SPATIAL AUTOREGRESSIVE MODEL FOR MODELING OF HUMAN DEVELOPMENT INDEX IN EAST JAVA PROVINCE

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International Journal of Mechanical Engineering and Technology (IJMET) Volume 10, Issue 01, January 2019, pp. 626 62, Article ID: IJMET_10_01_06 Available online at http://www.iaeme.com/imet/issues.

1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 10, Issue 01, January 2019, pp , Article ID: IJMET_10_01_06 Available online at ISSN Print: and ISSN Online: 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 , 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 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 (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 editor@iaeme.com

2 Wara Pramesti and Agus Suharsono reached 69.74, an increase of 0.79 points compared to East Java HDI in 2015 which was only (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. Mangkoedihardo, 2007; Mangkoedihardo 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 wi = 1 for areas that intersect the sides and angles of the observed area and the value of wi = 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), editor@iaeme.com

3 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.).. 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. 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 2,289 0,0001 X1 1,956 0,00001 X2 0, ,00471 X 0, ,00000 X4 0, ,89477 X5 1, ,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), X (PPK), X4 (PPM) editor@iaeme.com

4 Wara Pramesti and Agus Suharsono and X5 AHS are considered constant and when X1 (RRLS) increases, the East Java HDI will also increase, as well as X1 (RLLS), X (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: y ˆ = 2, ,956x1 + 0,15495 x2 + 0, x + 0, x 4 + 1, 07615x5 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 with a probability value of 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 lies in the interval 0 < <1.2614, which means that the independence assumption is not fulfilled. Normality testing is used Kolmogorov Smirnov Test with a probability value of 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..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 greater than the I o value, it can be said that the observations form a cluster or group pattern. In Moran's I test, the probability value of was less than α, it can be concluded that there are spatial dependencies or interrelationships between regions... 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) 8,888 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 and , 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).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 below: editor@iaeme.com

5 Spatial Autoregressive Model for Modeling of Human Development Index in East Java Province Table Results of Estimated Parameters in the SAR Model Variable Estimate Std. Error t-value Prob. Rho 0, , Intercept 21,654 4, ,00000 X1(RRLS) 1, X2(AMH) 0,0962 0, ,12 0,07 X(PPK) 0, ,264e , X4(PPM) -0, , , ,54292 X5(AHS) 1, , R-Square (R 2 ) = 99,16% Based on Table, 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 less than alpha (5%). From Table, 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 yˆ = 21,7 0,11 i n = 1, i WiY + 1,6 xi1 + 0,09xi 2 + 0,0007xi 0,02xi 4 + 1, 15xi5 From the results of the analysis in Table, 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 and a probability value of more than. For RRLS (X1), AMH (X2), PPK (X) 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 (). The model formed becomes: y ˆ = 21,7 0,07 y 0,07 y + 1,6 x + 0,09x + 0,0007x 0,02x + 1, 15x 1 2 i1 i2 i i 4 i5 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 Determination coefficient R 2 obtained at 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 (X), 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 = editor@iaeme.com

6 Wara Pramesti and Agus Suharsono.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 reect 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 with du = and 4 - du = , then the Durbin-Watson value lies between du and 4 - du, which means failing to reect 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 more than α (0.05), it was decided to fail to reect H0, which means that the residual assumptions are normally distributed. 4. CONCLUSION Based on the obectives 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: yˆ = 21,7 0,11 i n = 1, i WiY + 1,6 xi1 + 0,09xi 2 + 0,0007xi 0,02xi 4 + 1, 15xi5 2. Factors that influence the HDI of districts / cities in East Java are RRLS, AMH, PPK, and AHS REFERENCES [1] Anselin, L. (1988). Spatial Econometrics: Methods and Models. Dordrecht: Kluwer Academic Publishers. [2] BPS (2017), Indeks Pembangunan Manusia Indonesia [] Dwi, MP dan Vita R,(2015), Pemodelan Indeks Pembangunan Manusia (IPM) Provinsi Jawa Timur Dengan Menggunakan Metode Regresi Logistik Ridge, Jurnal Sains dan Seni ITS, vol 4 No 2. [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] Mangkoedihardo, S. (2007). Physiochemical Performance of Leachate Treatment, a Case Study for Separation Technique. Journal of Applied Sciences, 7(2), [7] Mangkoedihardo, S. and Triastuti, Y. (2011). Vetiver in Phytoremediation of Mercury Polluted Soil with the Addition of Compost. Journal of Applied Sciences Research, 7(4): [8] Novian T dan Rita R, (2016), Pemodelan Indeks Pembangunan Manusia Menggunakan Spatial Panel Fixed Effect (Studi Kasus: Indeks Pembangunan Manusia Propinsi Jawa Tengah ), Jurnal Gaussian vol 5 No 1, pp [9] Novianto, M.A., Suhartono, Prastyo, D.D., Suharsono, A., Setiawan., (2018). GSTARIX Model for Forecasting Spatio-Temporal Data with Trend, Seasonal and Intervention, Journal of Physics: Conference Series, IOP Conf, ICRIEMS 5. Yogyakarta, Indonesia [10] Sumarminingsih, E., Setiawan, Suharsono, A., Ruchana, B.N., (2018). Spatial vector auto regressive model with calendar variation for East Java inflation and money supply. Applied Mathematics and Information Sciences, Vol 12, no 6, Nov 2018, pp editor@iaeme.com

7 Spatial Autoregressive Model for Modeling of Human Development Index in East Java Province [11] Suharsono, A., Ahmad, IS., Wibisono, A. and Pramesti, W. (2018). Modeling of Autoregressive Moving Average and Vector Autoregressive for Forecasting Stock Price Index in ASEAN Countries, International Journal of Mechanical Engineering and Technology, 9(11), pp [12] Wara P dan Artanti I, (2018), East Java Human Development Index Modeling with Spatial Regression Approach, Advances in Social Science, Education and Humanities Research, volume 226, 1st International Conference on Social Sciences (ICSS 2018) editor@iaeme.com

SPATIAL MODELING FOR HUMAN DEVELOPMENT INDEX IN CENTRAL JAVA

SPATIAL MODELING FOR HUMAN DEVELOPMENT INDEX IN CENTRAL JAVA Moh. Yamin Darsyah 1) Iswahyudi Joko Suprayitno 2) Bambang W Otok 3) Brodjol SS Ulama 4) ABSTRACT Human Development Index (HDI) is one of measuring