the basis for the formation of appropriate spatial
regression models. The Lagrange Multiplier test results can be seen in Table 2 below:
Table 2 Lagrange Multiplier Test Results
Test Value P-Value
LM lag (SAR) 8,8883 0,00287
LM error (SEM) 0,2472 0,61905
Significance Level α = 5%
In Table 2 shows that from the Lagrange Multiplier test results obtained the probability values
of Lagrange Multiplier (Lag) and Lagrange Multiplier (error) respectively, which are 0.00287
and 0.61905, so it can be decided that there is a spatial dependence on the response variable. The
probability value from the smallest Lagrange Multiplier test results will be used for modeling.
Based on Table 2, the model used is the Spatial Autoregresive Model (SAR)
3.4. Spatial Autoregressive Model (SAR)
Based on the results of the Lagrange Multiplier (LM) test, there is a spatial lag dependence on
the response variable, then the analysis is done using Spatial Autoregressive (SAR) modeling.
The test results can be seen in table 3 below:

Table 3 Results of Estimated Parameters in the SAR Model
Variable Estimate Std. Error t-value Prob.
Rho 0,108922 0.0322441 3,37806 0.00073
Intercept 21,3654 4,3668 4.89269 0,00000
X1(RRLS) 1,3607 0.201249 6.76127 0.00000
X2(AMH) 0,0933632 0,0439702 2,12333 0,03373
X3(PPK) 0,000713399
8,264e-
005
8,63393 0.00000
X4(PPM) -0,0195066 0,0320619
-
0,60840
0,54292
X5(AHS) 1,15195 0.169706 6,78792 0.00000
R-Square (R2
) = 99,16%
Based on Table 3, it can be seen that there is an effect of location dependence on an area with
another region, which is indicated by the Rho value with a probability value of 0.00073 less than
alpha (5%). From Table 3, it can also be seen that the factors that influence the increase in HDI
are RRLS, AMH, PPK and AHS variables.
The Spatial Autoregressive (SAR) model obtained
∑≠=
+−+++−=
n
jij
iiiiijiji xxxxxYWy
,1
54321 15,102,00007,009,036,111,037,21ˆ
From the results of the analysis in Table 3, it is known that there is only one independent
variable that is not significant, namely the percentage of poor people (X4), which has a value of
-0.60840 and a probability value of 0.54292 more than. For RRLS (X1), AMH (X2), PPK (X3)
and AHS (X5) variables, each has a probability value of less than 0.05, so it can be concluded
that the variable length of school years, literacy rates, expenditure per capita and school
expectations have a significant effect on the Human Development Index in East Java districts /
cities.
Based on the model obtained if the literacy rate, per capita expenditure and school
expectations are considered constant and the average length of school increases, the East Java
HDI will also increase. If the average length of school, literacy rate, percentage of poverty and
school expectations are considered constant and per capita expenditure rises, the East Java HDI
will rise. Likewise for other variables.
The significant coefficient ρ indicates that if a region is surrounded by other regions as much
as k, then the influence of each surrounding region is 0.11 times the average response variable
around it. The following is an example if the SAR model observed was Pacitan District. Pacitan
Regency has an area code (1) bordering on Ponorogo Regency which has an area code (2), and
Trenggalek Regency with an area code (3). The model formed becomes:
54321321
15,102,00007,009,036,1037,0037,037,21ˆ iiiii
xxxxxyyy +−+++−−=
This model can be interpreted that if other factors are considered constant, and if the literacy
rate rises by one unit, it will increase the value of the Human Development Index by 0.09 units
with each district in the vicinity namely Ponorogo Regency, and Trenggalek each giving a close
influence amounting to 0.037.
Determination coefficient R2
obtained at 0.9916 or 99.16% shows that variations in the
Human Development Index can be explained by the average length of school (X1), literacy rate
(X2), per capita expenditure (X3), percentage of poor population (X4), numbers school
expectations (X5), amounting to 99.16% and the rest of 0.84% explained by other variables not
in the model. This SAR model has AIC = 67.1151

3.5. Test the Spatial Autoregressive Model (SAR) Assumption
After obtaining the spatial regression equation model with the SAR model, then testing the
assumption of residual variance homogeneity, the residual assumption is normally distributed.
The test results show that both assumptions are fulfilled.
The test for residual variance homogeneity is the Breusch-Pagan test. From the test results
obtained a probability value of 0.06 more than α (0.05), it can be decided to fail to reject H0, so
it can be concluded that the residual variance in the model is homogeneous. Independent
assumption test with Durbin Watson test. The Durbin Watson value obtained is 1.87031 with du
= 1.7916 and 4 - du = 2.2084, then the Durbin-Watson value lies between du and 4 - du, which
means failing to reject H0, so it can be concluded that there is no autocoreation. Testing the
residual normality assumptions was carried out using the Kolmogorov-Smirnov test. Based on
the test results obtained a probability value of 0.054 more than α (0.05), it was decided to fail to
reject H0, which means that the residual assumptions are normally distributed.
4. CONCLUSION
Based on the objectives of the research and data analysis, it can be concluded:
1. The SAR model was formed to model the district / city HDI in East Java by using Queen
Contiguity weighting:
∑≠=
+−+++−=
n
jij
iiiiijiji xxxxxYWy
,1
54321 15,102,00007,009,036,111,037,21ˆ
2. Factors that influence the HDI of districts / cities in East Java are RRLS, AMH, PPK, and
AHS
REFERENCES
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Academic Publishers.
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[4] Lee, J., & Wong, D.W.S., (2001). Statistical Analysis with Arcview GIS. John Wiley and
Sons, New York.
[5] LeSage. J.P., (1999), “The Theory and Practice of Spatial Econometrics”, Asia Pasific Press.
[6] Mangkoedihardjo, S. (2007). Physiochemical Performance of Leachate Treatment, a Case
Study for Separation Technique. Journal of Applied Sciences, 7(23), 3827-3830.
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[8] Novian T dan Rita R, (2016), Pemodelan Indeks Pembangunan Manusia Menggunakan
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2008 - 2013), Jurnal Gaussian vol 5 No 1, pp. 173-182.
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[10] Sumarminingsih, E., Setiawan, Suharsono, A., Ruchjana, B.N., (2018). Spatial vector auto
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[11] Suharsono, A., Ahmad, IS., Wibisono, A. and Pramesti, W. (2018). Modeling of
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Regression Approach, Advances in Social Science, Education and Humanities Research,
volume 226, 1st International Conference on Social Sciences (ICSS 2018).

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