Journal of Mathematics and Statistics 10 (2): 130-138, 2014 ISSN: 1549-3644 © 2014 Science Publications doi:10.3844/jmssp.2014.130.138 Published Online 10 (2) 2014 (http://www.thescipub.com/jmss.toc) MAPPING OF ILLITERACY AND INFORMATION AND COMMUNICATION TECHNOLOGY INDICATORS USING GEOGRAPHICALLY WEIGHTED REGRESSION 1Rokhana Dwi Bekti, 2Andiyono and 3Edy Irwansyah 1,2 Department of Statistics and Computer Science, 3Department Computer Science, 1,2,3 School of Computer Science, Bina Nusantara University, Jl. K.H Syahdan no. 9, Palmerah, Jakarta Barat, 11480, Indonesia Received 2013-04-12; Revised 2013-07-16; Accepted 2014-02-15 ABSTRACT Geographically Weighted Regression (GWR) is a technique that brings the framework of a simple regression model into a weighted regression model. Each parameter in this model is calculated at each point geographical location. The significantly parameter can be used for mapping. In this research GWR model use for mapping Information and Communication Technology (ICT) indicators which influence on illiteracy. This problem was solved by estimation GWR model. The process was developing optimum bandwidth, weighted by kernel bisquare and parameter estimation. Mapping of ICT indicators was done by P-value. This research use data 29 regencies and 9 cities in East Java Province, Indonesia. GWR model compute the variables that significantly affect on illiteracy ( α = 5%) in some locations, such as percent households members with a mobile phone (x 2), percent of household members who have computer (x 3) and the percent of households who access the internet at school in the last month (x 4). Ownership of mobile phone was significant ( α = 5%) at 20 locations. Ownership of computer and internet access were significant at 3 locations. Coefficient determination at all locations has R 2 between 73.05-92.75%. The factors which affecting illiteracy in each location was very diverse. Mapping by P-value or critical area shows that ownership of mobile phone significantly affected at southern part of East Java. Then, the ownership of computer and internet access were significantly affected on illiteracy at northern area. All the coefficient regression in these locations was negative. It performs that if the number of mobile phone ownership, computer ownership and internet access were high then illiteracy will be decrease. Keywords: Geographically Weighted Regression, Mapping, Illiteracy, ICT Indicators 1. INTRODUCTION of covariance structure through autoregressive model (Anselin, 1988; LeSage and Pace, 2009; Zheng and Zhu, There are several development spatial modeling, 2012). In space time data also known as Space Time such as area and point approach model. Area models Autoregressive (STAR) model (Giacinto et al ., 2005) are Spatial Autoregressive Models (SAR), Spatial and Conditional Autoregressive (CAR) (Lekdee and Error Model (SEM), Spatial Durbin Model (SDM) and Ingsrisawang, 2013). Spatial Autoregressive Moving Average (SARMA). Bekti and Sutikno (2012) have used SDM to These models use dependency relationship in the form modeling on diarrhea and factors which influenced it. Corresponding Author: Rokhana Dwi Bekti, Department of Statistics and Computer Science, Jl. K.H Syahdan no. 9, Palmerah, Jakarta Barat, 11480, Indonesia Science Publications 130 JMSS Rokhana Dwi Bekti et al. / Journal of Mathematics and Statistics 10 (2): 130-138, 2014 Bekti and Sutikno (2010) have modeled the extreme coefficient in housing research and residuals in relationship between an assets society with HCI spatial distribution of precipitation and crop yields. through the SLM and the SEM approach to the area in Another methods for illustrate spatial relationships is East Java, Indonesia. by ‘K’luster Analysis by Tree Edge Removal Anselin and Rey (2010) noted that spatial (SKATER). This method calculating based on heterogeneity raises even greater methodological clustering analysis then illustrates it on mapping, such issues, because it suggests that any attempt to find as research by Rachmawati and Bekti (2013). universal principles that apply everywhere on the This research performs GWR for modeling in earth’s surface is fundamentally problematic. Analysis education problems in East Java Indonesia. Education should focus on estimating, interpreting the inevitable is one of primary need to improve the community variation in parameters and adopting a methodological quality of life and welfare. The rate of illiteracy is one position. Local or place-based analysis is more indicator of the level of education. Central Bureau of consistent with this position, such as Anselin’s LISA Statistics Indonesia noted that in 2010, there were (Anselin, 1995) and the Geographically Weighted 7,09% illiterate people which aged over 15 years. This Regression (Fotheringham et al ., 2002). number was decreased from 2009. In 2010, East Java Geographically Weighted Regression (GWR) is a Province has the higher percent illiterate people than technique that brings the framework of a simple other province in Java and Sumatera Island. This regression model into a weighted regression model. number was 11,66% illiterate people which aged over Each parameter in this model is calculated at each point 15 years, 2,39% people aged 15-44 years and 26,22% geographical location, so that each point in different people aged over 44 years. geographic location has different regression parameter. The development of Information and Communication GWR also called as method of spatial model based on Technology (ICT) is one factor that influence on point area. Another method is Geographically Weighted illiteracy. It has an impact on education, especially in Poisson Regression (GWPR). learning and education. Central bureau of statistics Sarma et al . (2011) were used GWR, Ordinary Least Indonesia noted that it has some indicators, such the Square (OLS) and Geographic Information System ownership of fixed-line telephone, mobile phone, (GIS) to evaluate the long ‐term trends in agricultural computer and internet access. D’Silva et al . (2011) was productivity. An important catalyst for better shown that ICT is an important mechanism to further integration of GIS and spatial data analysis for boost rural development in Malaysia. Then, Astiwi improved interpolation has been the development of (2011) was show that there are some activities to local spatial statistical techniques. Spatial analysis and decrease illiteracy in East Java Indonesia, such as Geographic Information Systems (GIS) are much community literacy movement. The activity is a improve library management to more interesting, such as using a related. Mapping the spatial distribution can be perform computer with software literacy lessons. by GIS, such as Ibrahim et al . (2012) who perform mapping honeybee plants. GIS are important to perform Some regencies and cities in East Java have almost four basic functions on spatial data: Input, storage, the same characteristics in among neighboring and analysis and output. Sarma et al . (2011) also noted that adjacent regencies or cities. For example, Madura GIS can perform predicting and mapping. Island has the high percent illiterate people. Mapping can demonstrate and visualize the spatial Bondowoso Regency, Situbondo and Probolinggo analysis. Matthews and Yang (2012) were doing it. It Regency which adjacent with Madura Island have used GWR for mapping the results of local statistics. high percent illiterate people too. It shows that there is Matthews and Yang (2012) use parameter estimate and t- an influence factor or spatial locations. value because the spatial distribution of the parameter To get spatial relathionship between illiteracy and estimates must be presented in concert with the ICT indicators in East Java Province Indonesia, this distribution of significance. It yields meaningful research was modelling these variable by GWR. This interpretation of results. Cho et al . (2009), Sarma et al . method calculate parameter at each point location. It also (2011) also represents a major improvement in has done mapping ICT indicators which influence in visualizing GWR results, respectively use mapping of every regencies and cities area. Science Publications 131 JMSS Rokhana Dwi Bekti et al. / Journal of Mathematics and Statistics 10 (2): 130-138, 2014 ⋯ 2. MATERIALS AND METHODS 1xx11 12 x 1k 1xx⋯ x X = 21 22 2k 2.1. Geographically Weighted Regression (GWR) ⋮⋮ ⋮⋱⋮ ⋯ GWR method is a technique that brings the 1xxn1 n2 x nk framework of a simple regression model into a weighted T y= [] y,y ,...y regression model (Fotheringham et al ., 2002). It was 1 2 n introduced to the geography literature by Brunsdon et al . (1996). This model is the locally linear regression. It Wi1 0 ... 0 based on non-parametric technique of locally weighted 0 W ... 0 W(i) = i2 regression developed in statistics for curve fitting and ⋮ ⋮ ⋮ ⋮ smoothing applications (Fischer and Getis, 2010). It 0 0 ... W yields parameter estimations which localized to each in point or the location where data is collected. The β ()()()u ,v β u ,v ... β u ,v 011 111 p11 dependent variable is predicted by each independent . variable which coefficient regression depends on the β = . location where the data is observed. . Each parameter will be estimated at each point of the β ()()()u ,v β u ,v ... β u ,v geographical location so that each point of geographic 0nn 1nn pnn location has the different parameter estimation. This will give a variation on the regression parameter 2.2. Weighted values in a set geographical area. If the parameters estimation in each location is constant, the GWR Weighted is show the neighboring relationship models are called global models. This means that each among locations on the model. It is important because it location have the same model. represents the weighted value of the location of the The general function of GWR model is in (1): observation data with one another so that need accuracy weighting method. There are several weight functions p =β()() +β +ε (Fotheringham et al ., 2002) such us Inverse distance yi 0ii u,v∑ kiiik u,vx i (1) k= 1 function, Kernel Gauss function and Kernel Bisquare function. In this research was use Kernel Bisquare Where: function in (4).