Bogor, West Java, Indonesia

2018 IJSRSET Volume 4 Issue 4 Print ISSN: 2395-1990 Online ISSN : 2394-4099 Themed Section : Engineering and Technology Assessment Method for Weighting and Aggregation in Constructing Composite Indicators of Mixed Data Arni Nurwida *, Aji Hamim Wigena, Budi Susetyo Department of Statistics, Faculty of Mathematics and Sciences Natural, Bogor Agricultural University (IPB), ABSTRACT Bogor, West Java, Indonesia Composite indicators is often encountered in various studies especially in social sector. Composite indicators constructed from several steps such as weighting and aggregation. The classical weighting method such as weighting based on factor analysis and regression analysis cannot handle a mixture of numeric and categorical variables. Furthermore, using dependent variable as the estimator in weighting based on regression analysis sometimes untrustworthy or manipulable by respondents. One approach to addressing this problem is by using a weighting method based on factor analysis of mixed data. Besides that, the classical aggreagtion method such as linear additive method cannot handle a mixture of compensatory and non-compensatory variables. One approach to addressing this problem is by using a geometric aggreagtion method. The accuracy of weighting method based on factor analysis of mixed data and geometric aggreagtion in constructing composite indicators of mixed data is important to be studied. The case study conducted in constructing household welfare status of Dramaga village, Bogor regency by comparing weighting method based on factor analysis of mixed data, weighting based on multiple correspondence analysis, geometric aggreagtion, and linear aggreagtion method. The weighting method based on factor analysis of mixed data and the geometric aggreagtion provided the most accurate results. Keywords: Composite Indicators, Factor Analysis of Mixed Data, Geometric Aggreagtion, Household Welfare I. INTRODUCTION categorical variables (mixed data). The classical weighting procedure such as based on principal Composite indicators is a technique to compile individual indicators into a single index on the basis of underlying model. The goal is to measure components or factor analysis, regression analysis, and multiple correspondence analysis developed to handle only numeric or categorical variables. multidimensional concepts which cannot be captured by a single indicator, e.g. competitiveness, Weighting based on regression analysis using industrialization, sustainability, single market dependent variable as the estimator of the integration, knowledge-based society, etc (OECD, phenomenon sometimes untrustworthy or 2008). Composite indicators constructed from several steps such as weighting and aggregation. Weighting is a procedure to weight individual indicators, they manipulable by respondents. Sari (2011) found household income used as dependent variable in estimating poverty in West Nusa Tenggara and describe different importance in expressing Maluku Province is manipulated. This is happened multidimensional phenomenon (Mazziota & Pareto, 2013). The main problem in weighting is the because the respondent manipulated during the survey, they knowed that the puspose of the survey is individual indicators came from numeric and to determine beneficiaries of government programs. IJSRSET11844388 Received : 03 April 2018 Accepted : 15 April 2018 March-April-2018 [(4) 4 : 1070-1083] 1070

Also, Castano (2002) found weighting based on qualitative principal components that is not using dependent variable is more accurate than weighting based on least square regression that is using dependent variable. Therefore, weighting method based on factor analysis of mixed data can handle together both numeric and categorical variable and without dependent variable (Pages, 2004). Aggregation is a procedure to combine all variable components to form one composite indices (Mazziota & Pareto, 2013). The main problem in aggregation is the individual indicators came from compensatory and non-compensatory variables. The classical aggregation procedure such as linear additive methods developed to handle only compensatory variable (Tarabusi & Guarini, 2013). Therefore, geometric methods can handle together both compensatory and non-compensatory variables (OECD, 2008). This method is the combined method of compensatory and non-compensatory that called non-linear aggregation method. Statistics Indonesia (BPS) in TNP2K (2013) constructed Indonesian household welfare status by numeric and categorical variable using method based on regression analysis and household expenditure per capita as dependent variable. Therefore, this study want to examine weighting and aggreagtion methods in constructing individual indicators of mixed data in case of household welfare status in Dramaga village, Bogor regency, Indonesia by the social protection program data collection (PPLS) 2011. II. METHODS AND MATERIAL This study used social protection program data collection (PPLS) 2011 especially on Dramaga village, Bogor regency, Indonesia. Dramaga village has 775 households and 3155 household members. The variables that used are household welfare status criterions which consist of 15 numeric variables and 19 categorical variables as presented in Table 1. Table 1. research Variable Description Type Variable Description Type Age of household head Numeric Educational level of household head Categoric 1/Dependency ratio Numeric Working status of household head Categoric Net elementary and middle school Main occupational sector of Numeric enrolment ratio household head Categoric 1/Gross elementary and middle school enrolment ratio Numeric of residence mastery Categoric 1/Household size Numeric Wall material Categoric At least one of the household members graduated from middle school Numeric Roof material Categoric At least one of the household members graduated from high school Numeric Source of drinking water Categoric At least one of the household members graduated from college Numeric Way of getting drinking water Categoric 1/Number of school-aged child in elementary school Numeric Source of main lighting Categoric 1/Number of school-aged child in middle school Numeric Toilet facility Categoric 1/Number of school-aged child in high school Numeric Final stool disposal site Categoric Number of school-aged child in college Numeric Refrigerator ownership Categoric Proportion of household members working in the primary sector Numeric Motorcycle ownership Categoric Proportion of household members Main job position of household Numeric working in the secondary sector head Categoric Proportion of household members working in the tertiary sector Numeric Floor material Categoric Sex of household head Categoric Sector and main job position of h.h. Categoric Marital status of household head Categoric Working status of household head and residence mastery status Categoric 1071

Table 2. Research model Model Weighting Method based on Aggregation Method 1 Factor analysis of mixed data Linear 2 Factor analysis of mixed data Geometric 3 Multiple correspondence analysis Linear 4 Multiple correspondence analysis Geometric The steps in this study are as follows: 1. Data description 2. Constructing 4 models of Dramaga village household welfare status as presented in Table 2 3. Weighting individual indicators using the method based on factor analysis of mixed data: a. Weighting numeric variables using a technique described in OECD (2008). The first step is choosing a number of factor (F) that have cumulative variance larger than 60% and eigenvalue larger than 1. The next step refers to Nicoletti, Scarpetta, & Boylaud (2000) choosing the largest loading factor from the selected factors (F) for every numeric variable q. Then calculating the weight of numeric variable q as below: ( ) ( ) where is the weight of numeric variable q, largest loading factor,, is a factorial axis containing the factor of numeric variable q, is the largest loading ( ) is a variance of loading factor, and ( ) is total variance of loading factor, last step is converting and. to the value. The b. Weighting modalities of categorical variables using a technique of axis ordering consistency condition (AOC) by Asselin (2009). The first step is choosing a number of factor (F) that have eigenvalue larger than 1 as below: where is the eigenvalue of factor f,, is the discriminant value of categorical variable j and factor f,, is the number of households of modality,, is the loading factor f modality and categorical variable j, is total number of households. The next step is choosing the largest discriminant value from the selected factors (F) for every categorical variable j. Then calculating the weight of modalities below: of categorical variable j as where is the weight of modalities of categorical variable j, β is a factorial axis containing the largest discriminant value, is the loading factor β modalities and categorical variable j, is is the loading factor β the worst modalities and categorical variable j, and is the eigenvalue of factor β. 4. Weighting individual indicators using the method based on multiple correspondence analysis as belows: a. Converting numeric variables into categorical using the quantile methods with the number of modalities is 4 b. Calculating the weight of modalities of categorical variables using the same procedure on number 3.b 5. For weighting based on factor analysis of mixed data, constructing composite indicators for every household i using the linear aggreagtion method by summing the linear method for numeric 1072

variables (OECD, 2008) and for categorical variables (Asselin, 2009) as below: 6. For weighting based on factor analysis of mixed data, constructing composite indicators for every household i using the geometric aggreagtion method by summing the geometric method for numeric variables (OECD, 2008) and for categorical variables as below: 7. For weighting based on multiple correspondence analysis, constructing composite indicators for every household i using the linear and geometric aggreagtion for categorical variables only. 8. Constructing Dramaga village household welfare status as belows: a. Sorting the composite indicators from the smallest to largest b. Dividing the sorted composite indicators into 4 classes or status from status 1 to 4 using cuts off refers to BPS 9. Validating Dramaga village household welfare status compared with BPS using several test as belows: a. Mann-Whitney test b. Robust analysis ( ) c. Accuracy test d. Area Under the ROC Curve (AUC) 10. Choosing the best model which accepting in Mann-Whitney test, smallest, largest accuracy, and largest AUC 11. Explorating of Dramaga village household welfare status characteristics III. RESULTS AND DISCUSSION Dramaga village, Bogor regency in PPLS 2011 consists of 775 households and 3155 household members. The criterion variables of household welfare status in PPLS 2011 consist of numeric and categorical variables, and also complementary and noncomplementary variables. The complementary variables are at least one of the household members graduated from college with the proportion of household members working in primary sector, while the non-complementary variables are the age of the household head with the number of school-aged children in primary school. The PPLS 2011 contains households with the household welfare status of 1, 2, 3 and 4 with the number and percentage of households in every status presented in Table 3. The highest number of households is in status 3 (408 and 52.65%), followed by status 2 (224 and 28.90%), status 1 (108 and 13.94%), and status 4 (35 and 4.52%). Table 3. Number and percentage of the households Description 1 2 3 4 Number of 108 224 408 35 households households 13.94 28.90 52.65 4.52 Weighting The weighting process in constructing household welfare status of Dramaga village conducted using two methods. The first method used weighting based on multiple correspondence analysis and the second method used weighting based on factor analysis of mixed data. Weighting based on Multiple Correspondence Analysis The weighting based on multiple correspondence analysis can only handle categorical variables, so that the numeric variables must be categorized first. Categorization of numeric variables using the quantile techniques with the number of modalities are 4 (Table 4). Weighting procedure conducted to all modalities of categorical variables. Table 4 presented that the value of J*50%*eigenvalue at least 1 is in the 1073

first 12 factors (1.01), so that the number of factor to be used is 12. Weighting variables used the loading factor and eigenvalue from the factor that gived the largest discriminant value. Table 5 present that the largest discriminant value of variable to are at factor 1, 8, 12, 8, 3, 1, 1, 5, 1, 4, 11, 10, 4, 6, 6, 8, 9, 9, 12, 5, 1, 8, 4, 1, 2, 2, 7, 1, 1, 12, 8, 3, 3, and 4, respectively, so that those are the factor of loading and eigenvalue to be used for weighting variables. The weight constructed from the gap between the loading factor and the loading factor from the worst-off modalities, then divided by the eigenvalue square root. The categorical weight based on multiple correspondence analysis presented in Table 6. Table 4. The value of J*50%*eigenvalue of the categorical variables on weighting based on multiple correspondence analysis Factors Description 1 2 3 4 5 6 7 8 9 10 11 12 13 14 J*50%*Eigenvalue 3.36 2.08 1.76 1.60 1.28 1.26 1.21 1.18 1.11 1.09 1.07 1.01 0.96 0.89 Table 5. Discriminant of the categorical variables on weighting based on multiple correspondence analysis Factors 1 2 3 4 5 6 7 8 9 10 11 12 0.44 0.01 0.06 0.01 0.00 0.01 0.01 0.21 0.08 0.03 0.02 0.04 0.14 0.11 0.14 0.03 0.08 0.01 0.02 0.36 0.08 0.05 0.03 0.03 0.03 0.05 0.03 0.02 0.05 0.01 0.02 0.02 0.02 0.02 0.03 0.15 0.09 0.06 0.01 0.00 0.02 0.03 0.04 0.19 0.01 0.01 0.03 0.08 0.40 0.29 0.86 0.04 0.10 0.29 0.22 0.04 0.03 0.24 0.04 0.04 0.35 0.01 0.00 0.04 0.01 0.02 0.01 0.03 0.01 0.00 0.02 0.02 0.38 0.02 0.00 0.03 0.01 0.02 0.01 0.03 0.01 0.00 0.01 0.03 0.16 0.11 0.01 0.03 0.29 0.01 0.27 0.05 0.03 0.08 0.01 0.03 0.64 0.33 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.65 0.35 0.03 0.76 0.12 0.13 0.02 0.12 0.37 0.04 0.05 0.03 0.01 0.01 0.01 0.05 0.10 0.33 0.43 0.13 0.21 0.22 0.61 0.06 0.01 0.00 0.00 0.02 0.02 0.00 0.01 0.02 0.01 0.02 0.00 0.00 0.01 0.00 0.00 0.03 0.00 0.00 0.01 0.01 0.01 0.02 0.01 0.01 0.01 0.03 0.02 0.02 0.02 0.19 0.05 0.11 0.04 0.14 0.03 0.05 0.00 0.00 0.00 0.00 0.00 0.16 0.01 0.11 0.00 0.11 0.01 0.03 0.00 0.01 0.01 0.00 0.03 0.00 0.00 0.04 0.01 0.01 0.01 0.01 0.01 0.08 0.00 0.02 0.03 0.02 0.05 0.00 0.08 0.04 0.02 0.03 0.01 0.05 0.01 0.03 0.02 0.01 0.05 0.01 0.12 0.01 0.10 0.07 0.03 0.05 0.00 0.03 0.02 0.00 0.00 0.02 0.00 0.00 0.00 0.06 0.06 0.04 0.01 0.04 0.06 0.00 0.00 0.02 0.00 0.00 0.00 0.04 0.67 0.42 0.01 0.08 0.25 0.13 0.06 0.06 0.10 0.20 0.08 0.41 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.02 0.01 0.01 0.00 0.00 0.68 0.44 0.04 0.81 0.38 0.25 0.09 0.17 0.50 0.25 0.13 0.47 0.65 0.35 0.01 0.06 0.11 0.33 0.45 0.14 0.21 0.24 0.61 0.07 0.11 0.29 0.07 0.04 0.06 0.08 0.01 0.09 0.07 0.03 0.06 0.04 0.05 0.21 0.03 0.04 0.16 0.05 0.02 0.09 0.03 0.03 0.05 0.05 0.00 0.02 0.01 0.01 0.11 0.02 0.15 0.00 0.00 0.03 0.01 0.00 0.24 0.04 0.02 0.03 0.05 0.01 0.05 0.14 0.01 0.03 0.00 0.00 0.11 0.04 0.03 0.01 0.03 0.03 0.02 0.02 0.01 0.02 0.02 0.01 0.05 0.05 0.03 0.00 0.01 0.01 0.01 0.02 0.03 0.01 0.04 0.11 0.00 0.01 0.00 0.01 0.03 0.00 0.00 0.03 0.00 0.00 0.00 0.00 0.35 0.31 0.84 0.02 0.13 0.27 0.22 0.03 0.06 0.23 0.05 0.03 0.20 0.17 0.73 0.24 0.16 0.06 0.09 0.03 0.05 0.03 0.03 0.00 0.17 0.22 0.49 0.62 0.10 0.03 0.01 0.00 0.01 0.03 0.03 0.01 1074

Table 6. Weight of the variables on weighting based on multiple correspondence analysis Modalities Weight Modalities Weight Modalities Weight 0.00 0.61 Tap water 0.47 2.82 0.00 Bottled water 1.77 5.46 1.96 No buying 0.00 3.10 2.02 Buying 0.86 0.00 1.09 No electricity 0.00 1.07 0.00 1.37 1.79 0.88 PLN with 2.89 2.24 1.39 No toilet 0.00 0.00 0.12 Public 1.33 3.70 0.00 Self-owned 3.06 7.54 0.68 Others 0.00 2.86 0.88 Holes 0.00 0.00 1.09 River/lake/sea 2.45 0.84 Female 0.00 Septic tank 2.52 0.92 Male 1.67 No 0.00 3.37 No married 0.00 Yes 0.28 0.00 Married 1.25 No 0.00 1.53 Elementary school 0.00 Yes 0.31 1.67 Middle school 0.80 No working 0.00 0.15 High school 0.21 Others 0.13 0.00 College 6.48 Laborer/employee 2.14 0.47 No working 0.00 Self-employed 5.08 0.31 Working 0.12 Soil 0.00 3.08 No working 0.00 No soil 5.85 0.00 Tertiary 8.15 No working 0.00 0.10 Secondary 9.02 Tertiary and others 7.91 1.29 Primary 7.07 Tertiary and laborer/ emp. 10.48 6.97 Others 0.00 Tertiary and self-employed 7.25 0.00 Free rental 3.55 Secondary and others 8.89 0.28 Contract/lease 4.70 Secondary and laborer/emp. 9.97 0.00 Self-owned 3.04 Secondary and self- employed 7.39 0.21 Others 0.00 Primary and others 6.93 0.66 Wood 4.01 Primary and laborer/emp. 10.03 0.95 Wall 0.49 Primary and self-employed 6.79 0.00 Others 0.00 No working and free rental 0.00 9.85 Asbestos 1.12 No working and contract/lease 2.35 3.56 Tiles 1.67 No working and self-owned 3.24 3.28 Others 0.00 Working and others 13.04 0.00 Unprotected wells 1.47 Working and free rental 11.39 4.24 Protected wells 2.20 Working and contract/lease 12.85 6.21 Drilling wells 1.74 Working and self-owned 11.36 0.00 Weighting based on Factor Analysis of Mixed Data The weighting based on factor analysis of mixed data can handle a mixture of numeric and categorical variables. The first step is weighting the numeric variables. Table 7 presented that the percentage of cumulative variance at least 60% and the eigenvalue at least 1 is in the first 17 factors (60.91% and 1.23), so that the number of factor to be used is 17. Weighting numeric variables used the loading factor and the variance proportion from the factor that gived the largest loading factor value. Table 8 presented the largest loading factor of variable to are at factor 1 (Y = 0.42), 12 (Y = 0.23), 11 (Y = 0.14), 7 (Y = 0.16), 1 (Y = 0.31), 2 (Y = 0.34), 2 (Y = 0.25), 14 (Y = 0.19), 1 (Y = 0.21), 1 (Y = 0.08), 11 (Y = 1075

0.18), 11 (Y = 0.04), 2 (Y = 0.32), 1 (Y = 0.18), dan 3 (Y = 0.36), respectively. Then the largest loading factor weighted by the variance proportion and converted to a value with total 1 and range [0,1]. This conversion is the numeric weights that presented in Table 9. The next step is weighting the categorical variables. The categorical weighting procedure is the same as with categorical weighting based on multiple correspondence analysis. Table 10 presented that the value of J*50%*eigenvalue at least 1 is in the first 11 factors (1.23), so that the number of factor to be used is 11. Table 11 presented that the largest discriminant value of variable to are at factor 1, 1, 5, 5, 1, 1, 5, 2, 7, 4, 4, 4, 3, 3, 1, dan 1, respectively, so that those are the factor of loading and eigenvalue to be used for weighting variables. The categorical weight based on factor analysis of mixed data presented in Table 12. Table 7. Eigenvalue and cumulative variance of the numeric variables Description Factors 1 2 3 4 5 6 7 8 9 Eigenvalue 6.47 3.95 2.99 2.55 2.4 2.3 2.21 2.13 2.02 Cumulative Variance (%) 9.96 16.03 20.63 24.55 28.23 31.78 35.17 38.44 41.55 10 11 12 13 14 15 16 17 18 Eigenvalue 1.94 1.85 1.72 1.62 1.48 1.4 1.34 1.23 1.19 Cumulative Variance (%) 44.53 47.38 50.03 52.52 54.8 56.96 59.02 60.91 62.74 Numeric Table 8. Loading factor of the numeric variables Factors 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.42 0.01 0.00 0.00 0.00 0.01 0.01 0.02 0.00 0.01 0.00 0.02 0.00 0.01 0.00 0.00 0.00 0.04 0.02 0.04 0.01 0.00 0.01 0.00 0.00 0.03 0.18 0.04 0.23 0.00 0.05 0.03 0.01 0.00 0.02 0.04 0.03 0.00 0.03 0.00 0.05 0.04 0.11 0.01 0.14 0.03 0.00 0.01 0.11 0.03 0.00 0.03 0.03 0.07 0.01 0.08 0.01 0.16 0.07 0.10 0.02 0.04 0.10 0.01 0.01 0.02 0.02 0.00 0.31 0.27 0.05 0.01 0.05 0.03 0.05 0.00 0.00 0.01 0.00 0.01 0.01 0.00 0.01 0.00 0.02 0.08 0.34 0.10 0.02 0.00 0.01 0.00 0.02 0.00 0.02 0.03 0.09 0.03 0.00 0.01 0.00 0.01 0.03 0.25 0.12 0.07 0.02 0.01 0.00 0.02 0.00 0.02 0.00 0.07 0.04 0.01 0.08 0.03 0.00 0.00 0.02 0.04 0.17 0.05 0.05 0.02 0.00 0.00 0.01 0.00 0.06 0.00 0.19 0.00 0.01 0.00 0.21 0.03 0.03 0.02 0.00 0.00 0.01 0.00 0.02 0.11 0.00 0.11 0.00 0.02 0.00 0.00 0.00 0.08 0.04 0.01 0.00 0.00 0.00 0.01 0.00 0.01 0.01 0.03 0.03 0.00 0.02 0.00 0.01 0.03 0.04 0.07 0.02 0.00 0.02 0.00 0.02 0.02 0.06 0.02 0.18 0.01 0.01 0.02 0.11 0.02 0.00 0.00 0.01 0.02 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.04 0.04 0.01 0.01 0.02 0.01 0.00 0.22 0.32 0.02 0.22 0.05 0.00 0.01 0.00 0.00 0.00 0.00 0.02 0.01 0.00 0.00 0.00 0.01 0.18 0.05 0.11 0.03 0.04 0.09 0.15 0.00 0.02 0.08 0.00 0.01 0.00 0.00 0.00 0.00 0.01 0.09 0.22 0.36 0.05 0.00 0.01 0.00 0.01 0.00 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.01 Table 9. Weight of the numeric variables Numeric Weight Numeric Weight Numeric Weight 0.192 0.095 0.024 0.028 0.070 0.005 0.018 0.020 0.091 0.024 0.095 0.082 0.140 0.038 0.077 1076

Table 10. The value of J*50%*eigenvalue of the categorical variables on weighting based on factor analysis of mixed data Factors Description 1 2 3 4 5 6 10 11 12 13 14 15 J*50%*Eigenvalue 15.33 4.39 2.95 2.44 2.46 2.38 1.90 2.02 1.68 1.38 1.23 0.77 Table 11. Discriminant of the categorical variables on weighting based on factor analysis of mixed data Factors 1 2 3 4 5 6 7 8 9 10 11 2.26 0.08 0.21 0.02 0.06 0.11 0.08 0.04 0.02 0.00 0.01 2.45 0.16 0.20 0.01 0.08 0.12 0.10 0.03 0.03 0.00 0.01 0.97 0.60 0.31 0.60 0.34 0.31 0.17 0.06 0.02 0.06 0.01 4.68 0.96 0.01 0.00 0.00 0.01 0.01 0.00 0.00 0.01 0.00 4.76 1.23 1.72 1.50 0.05 0.47 0.34 0.06 0.08 0.19 0.07 0.07 0.05 0.21 0.33 0.95 1.43 0.50 1.46 0.16 0.23 0.38 0.05 0.03 0.05 0.01 0.01 0.00 0.01 0.00 0.04 0.15 0.02 0.08 0.01 0.10 0.00 0.01 0.01 0.02 0.00 0.04 0.02 0.00 0.10 0.13 0.05 0.08 0.56 0.07 0.48 0.06 0.04 0.44 0.11 0.03 0.01 0.02 0.03 0.43 0.05 0.43 0.00 0.02 0.16 0.06 0.01 0.05 0.01 0.01 0.02 0.01 0.06 0.07 0.01 0.08 0.01 0.06 0.32 0.12 0.03 0.17 0.06 0.02 0.08 0.07 0.36 0.02 0.07 0.23 0.11 0.01 0.22 0.04 0.11 0.19 0.09 0.29 0.10 0.19 0.24 0.12 0.01 0.00 0.01 0.03 0.05 0.11 0.01 0.00 0.35 0.25 0.19 0.03 0.00 0.00 0.03 0.02 0.09 0.01 0.00 4.85 1.54 0.31 0.17 0.48 0.08 0.26 0.19 1.10 0.13 0.60 0.03 0.04 0.00 0.03 0.01 0.01 0.01 0.01 0.00 0.05 0.00 4.93 1.77 1.96 1.67 0.56 0.53 0.62 0.25 1.27 0.31 0.67 4.72 1.06 0.22 0.35 0.97 1.45 0.52 1.46 0.16 0.25 0.38 Table 12. Weight of the variables on weighting based on factor analysis of mixed data Modalities Weight Modalities Weight Modalities Weight Female 0.00 Tiles 13.19 No working 0.00 Male 9.46 Others 0.00 Others 13.97 No married 0.00 Unprotected wells 1.61 Laborer/employee 17.56 Married 9.16 Protected wells 3.09 Self-employed 12.70 Elementary sc. 0.00 Drilling wells 0.91 Soil 0.00 Middle sch. 5.01 Tap water 1.84 No soil 6.07 High sch. 7.20 Bottled water 3.39 No working 0.00 College 3.96 No buying 0.00 Tertiary and others 13.74 No working 0.00 Buying 5.15 Tertiary and laborer/emp. 17.65 Working 14.31 No electricity 0.00 Tertiary and self-employed 12.76 No working Secondary and others 0.00 6.55 15.29 Tertiary 14.11 PLN with e.m. 10.24 Secondary and laborer/emp. 17.31 Secondary 15.54 No toilet 0.00 Secondary and self- emp 12.44 Primary 12.07 Public 1.87 Primary and others 11.79 Others 0.00 Self-owned 2.79 Primary and laborer/emp. 17.82 Free rental 65.41 Others 0.00 Primary and self-employed 11.36 Contract/lease 76.34 Holes 6.38 No working and free rental 0.00 Self-owned 67.81 River/lake/sea 4.20 No working and contract/ls. 3.17 Others 0.00 Septic tank 6.53 No working and self-owned 4.02 Wood 5.86 No 0.00 Working and others 21.58 Wall 4.67 Yes 2.60 Working and free rental 18.76 Others 0.00 No 0.00 Working and contract/lease 20.29 Asbestos 13.18 Yes 3.67 Working and self-owned 18.12 1077

Dramaga Village Household Welfare The household welfare status of Dramaga village obtained by ranking the household welfare index from the smallest to the largest and then dividing into 4 status from status 1 to status 4 with the cuts off refer to Dramaga village household welfare status in PPLS 2011. The number of households in every status presented in Table 16. Table 16. Number of the households in every status PPLS 2011 Weighting based on Multiple Correspondence Analysis Weighting based on Factor Analysis of Mixed Data Linear Aggregation Geometric Aggregation Linear Aggregation Geometric Aggregation 1 108 108 69 108 108 2 224 224 246 224 224 3 408 408 392 408 408 4 35 35 68 35 35 Validation Test The validation test in constructing household welfare status of Dramaga village c7onducted using 4 tests (Table 17). The first test is Mann-Whitney test, the second test Weighting Method Weighting based on Multiple Correspondence Analysis Weighting based on Factor Analysis of Mixed Data Table 17. Mann-Whitney test to PPLS 2011 is the average of the absolute differences in households rank ( ), the third test is the classification accuracy test, and the last test is the value of the area under the ROC curve (AUC). Aggregation Method P-Value of Mann-Whitney Test Accuracy (%) AUC (%) Linear 1.00 0.50 53.81 76.59 Geometric 0.02 0.66 42.45 67.86 Linear 1.00 0.70 44.00 59.22 Geometric 1.00 0.46 57.68 78.27 The Mann-Whitney test conducted to prove that the computed Dramaga village household welfare status is the same as in PPLS 2011 statistically. Accepting means there are similarities between them. The p- value of Mann-Whitney test grether than α (=0.05) found in weighting method based on factor analysis of mixed data with geometric aggregation (1.00) and linear aggregation (1.00), and weighting based on multiple correspondence analysis with linear aggregation (1.00), it means that there are similarities with PPLS 2011. Meanwhile, the weighting method based on multiple correspondence analysis with geometric aggregation had the p-value (=0.02) less than α (=0.05), it means that there are not similarities with PPLS 2011. The average of the absolute differences in households rank ( ) closest to 0 found in weighting method based on factor analysis of mixed data with geometric aggregation (0.46). Then followed by weighting based on multiple correspondence analysis with linear aggregation (0.50), weighting based on multiple correspondence analysis with geometric aggregation (0.66), and weighting based on factor analysis of mixed data with linear aggregation (0.70). The highest of classification accuracy found in weighting method based on factor analysis of mixed data with geometric aggregation (57.68%). Then followed by weighting based on multiple correspondence analysis with linear aggregation (53.81%), weighting based on factor analysis of mixed data with linear aggregation (44.00%), and weighting based on multiple correspondence analysis with geometric aggregation (42.45%). The highest AUC value found in weighting method based on factor 1078

analysis of mixed data with geometric aggregation (78.27%). Then followed by weighting based on multiple correspondence analysis with linear aggregation (76.59%), weighting based on multiple correspondence analysis with geometric aggregation (67.86%), and weighting based on factor analysis of mixed data with linear aggregation (59.22%). Thus, it can be concluded that based on the three tests, the weighting method based on factor analysis of mixed data with geometric aggregation is the best model. Characteristics of The Dramaga Village Household Welfare based on The Best Model Characteristics of Dramaga village household welfare status based on the best method can be explained by Anova and Manova test (Table 19), correlation test of the numeric variables (Table 20), and characteristic test of the categorical variables (Table 21 and 22). Descriptive statistics of the Dramaga village household welfare index in every status presented in Table 18. Anova and Manova test conducted to prove that among Dramaga village household welfare status statistically significant different (Table 18). Rejecting means there are significantly different. Anova test computed to Dramaga village household welfare index, while Manova test to all variables. The p-value of Anova and Manova test less than α (=0.05), it means among the status significantly different. Table 19 presented that the high value of Dramaga village household welfare status associated with the high value of the numeric variables. Table 20 and 21 presented the characteristics of status 1, 2, 3, and 4 respectively, based on the categorical variables. The sex of the household head in status 1, 2, and 3 is male, while it is female in status 4. The marital status of the household head in status 1, 2, and 3 is married, while it is not married in status 4. The educational level of the household head in all status is elementary school level. The working status of the household head in all status is working. The main occupational sector of the status is tertiary. household head in all The status of residence mastery in all status is selfowned. The wall material in status 1, 2, and 4 is wall, while it is the others in status 3. The roof material in all status is tiles. The source of drinking water in all status is protected wells. The way of getting the drinking water in all status is not buying. The source of main lighting in all status is electric meter. The toilet facility in all status is self-owned. The final stool disposal site in status 1 and 2 is in septic tank, while it is in the river/lake/sea in status 3 and 4. The refrigerator and motorcycle ownership in all status is none. The main job position of the household head in all status is the others. The floor material in all status is not soil. Table 18. Descriptive statistics of Dramaga village household welfare index in every status Number of households Mean Standard Deviation Min Max 1 108-5.88 1.09-10.67-4.79 2 224-2.45 1.23-4.79-0.22 3 408 3.61 2.34 0.08 8.60 4 35 9.76 1.33 8.62 14.34 Total 775 0.81 4.54-10.67 14.34 Table 19. Anova and Manova test of Dramaga village household welfare status Anova Manova df 1 df 2 F P-Value df 1 df 2 Wilks F P-Value 1 2 3 4 3 771 3289.00 0.00 3 771 0.000 129.27 0.000 2 1 1 330 607.80 0.00 1 330 0.000 314.95 0.000 3 1 1 514 1676.00 0.00 1 514 0.000 878.56 0.000 4 1 1 141 4845.00 0.00 1 141 0.000 496.09 0.000 3 2 1 630 1299.00 0.00 1 630 0.000 908.06 0.000 4 2 1 257 2898.00 0.00 1 257 0.000 651.25 0.000 4 3 1 441 234.80 0.00 1 441 0.001 439.37 0.000 1079

Table 20. Correlation test between the numeric variables and Dramaga village household welfare status Numeric Correlation (%) Numeric Correlation (%) Numeric Correlation (%) 47.43 3.38 18.11 49.10 26.22 8.05 21.03 13.16 58.16-17.13 55.49 43.80 60.98 40.51 46.44 Modalities Table 21. Characteristics of the categorical variables of status 1 and 2 Test Values Variable Modalities Test Values Variable 1 2 Male -20.56 16.28 90.74 77.68 Male -31.47 34.05 91.52 77.68 Married -18.10 17.14 88.89 72.26 Married -26.82 35.71 89.29 72.26 Elementary 11.03 14.75 80.56 76.13 Elementary 10.80 24.75 65.18 76.13 Working -22.05 15.87 91.67 80.52 Working -33.82 33.17 92.41 80.52 Tertiary 6.05 15.40 62.04 56.13 Tertiary 8.04 31.72 61.61 56.13 Self-owned -23.79 13.79 92.59 93.55 Self-owned -30.42 28.00 90.63 93.55 Wall -24.78 13.32 90.74 94.97 Wall -44.07 29.21 95.98 94.97 Tiles -14.12 13.15 84.26 89.29 Tiles -24.62 28.32 87.50 89.29 Protected Protected 13.55 13.56 79.63 76.13 wells wells -20.73 28.99 76.34 76.13 No buying 15.28 14.07 87.96 87.10 No buying 25.31 29.04 87.50 87.10 PLN with PLN with 31.59 13.83 93.52 3.74 47.96 28.72 96.43 3.74 Self-owned -14.57 14.63 92.59 75.87 Self-owned -16.22 29.42 90.63 75.87 Septic tank -2.21 16.05 48.15 41.81 Septic tank -0.09 33.33 48.21 41.81 No 3.33 14.38 12.96 60.13 No 1.13 25.11 14.73 60.13 No 7.26 13.47 12.96 76.65 No 11.07 27.27 14.73 76.65 Others 15.476 17.09 0.00 66.45 Others 16.14 32.04 0.45 66.45 No soil -74.95 13.69 97.22 98.97 No soil -110.25 29.20 100.00 98.97 Tertiary, Others Working, Self-owned 4.52 16.19 52.78 45.42-17.18 15.66 84.26 74.97 Tertiary, Others Working, Self-owned 5.98 30.11 47.32 45.42-24.48 32.19 83.48 74.97 Modalities Table 22. Characteristics of the categorical variables of status 3 and 4 Test Values Variable Modalities Test Values Variable 3 4 Male -13.64 47.84 70.59 77.68 Female 6.18 13.87 68.57 22.32 Married -8.46 46.07 63.24 72.26 Not married 15.73 13.49 82.86 72.26 Elementary 27.69 55.75 80.64 76.13 Elementary 11.11 4.75 80.00 76.13 Working -14.61 46.63 71.32 80.52 Working -1.68 4.33 77.14 80.52 Tertiary -7.54 48.05 51.23 56.13 Tertiary -0.71 4.83 60.00 56.13 Self-owned -66.57 53.66 95.34 93.55 Self-owned -12.20 4.55 94.29 93.55 Wall -63.34 52.99 95.59 94.97 Wall -15.73 4.48 94.29 94.97 Others -41.42 53.61 90.93 89.29 Tiles -15.73 4.91 97.14 89.29 Protected Protected -25.68 52.20 75.49 76.13 wells wells 6.45 4.24 71.43 76.13 No buying 30.51 52.59 87.01 87.10 No buying 1.00 4.30 82.86 87.10 PLN with PLN with 76.05 53.02 96.81 3.74 15.73 4.43 94.29 3.74 Self-owned -20.82 51.19 95.34 75.87 Self-owned -7.82 4.76 94.29 75.87 River/lake/sea 3.69 56.10 50.74 47.61 River/lake/sea 2.49 5.15 54.29 47.61 No 8.46 56.22 15.20 60.13 No 1.19 4.29 11.43 60.13 No 20.23 54.71 15.20 76.65 No 8.42 4.55 11.43 76.65 1080

Others -9.85 46.80 0.00 66.45 Others -1.19 4.08 0.00 66.45 No soil -164.52 52.80 99.26 98.97 No soil -15.73 4.30 94.29 98.97 Tertiary, Tertiary, -4.61 48.85 42.16 45.42 Others Others -0.48 4.55 48.57 45.42 Working, Working, -13.85 47.85 68.14 74.97 Self-owned Self-owned -1.44 4.30 71.43 74.97 Comparison of The Dramaga Village Household Welfare based on The Best Model and PPLS 2011 The comparison of the Dramaga village household welfare status based on the best model and PPLS 2011 can be explained by correlation test of the numeric variables (Table 23) and characteristic test of the categorical variables (Table 24 and 25). Table 23 showed that the correlation between numeric variables and Dramaga village household welfare status based on the best method is larger than PPLS 2011 with the test statistic is 0.77. This means that the best model gave more accurate results than PPLS 2011. Table 24 and 25 showed that most of the characteristics of the best model and PPLS 2011 are similar even in status 1, 2, 3, and 4, especially in sex of the household head, marital status of the household head, educational level of the household head, working status of the household head, main occupational sector of the household head, wall material, roof material, source of drinking water, way of getting the drinking water, source of main lighting, toilet facility, motorcycle ownership, main job position of the household head, and floor material. The different characteristics between the best model and PPLS 2011 only in 3 variables, the first is the status of residence mastery especially in status 3, the best model is self-owned, while it is contract/lease in PPLS 2011. The second is final stool disposal site especially in status 1, the best model is septic tank, while it is river/lake/sea in PPLS 2011. The last is refrigerator ownership especially in status 4, the best model is no refrigerator, while it has refrigerator in PPLS 2011. Numeric Table 23. Comparison of the numeric variables correlation test Correlation (%) Numeric Correlation (%) Numeric Correlation (%) PPLS 2011 Best Model PPLS 2011 Best Model PPLS 2011 Best Model 14.98 48.16 16.97 3.17 5.57 18.11 18.62 47.89 31.90 26.55 7.37 8.05 10.27 21.46 7.35 11.84 52.62 58.57 12.63-17.31 28.25 55.67 31.42 43.87 58.07 61.37 20.40 40.57 39.25 46.04 Table 24. Comparison of the categorical characteristics of status 1 and 2 1 2 PPLS 2011 Best model PPLS 2011 Best model Male Male Male Male Married Married Married Married Elementary Elementary Elementary Elementary Working Working Working Working Tertiary Tertiary Tertiary Tertiary Self-owned Self-owned Self-owned Self-owned Wall Wall Wall Wall Tiles Tiles Tiles Tiles Protected wells Protected wells Protected wells Protected wells No buying No buying No buying No buying 1081

Self-owned Self-owned Self-owned Self-owned River/lake/sea Septic tank Septic tank River/lake/sea No No No No No No No No Others Others Others Others No soil No soil No soil No soil Tertiary, Others Tertiary, Others Tertiary, Others Tertiary, Others Working, Self-owned Working, Self-owned Working, Self-owned Working, Self-owned Table 25. Comparison of the categorical characteristics of status 3 and 4 3 4 PPLS 2011 Best model PPLS 2011 Best model Male Male Female Female Married Married Not married Not married Elementary Elementary Elementary Elementary Working Working Working Working Tertiary Tertiary Tertiary Tertiary contract/lease Self-owned Self-owned Self-owned Wall Wall Wall Wall Tiles Others Tiles Tiles Protected wells Protected wells Protected wells Protected wells No buying No buying No buying No buying Self-owned Self-owned Self-owned Self-owned River/lake/sea River/lake/sea River/lake/sea River/lake/sea No No Yes No No No No No Others Others Others Others No soil No soil No soil No soil Tertiary, Others Tertiary, Others Tertiary, Others Tertiary, Others Working, Self-owned Working, Self-owned Working, Self-owned Working, Self-owned IV. CONCLUSION The algorithm of weighting method based on factor analysis of mixed data can handle a mixture of numeric and categorical variables, so it make easier to weight the mixed type variables of numeric and categorical. Constructing composite indicators of numeric and categorical variables using weighting method based on factor analysis of mixed data is more accurate than using weighting based on multiple correspondence analysis. The non-linear aggreagtion method developed to handle a mixture of compensatory and noncompensatory variables. Constructing composite indicators of compensatory and non-compensatory variables using geometric aggreagtion method is more accurate than using linear aggreagtion method in weighting method based on factor analysis of mixed data. The best model of constructing Dramaga village household welfare status by using weighting method based on factor analysis of mixed data and geometric aggreagtion method. The use of weighting method based on factor analysis of mixed data and geometric aggreagtion method gave more accurate results in individual classification. Constructing Dramaga village household welfare status using the best model gave the classification accuracy of 57.68% with the AUC of 78.27% and the absolute differences in households rank ( ) of 0.46. The correlation between numeric variables and Dramaga village household welfare status based on the best method is larger than PPLS 2011. This proved that using weighting method based on factor analysis 1082

of mixed data and geometric aggreagtion method in constructing Dramaga village household welfare status gave more accurate results. The Dramaga village household welfare status based on the best model characterized by sex of the household head, marital status of the household head, wall material, and final stool disposal site. The sex of the household head in status 1, 2, and 3 is male, while it is female in status 4. The marital status of the household head in status 1, 2, and 3 is married, while it is not married in status 4. The wall material in status 1, 2, and 4 is wall, while it is the others in status 3. The final stool disposal site in status 1 and 2 is in septic tank, while it is in the river/lake/sea in status 3 and 4. [5]. Pages, J. (2004). Analyse Factorielle de Donnees Mixtes. Revue de Statistiquee, 52(4), 93-111 [6]. Sari, W.J. (2011). Pembentukan Indikator Sasaran Dengan Proxy Means Test Berdasarkan Metode Princals, Depok: Universitas Indonesia [7]. Tarabusi, E.C., & Guarini, G. (2013). An Unbalance Adjustment Method for Development Indicators. Social Indicators Research, 112(1), 19-45 [8]. Tim Nasional Percepatan Penanggulangan Kemiskinan TNP2K]. (2013). Pembangunan Basis Data Terpadu untuk Mendukung Program Perlindungan Sosial, Jakarta: Author Besides that, most of the characteristics of Dramaga village household welfare status based on the best model are similar with PPLS 2011. The different characteristics between the best model and PPLS 2011 are only in the status of residence mastery, the final stool disposal site, and the refrigerator ownership. V. REFERENCES [1]. Castano, E. (2002). Proxy Means Test Index for Targeting Social Programs: Two Methodologies and Empirical Evidence. Lecturas de Economia, 56(1), 135-144 [2]. Mazziotta, M., & Pareto, A. (2013). Methods for Constructing Composite Indices: One for All or All for One?. Rivista Italiana di Economia Demografia e Statistica, 67(2), 67-80 [3]. Nicoletti, G., Scarpetta, S., & Boylaud, O. (2000). Summary Indicators Of Product Market Regulation With An Extension To Employment Protection Legislation. ECO/WKP. 226(1), 19-23 [4]. Organisation for Economic Co-Operation and Developement OECD]. (2008). Handbook on Constructing Composite Indicators Methodology and User Guide, Paris: Author 1083