Title Science and Technology Indonesia e-ISSN:2580-4391 p-ISSN:2580-4405 Vol. 8, No. 2, April 2023 Research Paper Spatial Autoregressive Quantile Regression with Application on Open Unemployment Data Ferra Yanuar1*, Tasya Abrari1, Izzati Rahmi HG1, Aidinil Zetra2 1Department of Mathematics and Data Science, Andalas University, 25163, Indonesia2Department of Political Sciences, Andalas University, 25163, Indonesia *Corresponding author: ferrayanuar@sci.unand.ac.id AbstractThe Open Unemployment Level (OUL) is the percentage of the unemployed to the total labor force. One of the provinces withthe highest OUL score in Indonesia is West Java Province. If an object of observation is affected by spatial effects, namely spatialdependence and spatial diversity, then the regression model used is the Spatial Autoregressive (SAR) model. Quantile regressionminimizes absolute weighted residuals that are not symmetrical. It is perfect for use on data distribution that is not normallydistributed, dense at the ends of the data distribution, or there are outliers. The Spatial Autoregressive Quantile Regression (SARQR)is a model that combines spatial autoregressive models with quantile regression. This research used the data regarding OUR in WestJava in 2020 from the Central Bureau of Statistics. This study develops to modeling the Open Unemployment Level in all province inIndonesia using modified spatial autoregressive model with the quantile regression approach. This study compares the estimationresults based on SAR and SARQR models to obtain an acceptable model. In this study, it was found that the SARQR model isbetter than SAR at dealing with the problems of dependency and diversity in spatial data modeling and is not easily affected by thepresence of outlier data. KeywordsOpen Unemployment Level (OUL), Spatial Effects, SAR, SARQR, The Outlier Received: 10 January 2023, Accepted: 11 April 2023 https://doi.org/10.26554/sti.2023.8.2.321-329 1. INTRODUCTION Unemployment is a phenomenon that occurs in all developing countries, including Indonesia. One of the causes of unem- ployment is the lack of job opportunities that are not balanced by the number of job seekers in an area. This leads to an in- crease in the number of unemployed. An indicator to measure high unemployment in an area is the Open Unemployment Level (OUL). OUL is the percentage of unemployed in the total labor force. West Java Province is one of Indonesia’s top three provinces with the highest Open Unemployment level. The OUL situation in West Java Province in August 2021 was 9.82 percent, down 0.64 percentage points compared to Au- gust 2020 (Central, 2021) . However, this value is still too high above the national average. It is necessary to identify which factors are significant in reducing OUL. Factors between regions usually tend to be involved as one factor affecting OUL in an area (Dai and Jin, 2021; Weisberg, 2014), known as spatial effects. Spatial effects are divided into two parts: spatial dependence and spatial diversity. Spatial dependence occurs due to the relationship between regions, while spatial diversity occurs due to the diversity between one region and another. If this happens, the data modeling method used is the Spatial Autoregressive (SAR) regression method (Ver Hoef et al., 2018) . The existence of outlier data will also affect the modeling method used (Yanuar et al., 2023) . Influential outlier data cannot be thrown away because it will eliminate important information related to the data (Yasin et al., 2020; Yasin et al., 2022). Modeling for data containing spatial effects and outliers uses the Spatial Autoregressive Quantile Regression (SARQR) method (Dai and Jin, 2021; Dai et al., 2020; Jin et al., 2016). There has recently been an increase in the research on esti- mating and testing spatial autoregressive quantile models. Jin et al. (2016) explored the quantile regression approach for par- tially linear spatial autoregressive models with possibly varying coefficients using B-spline. (Dai et al., 2022) . Dai et al. (2020) investigated fixed effects quantile regression for general spatial panel data models with both individual fixed effects and time effects based on the instrumental variable method. Dai and Jin (2021) employed the minimum distance quantile regres- https://crossmark.crossref.org/dialog/?doi=10.26554/sti.2023.8.2.321-329&domain=pdf https://doi.org/10.26554/sti.2023.8.2.321-329 Yanuar et. al. Science and Technology Indonesia, 8 (2023) 321-329 sion (MDQR) methodology for estimating the SAR panel data model with individual fixed effects. Zhang et al. (2021a) stud- ied a penalized quantile regression for a spatial panel model with fixed effects. To fill the research gap, this study applied a SARQR model that integlevels the spatial correlations and quantile effects to estimate the effects of regional factors on the Open Unemploy- ment level in West Java province and how they vary with the figure of the Open Unemployment level. It aims to answer the following questions: how SAR and SARQR can produce the acceptable model of Open Unemployment level?, what are the effects of risk factors of Open Unemployment level, and how do they vary across the distribution of the Open Unemploy- ment level?, how does the Open Unemployment level affect the above effects?. The rest of the study is organized as fol- lows. Section 2 describes the available data used in this study. Section 3 introduces the SAR and SARQR models. Section 4 reports the modelling results and discusses the parameter estimations. Section 5 summarizes the remarkable findings and gives further directions. 2. EXPERIMENTAL SECTION 2.1 Materials In this section, the data used in this study is secondary data obtained from the Central Bureau of Statistics for West Java Province from 1 January to 31 December in 2020 (Central, 2021) . West Java Province consists of 18 regencies and 9 cities. The variable used is the percentage of the population (X1), which is the total population in the district/city divided by the total population of the province multiplied by 100%, the percentage of poor people (X2), the Labor Force Participation Level or LFPR (X3), abbreviated Gross Regional Domestic Product or GRDP (X4) and the percentage of Human Devel- opment Index or % HDI (X5) (Candraningtyas and Santosa, 2022; Hapsari and Hasmarini, 2022). The response variable is the Open Unemployment Level or OUL . 2.2 Methods To apply the SAR method, several stages of testing are required to ensure that the SAR method is suitable for modelling the cases raised. Multicollinearity is a condition with a correlation between the independent variables in the regression model. Multicollinearity can be detected using the Variance Inflation Factor (VIF) value as follows (Xu and Huang, 2015) : VIF1 = 1 1 − R21 (1) with Rl 2 is determinant coefficient for predictor variable l, for l = 1,. . . , p. If the VIF value is less than 5, multicollinearity does not occur in the regression model (Yu et al., 2021) . A spatial weighting matrix is a matrix that describes the relationship of each region. The spatial weighting matrix is denoted by W with size n×n, where n represents the number Figure 1. Box plot of variables (a) % Population (X1), (b) % Poor population (X2), (c) LFPR (X3), (d) GRDP (X4), (e) % HDI (X5), and (f) OUL (Y) of observation areas. The spatial weighting matrix is obtained based on the results of standardized contiguity. Matrix conti- guity has three types of contact, namely rook contiguity (side contact between regions), bishop contiguity (corner contact be- tween regions) and queen contiguity (side touch and corner points between regions). Matrix contiguity has a value of 1 if between regions meet the type of contact (Dai and Jin, 2021; Yasin et al., 2020). 2.3 Spatial Effects Spatial effects consist of spatial dependence and spatial diversity. To determine the existence of spatial dependence between regions, a test was carried out with the Moran Index. Moran’s index measures the relationship of observations between an area and other areas close to each other. Moran’s index is defined as follows (Tribhuwaneswari et al., 2022) : I = n ∑n i=1 ∑n j=1 wi j(yi − ȳ)(yj − ȳ)∑n i=1 ∑n j=1 wi j ∑n j=1(yj − ȳ)2 (2) © 2023 The Authors. Page 322 of 329 Yanuar et. al. Science and Technology Indonesia, 8 (2023) 321-329 Figure 2. Spatial Distribution of Open Unemployment Level in West Sumatra (In Percentage) = ∑n i=1 ∑n j=1 wi j(yi − ȳ)(yj − ȳ) S2 ∑n i=1 ∑n j=1 wi j with i and j are the number of data (n), for i≠j, yi is the response variable for all observations i, ȳ is the mean of y, wi j is element of spatial weighting matrix W, and S2 is sample vari- ance. If I is positive, adjacent areas have similar values, and the data pattern tends to be clustered. If I is negative, it means that adjacent areas have different values, and the data pattern tends to spread out. If I is 0, it means no spatial dependence detected (Huang et al., 2010) . The existence of spatial dependence on the dependent variable is also checked in the hypothesis model. The Lagrange Multiplier test is used to determine spatial de- pendence, with the general form of the Lagrange Multiplier as follows (Anselin and Anselin, 1988) : LMlag = ( U′WY S2 )2 nP (3) with nP = T + (WX 𝛽)′M(MX 𝛽) S2 , T = trace((W +W ′)W ), M = I − X(X′X)−1X′, s2 = U′U n , U as a remainder. Where X is matrix of independent variables of size n ×(k+1) and 𝛽 is factor of the regression coefficient of size (k+1) ×1. If the LM lag> X2𝛼,1, it indicates that there is a spatial depen- dence on the dependent variable. If a model contains spatial dependence, the modelling is carried out using a Spatial Autore- gressive model (Anselin and Anselin, 1988) . As for detecting spatial diversity, it can use the Breush-Pagan (BP) test with the following formula: BP = 1 2 ( f ′X)(X′X)−1(X′ f ) (4) where f is a vector where its elements are Û2i �̂� -1 while Û1 is observation from the regression estimation result and �̂� is the variance of the residuals, if the BP >X2𝛼,k−1 means that there is spatial variation between observation areas at significant 𝛼. Parameter k represent the number of independent variables involves in the model. 2.4 Quantile Regression The quantile regression method uses the approach of separating the data into certain quantile groups that may have different estimated values (Yanuar et al., 2022; Yanuar et al., 2019). The linear regression equation model for the quantile 𝜏 is as follows (Davino et al., 2013; Yanuar and Zetra, 2021): Y = X 𝛽𝜏 +U , (5) Y = vector of dependent variables of size n × 1, X : matrix of independent variables of size n × (k + 1), 𝛽𝜏 : factor of the regression coefficient of quantiles of size(k + 1) × 1depending on the quantile−𝜏 , U : vector of residuals of size n × 1. The parameter estimation using the regression quantile method is obtained by minimizing the sum of the absolute values of the errors with weights 𝜏 for positive errors and (1-𝜏) for negative errors, formulated as follows: arg min𝛽 ∈\ n∑︁ i=1 𝜌𝜏 (yi − xi 𝛽i) with loss function 𝜌𝜏 (U)=[𝜏-I(U<0)]U. Where I(.) is the indicator function, its value is one when I(.) is accurate and zero otherwise. While 𝜌𝜏 (U) is the loss function which is defined as follows 𝜌𝜏 (U) = { U𝜏 , i fU > 0 U(𝜏 − 1) otherwise 2.5 Spatial Autoregressive Model (SAR) The SAR model is a linear model with a spatial correlation of the dependent variables. The SAR model is written as follows (Anselin and Anselin, 1988) : Y = _WY + X 𝛽 +U , U ∼ N(0, 𝜎2I) (6) © 2023 The Authors. Page 323 of 329 Yanuar et. al. Science and Technology Indonesia, 8 (2023) 321-329 Where _ represents spatial autoregressive coefficient, which shows the magnitude of spatial dependence between regions, W denotes spatial weighting matrix of size n×n, and 𝛽 is quantile regression coefficient vector of size (k+1) ×1. Parameter estimation of the SAR model can be estimated using the maximum likelihood estimation (MLE) method by assuming that the residual u is random variable from the nor- mal distribution, N(0,𝜎2). Parameter estimation for 𝛽 in the SAR model is obtained as follows: 𝛽 = (X′X)−1X′(1−_W )Y (7) While the estimation of parameter 𝜎2in the SAR model is obtained as follows: �̄� 2 = 1 n ((I − _W )Y −Y 𝛽)′((I − _W )Y − X 𝛽), (8) Parameter estimation _ can be obtained using a numerical approach (Anselin and Anselin, 1988) . Figure 3. Spatial Outliers in the SAR Model 2.6 Spatial Autoregressive Quantile Regression Model (SARQR) The SARQR model is a model that combines spatial autore- gressive models with quantile regression. The SARQR has the spatial autoregressive coefficient (_ ) and the regression vector ( 𝛽 ), which depend on certain quantile values (𝜏) (McMillen, 2015; Ver Hoef et al., 2018). The development of SAR mod- elling on the quantile 𝜏th is specifically defined as follows (Lum and Gelfand, 2012) : Y = _𝜏WY + X 𝛽𝜏 +U. (9) Figure 4. Spatial Outliers Test Based on SARQR Model at 𝜏=0.45. The value of the spatial autoregressive coefficient in the SARQR model shows the magnitude of the spatial dependence between adjacent areas. The IVQR (Instrumental Variable Quantile Regression) method is used to estimate parameters in the SARQR model (Yu et al., 2021) . The assumptions used in estimating the parameters in SARQR model are as follows (Zhang et al., 2021a) : 1. P(ui≤0)=𝜏, for every i=1,2,...,n 2. supn≥1 max1≥i≥n E(ui) ≤ ` < ∞, 3. U ∼ N (0,_ 2I). Getting the parameters _𝜏 and 𝛽𝜏 are done by minimizing Equation (10) respect to each parameter. argmin E = 𝜌𝜏 ©­«yi − _𝜏 n∑︁ i=j 𝜔i jyj − X′i 𝛽𝜏 − g(Xi , Zi) ª®¬  (10) Where g(Xi, Zi) is a linear function as instrumental vari- able quantile regression (IVQR). The steps for estimating the parameters based on IVQR in the SARQR model are as follows (Su and Yang, 2011; Zhang et al., 2021b): 1. Set a specific value for _ , and do the quantile regression modeling at 𝜏th quantile, which is defined as ( 𝛽𝜏 (_), �̄�𝜏(_)) = argmin𝛽 𝛾Q𝜏 ( 𝛽 , _ , 𝛾) 2. To calculate the estimated value of the IVQR is done by minimizing the vector of the estimated variable instru- ment �̄�𝜏 (_ ) _̂𝜏 = argmin_ �̂�𝜏 (_)Â(�̂�𝜏 (_))′ where Â=A+Op(1), A is a positive definite matrix. 3. The estimator 𝛽 is obtained in the following way. 𝛽𝜏 = 𝛽𝜏−1_̂𝜏−1 Repeat the above steps for each quantile 𝜏. At each quan- tile 𝜏, different estimating parameters are obtained. © 2023 The Authors. Page 324 of 329 Yanuar et. al. Science and Technology Indonesia, 8 (2023) 321-329 3. RESULTS AND DISCUSSION Table 1 and Figure 1 present respectively the descriptive and box plot of data used in this study. Figure 1 informs us that there are outliers on the population percentage (X1), GRDP (X4) and OUL (Y). Furthermore, the multicollinearity test among independent variables were carried out to find out whether there was a cor- relation between each independent variable. The results of the multicollinearity test are presented in Table 2. Each variable has VIF value less than 5, meaning there is no multicollinearity problem between the independent variables. The spatial weighting matrix in this study uses the queen contiguity (side contact and corner points between regions). This study’s spatial units are districts/cities in West Java Province. The list of regencies/cities in the adjacent West Java is presented in Table 3. In this section, the empirical data regarding the Open Un- employment Level in 26 regions in West Java is employed to construct the OUL model. The first step is to estimate the Moran’s Index coefficient values based on Equation (2): I = n ∑n i=1 ∑n j=1 wi j(yi − ȳ)(yj − ȳ)∑n i=1 ∑n j=1 wi j ∑n j=1(yj − ȳ)2 = 0.5528 It is found that I value is positive, which means that ad- jacent areas have similar values and data patterns tend to be clustered. The next test is to estimate the Moran’s Index using Equation (2) above. It is obtained that value of Moran’s Index is 4.1451 where it indicated that there is a spatial dependence between regions in West Java Province. Furthermore, the La- grange Multiplier test was carried out to determine the spatial dependence on the dependent variable, as written in Equation (3). This study found that the Lagrange Multiplier value is 3.9572, which means that there is a spatial dependence on the dependent variable. Additionally, the heteroscedasticity test is also determined in the hypothesis model using the Breusch-Pagan test. Based on the data used in this study, the Breusch-Pagan’s value in this hypothesis model is 2.9538 (with p-value is 0.061). It indicates that the variances of Open Unemployment level among regions in East Java are the same. The SAR model was carried out because there is a spatial effect in the form of spatial dependence on the dependent variable, where the results of the parameter estimation of the SAR model can be seen in Table 4. Based on Table 4, it is found that not all independent vari- ables have a significant influence on district/city OUL in West Java Province. The independent variables that have significant effect on OUL are the percentage of poor people (X2) and LFPR (X3), indicated by p-value for corresponding predictor are smaller than the significance level 𝛼=0.1. Meanwhile, the percentage of the population (X1), GRDP (X4) and % HDI (X5) have no a significant effect on OUL. The purpose of this regression is to build the best model that can predict the dependent variable (OUL), so the spatial autoregression model of OUL in West Java Province obtained from data analysis is: �̂� =0.322WY + 13.041 + 0.143X1 + 0.295X2 − 0.302X3 + 0.005X4 + 0.142X5 Based on above equation, it can be explained that: _̂ =0.322, means that the Open Unemployment Level of each province has an effect of 0.322 times the average Open Unemployment Level of each neighboring province. An increase of 1% in the Poor population (X2) will increase the Open Unemployment Level by 0.295, where other variables are considered constant. The proposed model also informed us that an increase of 1% in the Labor Force Participation Level or LFPR (X3), will de- crease the Open Unemployment Level by 0.302, where other variables are considered constant. It is only the significant vari- ables can be interpreted, the non-significant variables give no meaning. Spatial effect testing in spatial dependence and spatial di- versity was conducted again on the SAR model. This is done to check whether the SAR model can handle spatial effects properly or not. In terms of spatial diversity, p-value = 0.8863 > 𝛼= 0.05 means that between regions have the same variance. In spatial dependence, p-value = 0.0155 < 𝛼 = 0.05 means that the SAR model still contains the effect of spatial dependence on the dependent variable. Furthermore, Moran’s scatterplot is figured to detect spatial outliers in the SAR model, as provided in Figure 3. In this figure, it is found that there are five spatial outliers in the SAR model, those are observations number 2, 3, 9, 17 and 23, denoted by star. Outliers will affect the parameter estimation results and decrease model accuracy. Therefore, the OUL model obtained based on SAR method could not be accepted. SARQR model is then applied to deal with spa- tial effects and data containing spatial outliers to obtain more acceptable model. SARQR modelling produces a model that may differ in each quantile. SARQR modelling uses the IVQR method as parameter estimation by minimizing the coefficients of the instrument variables for each quantile so that the optimal in- dependent variable parameters and spatial autoregressive co- efficients are obtained in the SARQR model. The results of parameter estimation for each quantile are presented in Table 5. It can be seen in Table 5 that percentage of the popula- tion (X1), percentage of poor population (X2), LFPR (X3), and GRDP (X4) are significant in selected quantile. The spatial autoregressive coefficients on the SARQR model are varies among quantiles, some are positive, other are negative, and several are close to zero. The SARQR model which has a positive spatial autoregressive coefficient, indicates that the dis- tricts/cities in the adjacent West Java Province have a positive influence on the districts/cities in the West Java Province in that quantile. The comparison between SAR and SARQR models based © 2023 The Authors. Page 325 of 329 Yanuar et. al. Science and Technology Indonesia, 8 (2023) 321-329 Table 1. Descriptive Statistics on Data Variable Mean Q1 Median Q3 % Population (X1) 3.85 2.13 3.49 5.03 % Poor Population (X2) 8.40 6.53 8.27 10.39 LFPR (X3) 64.56 61.88 64.09 67.75 GRDP (X4) 62.10 22.25 32.25 IPM % HDI (X5) 71.78 67.96 70.74 74.38 OUL (Y) 10.57 9.75 11.00 12.00 Table 2. Multicollinearity Test Results Independent Variable VIF % Population (X1) 1.76 % Poor population (X2) 2.69 LFPR (X3) 1.08 GRDP (X4) 1.69 % HDI (X5) 2.72 Table 3. The Neighboring Regions in West Java Regions Neighboring Regions Bogor Suka Bumi. Cianjur. Purwakarta. Karawang. Bekasi. Sukabumi City. City of Depok. and Bekasi Sukabumi Bogor. Cianjur. and Sukabumi City, Cianjur Bogor. Sukabumi. Bandung. arrowroot Purwakarta. West Bandung Cianjur. Garut. Sumedang. Subang. West Bandung. Bandung. Cimahi City Garut Cianjur. Bandung. Tasikmalaya. Sumedang Tasikmalaya Garut. Ciamis. Majalengka. Sumedang. Tasikmalaya City Ciamis Tasikmalaya. Kuningan. Majalengka. Tasikmalaya City. Banjar Kuningan Ciamis. Cirebon. Majalengka Cirebon Kuningan. Majalengka. Indramayu. Cirebon City Majalengka Tasikmalaya. Ciamis. Kuningan. Cirebon. Sumedang. Indramayu Sumedang Bandung. Garut. Tasikmalaya. Majalengka. Indramayu. Subang Indramayu Cirebon. Majalengka. Sumedang. Subang Subang Bandung. Sumedang. Indramayu. Karawang. Purwakarta. West Bandung, Purwakarta Bogor. Cianjur. Subang. Karawang. West Bandung Karawang Bogor. Subang. Purwakarta. Bekasi Bekasi Bogor. Karawang. Bekasi City, West Bandung, Cianjur. Bandung. Subang. Purwakarta. Bandung. Cimahi Bogor City Bogor Sukabumi City Sukabumi Bandung City Bandung. West Bandung. Cimahi City Cirebon City Cirebon Bekasi City Bogor. Bekasi. Depok Depok City Bogor. Bekasi Cimahi City Bandung. West Bandung. City of Bandung Tasikmalaya City Tasikmalaya. Ciamis Banjar City Ciamis © 2023 The Authors. Page 326 of 329 Yanuar et. al. Science and Technology Indonesia, 8 (2023) 321-329 Table 4. Model Estimation Results with the SAR Model Variable Estimated Mean Standard Error Z-Statistics p-value Constant 13.0411 9.9793 1.3072 0.1912 % Population (X1) 0.1432 0.1342 1.0654 0.2873 % Poor population (X2) 0.2951* 0.1564 1.8853 0.0593 LFPR (X3) -0.3022* 0.0763 -3.9491 0.0000 GRDP (X4) 0.0052 0.0053 0.8692 0.3850 % HDI (X5) 0.1421 0.0932 1.5332 0.1250 SAR coefficient (_ ) 0.3222 0.1701 1.8882 0.0572 * Significant at the significant level 𝛼=0.1,Z𝛼/2= 1.645 Table 5. Estimated Parameter Based on SARQR Quantile Parameters (𝜏) Constants X1 X2 X3 X4 X5 _ 𝜏 0.10 24.666 -0.294 -0.058 -0.363* 0.007 0.073 0.021 0.15 14.345 -0.249 0.164 -0.304* -0.000 0.126 0.023 0.20 14.832 -0.219 0.189 -0.305 -0.001 0.111 0.018* 0.25 -2.342 0.020 0.436 -0.157 0.009 0.139 0.015* 0.30 -2.342 0.019 0.436 -0.157 0.009 0.140 0.015* 0.35 5.601 0.125 0.410 -0.216 0.006 0.092 -0.019 0.40 11.052 0.263 0.389 -0.264 0.002 0.067 -0.001 0.45 14.659 0.197 0.426* -0.336* 0.005 0.104 -0.002* 0.50 14.916 0.147 0.429 -0.348* 0.006 0.119 0.000 0.55 12.145 0.123 0.487 -0.339* 0.006 0.145 -0.005 0.60 9.940 0.375* 0.415 -0.330* -0.001 0.187 0.005 0.65 13.055 0.316* 0.309 -0.288* -0.001 0.131 0.024 0.70 17.709 0.311* 0.269 -0.289* 0.001 0.067 -0.018* 0.75 11.128 0.357* 0.278 -0.233* -0.005 0.093 -0.018 0.80 -0.351 0.391* 0.325 -0.176 -0.009 0.187 -0.003 0.85 -2.357 0.385 0.262 -0.229 -0.016* 0.255 0.018* 0.90 -1.381 0.380 0.238 -0.236 -0.016* 0.252 0.018* 0.95 -1.381 0.380 0.238 -0.236 -0.017* 0.252 0.018* *Significant at level 𝛼=0.1 © 2023 The Authors. Page 327 of 329 Yanuar et. al. Science and Technology Indonesia, 8 (2023) 321-329 Table 6. The Comparison between SAR and SARQR Model. Model Spatial Dependency Test Spatial Diversity Test AICLM Value p-value BP Value p-value SAR 5.8601 0.0155 3.1674 0.0751 105.2200 SARQR 𝜏=0.10 0.0549 0.8146 1.8686 0.1716 71.6224 SARQR 𝜏=0.15 0.0052 0.9426 1.4958 0.2213 72.3596 SARQR 𝜏=0.20 0.0066 0.9353 1.5040 0.2146 69.7271 SARQR 𝜏=0.25 2.7343 0.0982 3.0631 0.0801 72.0653 SARQR 𝜏=0.30 3.6432 0.0563 3.0673 0.0799 72.3285 SARQR 𝜏=0.35 2.2484 0.1338 0.7179 0.3968 71.1260 SARQR 𝜏=0.40 3.1256 0.0771 0.5489 0.4588 75.6256 SARQR 𝜏=0.45 3.2947 0.0695 0.7238 0.3949 63.2113 SARQR 𝜏=0.50 2.7432 0.0977 0.8668 0.3518 72.1255 SARQR 𝜏=0.55 2.4893 0.1146 0.9020 0.3423 76.9123 SARQR 𝜏=0.60 2.9768 0.0845 0.7254 0.3944 77.1333 SARQR 𝜏=0.65 0.0300 0.8625 1.4136 0.2345 88.5306 SARQR 𝜏=0.70 2.4576 0.1170 1.3566 0.2411 91.0339 SARQR 𝜏=0.75 2.6164 0.1058 1.1538 0.2827 88.1333 SARQR 𝜏= 0.80 3.8364 0.0502 1.0257 0.3112 69.8960 SARQR 𝜏 = 0.85 1.8343 0.1756 1.0736 0.3001 77.7989 SARQR 𝜏 = 0.90 2.3478 0.1255 0.9457 0.3308 78.8910 SARQR 𝜏 = 0.95 2.3478 0.1255 0.9457 0.3308 78.8910 on the results of spatial dependency tests and spatial diversity test. The criteria for the best model is based on the smallest value of AIC (Akaike Information Criteria) (Yasin et al., 2020) , provided in Table 6. It can be informed in Tabel 6 that all p-value for spatial dependency test and spatial diversity test are all more than 0.05. It indicated that in these SARQR model, there is no spatial dependency on the dependent variable for each quantile. In other words, the SARQR model can overcome the problem of spatial dependence on the dependent variable. Furthermore, in the inter-regional spatial diversity test, both methods (SAR and SARQR) have resulted in the homogenous variance of inter- regional for each model, indicated by all p-value being higher than 0.05. It means no longer problem with inter-regional spatial diversity. Table 6 also informs us that model SARQR at all quan- tiles has a smaller value of AIC than the SAR model, with a model at 𝜏=0.45 having the smallest value of AIC. The spa- tial outliers will be detected in this quantile, as the example. Figure 4 shows that the SARQR quantile 0.45 model has no spatial outliers, meaning there is no longer an outlier problem in this SARQR model. The proposed model for estimating the Open Unemployment Level is based on this SARQR model at 𝜏=0.45: Ŷ = − 0.002WY + 14.659 − 0.197X1 + 0.426X2− 0.336X3 + 0.005X4 + 0.104X5 The proposed model at this 0.45 quantile informs us that: _̂ =0.002, means that the Open Unemployment Level of each province has an effect of 0.002 times the average Open Unem- ployment Level of each neighboring province. An increase of 1% in the Poor population (X2) will increase the Open Unem- ployment Level by 0.426, where other variables are considered constant. The proposed model also informed us that an in- crease of 1% in the Labor Force Participation Level or LFPR (X3), will decrease the Open Unemployment Level by 0.336, where other variables are considered constant. 4. CONCLUSION The comparison between the SAR model and the SARQR model based on the AIC value is the SARQR model is good at predicting OUL in West Java Province. The SARQR model is also proven to deal with spatial effect problems such as spa- tial dependence and spatial diversity and is not easily affected by the presence of outliers. The SARQR model can provide model information for each selected quantile of the response distribution, while the SAR model can only estimate the aver- age response model. It is recommended for further research to use other parameter estimation methods such as GML (Quasi Maximum Likelihood), GMM (Generalized Method of Moments), and 2SLS (Two Stage Least Square). The comparison study among those methods is also important. 5. ACKNOWLEDGMENT This research was funded by DRPM, the Deputy for Strength- ening Research and Development of the Ministry of Research and Technology/National Research and Innovation Agency of © 2023 The Authors. 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Page 329 of 329 INTRODUCTION EXPERIMENTAL SECTION Materials Methods Spatial Effects Quantile Regression Spatial Autoregressive Model (SAR) Spatial Autoregressive Quantile Regression Model (SARQR) RESULTS AND DISCUSSION CONCLUSION ACKNOWLEDGMENT