10 th National Convention on Statistics (NCS) EDSA Shangri-La Hotel October 1-2, 2007

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1 10 th National Convention on Statistics (NCS) EDSA Shangri-La Hotel October 1-2, 2007 Small Area Estimation of the Provincial Prevalence of Underweight Among 6-10 Year-Old Children in the Philippines by Myrsa M. Belarmino, Wilma L. Molano and Zita V.J. Albacea, Ph.D. For additional information, please contact: Author s name : Myrsa M. Belarmino Designation : Science Research Specialist II Affiliation : Food and Nutrition Research Institute, DOST Address : DOST Compound, Bicutan, Taguig, Metro Manila Tel. no. : (0632) loc myrsa@fnri.dost.gov.ph Co-author s name : Wilma L. Molano Designation : Supervising Science Research Specialist Affiliation : Food and Nutrition Research Institute, DOST Address : DOST Compound, Bicutan, Taguig, Metro Manila Tel. no. : (0632) loc wlm@fnri.dost.gov.ph / wilmalmolano@yahoo.com Co-author s name : Zita V.J. Albacea Designation : Associate Professor Affiliation : Institute of Statistics, U.P. Los Baños Address : College, Los Baños, Laguna Tel. no. : (06349) zvjalbacea@yahoo.com

2 Small Area Estimation of the Provincial Prevalence of Underweight Among 6-10 Year-Old Children in the Philippines 1 by Myrsa M. Belarmino, Wilma L. Molano and Zita V.J. Albacea, Ph.D. 2 ABSTRACT This paper aims to provide an empirical basis for an indirect method of estimation of the provincial prevalence of underweight among 6-10 year -old children in the Philippines. Using the direct estimates obtained derived from the 2003 National Nutrition Surveys, coupled with the use of census data and administrative records the paper presents reliable statistics at the provincial level. These provincial estimates could be used by the local government units in the formulation of programs and policies aiming at improving the nutritional status of the children, particularly the school-age children, in their respective provinces. A total of 3,436 children belonging to the 6-10 age-group from 17 regions of the country were the subjects of this paper. Direct estimates of the prevalence of underweight at the provincial level were generated. Measures of accuracy, precision and reliability, such mean square error, estimated bias and coefficient of variation of these direct estimates were also computed. These measures were used to compare the direct estimates and those obtained using the indirect technique or what is usually referred to as small area estimation technique. The direct method generated only 7.14% reliable estimates of prevalence of underweight children. It was observed that such unreliable estimates are mainly due to small sample size of observations obtained at the provincial level. An indirect estimation technique, specifically, empirical best linear unbiased predictor (EBLUP) procedure was employed to circumvent the problem of unreliable provincial estimates. Results showed that by employing the EBLUP procedure, more reliable provincial estimates for the proportions of underweight 6-10 year-old children can be obtained. Keywords: small area estimation, provincial prevalence of underweight 6-10 year old children I. INTRODUCTION The need and urgency for sub-national and even sub-regional data for local level planning and evaluation of programs need not be overemphasized. Unfortunately, this type of data is frequently not readily available. What have been available are statistical data at the national level provided by statistical producing-agencies. Statistical data at a lower level of disaggregation are almost always not available at the statistics producing -agencies due to several reasons like the sampling design of nationwide survey is designed to generate reliable estimates at the national level and sometimes at the regional level but seldom at a level lower than what had been mentioned and because of budget and time constraints. 1 Paper to be presented at the 10 th National Convention on Statistics, October 1-2, 2007, EDSA Shangri-la Hotel, Metro Manila, Philippines. 2 Science Research Specialist II and Supervising Science Research Specialist, respectively, Food and Nutrition Research Institute, Department of Science and Technology, Bicutan, Taguig, Metro Manila, and Associate Professor of Statistics, Institute of Statistics, College of Arts and Sciences, University of the Philippines Los Baños, College, Laguna, Philippines.

3 This is true not only in the Philippines, but also in other developing countries. Hence, the study of small area estimation seems to be inevitable. Censuses, sample surveys and other special studies do answer the statistical data needs of its users both for large and small areas but only for certain characteristics and only for the period covered by the statistical activity. Sample surveys, on the other hand, can be conducted more often since these are manageable and cheaper than the censuses and hence, can provide timely information. Although national surveys can generally provide reliable estimates at the national level and other relatively large domains, however, the estimates generated for small areas or domains may not be statistically reliable. The Food and Nutrition Research Institute of the Department of Science and Technology (FNRI-DOST) has been experiencing the problem of being unable to provide data at a lower level of disaggregation from the National Nutrition Surveys (NNS) and the Updating of the Nutritional Status of Filipino Children, the two identified statistically designated surveys of the Institute, because the sampling design was intended to produce reliable estimates at the national and regional levels only. There has always been a clamor by the nutrition community to provide smaller area/domain estimates in order to have an efficient and effective nutrition intervention programs. This is also the request of some local government units whose interest is the eradication of malnutrition in their respective localities. Realizing the importance of providing data at a level of disaggregation needed for local level program and policy development, it has become necessary for FNRI-DOST to start working on small area/domain estimation on nutrition statistics. As one of the initial undertakings of the Institute is the application of the small area estimation to generate estimates of the provincial prevalence of underweight among children aged 6 to 10 years. This undertaking specifically aimed to provide a method for generating reliable provincial prevalence of underweight children aged 6 to 10 years. II. METHODOLOGY The 6 th National Nutrition Surveys (NNS), particularly, the Anthropometry and the Food Consumption Surveys, conducted by the FNRI-DOST every five years provide the data on weight and height measurements of 0-10 year-old children, their birthday and sex. Furthermore, this data set provides the number of 0-10 year-old children who are classified as underweight, stunted and wasted and total number of 0-10 year-old sampled children.

4 The 2000 Census of Population and Housing (CPH) conducted by the National Statistics Office (NSO) was also used as source of the auxiliary variables that are utilized in the indirect estimation methods. The CPH provides information on the size and distribution of the population as well as the geographic, social, economic and cultural characteristics. In addition, it also provides data on the housing units and its characteristics. Other data used were administrative records gathered from several government agencies such as Department of Health (DOH), Department of Education (DepEd), National Nutrition Council and Bureau of Agricultural Statistics. Using the NNS data sets, direct estimates of the provincial prevalence of the underweight among children aged 6 to 10 years were computed and its measures of reliability were obtained. Such measures include mean square error, estimated bias and coefficient of variation. These measures were used to compare the direct estimates with other estimates generated using indirect techniques. Indirect estimates of the provincial prevalence of underweight children aged 6 to 10 years were obtained using the model-based approach. Possible correlates of the provincial prevalence coming from the 2000 CPH and administrative data sources were identified using correlation analysis. With these correlates, a regression model was fitted for the provincial prevalence of underweight children 6-10 years old. The best predicting model was obtained by conducting residual analysis which aims to test the assumptions of linearity, zero mean error, and independence of error terms. Likewise, the assumption of multicollinearity was evaluated. The best predicting model is used to generate the regression-synthetic estimate of the provincial prevalence of underweight children aged 6-10 years. The other indirect estimator is the empirical best linear unbiased predictor (EBLUP) estimator which is the weighted average of the direct and regression-synthetic estimators where the weight is equal to the variance of the error due to the modeling process over the total variation due to the modeling and sampling process. It was said that this EBLUP estimator takes proper account of the between area variation relative to the precision of the direct estimation. The performance of the indirect provincial estimates was evaluated by computing its mean square error and corresponding coefficient of variation. The indirect estimates were compared to direct estimates in terms of computed measures of accuracy, precision and reliability. Likewise, the composition of the set of identified 10 provinces with the highest prevalence of underweight generated in each method as well as the ranking of the provinces was compared across the three methods.

5 All the computations are performed using the software Stata Version 7.0 and SPSS for Windows version 9.0. III. RESULTS AND DISCUSSIONS A. Direct Estimates of the Provincial Prevalence of Underweight Children 6-10 Years Old In 2003 the estimated prevalence of underweight children among school-age children 6-10 years old is 25.6% with a coefficient of variation of 3.5%. This national estimate is reliable but the regional estimates are not. The regional estimates have high coefficients of variation which range from 10.3% to as high as 20.2%. Bicol region had the highest prevalence of underweight (36.1%) and the lowest prevalence was registered in NCR (15.7%). Table 1 presents the direct estimates of the provincial prevalence of underweight children aged 6-10 years of the top ten provinces with their corresponding measures of reliability and precision. Two provinces from Region 6 belong to the top ten in the prevalence of underweight with Aklan topping the list (75.03%) followed by Western Samar (67.82%) and Catanduanes (55.56%). Also among regions with two provinces belonging to the top ten with the highest underweight prevalence are Regions 5, 8 and CAR. Table 1. Top ten provinces with the highest direct estimates of prevalence of underweight children 6-10 years old, NNS Rank Region Province Name Underweight Prevalence Standard Error of the Estimate Coefficient of Variation 1 6 Aklan Western Samar Catanduanes Eastern Samar CAR Kalinga Ilocos Sur Masbate CAR Apayao Antique ARMM Basilan B Oriental Mindoro Table 2 shows the distribution of the provincial estimates of the prevalence of underweight children aged 6-10 years old using the direct estimation procedure. See Appendix Table 1 for the direct estimates of the prevalence of underweight per province. Twenty-nine out of ninety-eight provinces and cities had prevalence between 20-30%.

6 About fourteen percent of the provinces/cities had more than 40% prevalence of underweight and similar percentage of provinces/cities had prevalence of underweight school-age children with less than 10%. Table 2. Distribution of direct provincial estimates of the prevalence of underweight children 6-10 years old, NNS Prevalence of Count Underweight > Total Table 3 shows the distribution of mean-square errors of the direct provincial estimates for the prevalence of underweight school-age children. Majority (79.59%) of the mean square errors are greater than This implies that the estimates are less precise and accurate. Only 16 out of 98 provinces and cities have low mean square errors with values at most This implies that only 16.33% of the provinces and cities have precise and accurate estimates. Table 3.Distribution of mean-square errors of the direct provincial estimates for the prevalence of underweight children 6-10 years old, NNS 2003 Mean Square Error Count > Total A summary of the measures of reliability is shown in table 4. Almost half or 45.92% of the provincial estimates had coefficient of variations greater than 30%. This implies that most of the estimates are not reliable. Only 7 out of 98 provinces/cities have coefficient of variations at most 10%.

7 Table 4. Distribution of coefficient of variation of the direct provincial estimates of the prevalence of underweight children 6-10 years old, NNS Coefficient of Variation Count > Total B. Regression-Synthetic Estimates of the Provincial Prevalence of Underweight Children 6-10 Years Old The identified correlates of provincial prevalence of underweight children 6-10 years were used to find the best predicting model. Ordinary least squares method was first used to find the parsimonious model with the highest adjusted R 2. Using the regression estimates the weights to be used in the weighted least squares method were computed. The weighted least squares estimation procedure led to the estimated regression coefficients shown in Table 5. The regression coefficients are all significantly different from zero at 6% level of significance. The predicting model had an adjusted R 2 of 48.85%. Furthermore, the residuals of the model satisfied all the assumptions of linearity, normality, independence of error terms, zero mean error and homocedasticity. Table 5. Estimated regression coefficients of the predicting model for provincial proportion of underweight children aged 6-10 years using weighted least squares method. Predictor Estimated Standard Coefficient Error Provincial ratio of doctors in local government units to the total population Provincial ratio of hospital to total population Provincial proportion of housing units needing major repair Provincial proportion of households with at least one member not related to the household head Provincial proportion of housing units with roof made of strong materials Provincial proportion of barangays with one-half of the barangay proportion engaged in agriculture Provincial proportion of households headed by a person who completed grade 1 Provincial proportion of households with at least one member who is quadriplegic Provincial ratio of the total midwives in local government units to the total population Constant

8 Using the predicting model, the regression-synthetic estimates of the prevalence of underweight children 6-10 years old at the provincial level were computed. Table 6 shows that Western Samar registered the highest prevalence of underweight school-aged children 6-10 years old (53.63%) followed by Basilan (46.19%) and Eastern Samar (45.63%). Aklan that ranked first in the direct estimation is now ranked 7 th in this procedure. Table 6. Top ten provinces with the highest regression-synthetic estimates of the prevalence of underweight children 6-10 years old. Rank Region Province Name Underweight Prevalence Mean Square Error Coefficient of Variation 1 8 Western Samar Basilan Eastern Samar Masbate Oriental Mindoro Sarangani Aklan Negros Oriental Leyte Capiz The distribution of regression-synthetic provincial estimates of the prevalence of underweight children 6-10 years old is shown in Table 7. Thirty eight (38) out of the 98 or 38.78% provinces have underweight prevalence between 20 to 30%. About 23% of the provincial estimates falls between 30 to 40%. Table 7. Distribution of regression-synthetic provincial estimates of the prevalence of underweight children 6-10 years old. Prevalence of Underweight Count > Total Table 8 shows the distribution of mean square errors of the regression -synthetic provincial estimates for the prevalence of underweight 6-10 years old children. Regressionsynthetic provincial estimates resulted to lower mean square errors that is, more than half or 55.1% of the estimates have low mean square errors (at most 0.001). About 34% of the estimates falls between to and 11% of the estimates have mean square error greater than The results indicate that the regression-synthetic estimation procedure genrated more accurate and precise estimates as compared to the direct estimation method.

9 The reliability of the estimates are measured by the coefficient of variation of the estimates. From Table 9 majority of the regression-synthetic provincial estimates posted lower coefficients of variation. Thirty six percent (36%) of the estimates have coefficients at mo st 10% and 41 out of the 98 provinces have coefficients between 10 to 20%. The results also showed an improvement from the estimates obtained from the direct estimation procedure. More reliable estimates were obtained from this model-based procedure. Table 8.Distribution of mean-square errors of the regression-synthetic provincial estimates for the prevalence of underweight children 6-10 years old. Mean Square Error Count > Total Table 9. Distribution of coefficient of variation of the regression-synthetic provincial estimates of the prevalence of underweight children 6-10 years old. Coefficient of Variation Count > Total C. EBLUP Estimates of the Provincial Prevalence of Underweight Children 6-10 Years Old Table 10 shows the provincial estimates of the prevalence of underweight children 6-10 years old using the regression-synthetic EBLUP method. The top three prevalence of underweight school-aged children were Western Samar (62.65%) followed by Aklan (60.42%) and Catanduanes (54.95%). Catanduanes did not rank among the top ten highest prevalence of underweight estimates under the regression-synthetic estimation procedure, but in the EBLUP estimation results, it got the third rank similar with the results of the direct estimation method. However for the first 2 provinces, the result is reversed. Table 10. Top ten provinces with highest prevalence of underweight children 6-10 years old based on the EBLUP estimates. Rank Region Province Name Underweight Prevalence Mean Square Error Coefficient of Variation 1 8 Western Samar Aklan Catanduanes Eastern Samar Masbate Apayao

10 Rank Region Province Name Underweight Prevalence Mean Square Error Coefficient of Variation 7 15 Basilan Oriental Mindoro Antique Ilocos Sur In Table 11, 13% of the provinces have prevalence estimates below 10% while those provinces with the highest prevalence (greater than 40%) are about 10%. The highest frequency (33% of the provinces) of prevalence estimates falls between 20 to 30%. Table 11. Distribution of EBLUP provincial estimates of the prevalence of underweight children 6-10 years old. Prevalence of Underweight Count > Total From Table 12, the results of the EBLUP estimates posted 68% of the provinces have mean square error greater than Only 16% of the provinces have mean square errors at most The distribution of the mean square error of the estimates generated using the EBLUP method is more or less similar with the direct estimates. More than half of the estimates are not precise and accurate due to their high mean square errors. Table 12. Distribution of mean-square errors of the EBLUP provincial estimates for the prevalence of underweight children 6-10 years old. Mean Square Error Count > Total Similarly for the measurement of reliability, most of the EBLUP estimates have coefficients of variation that are greater than 10%. Table 13 shows the distribution of the coefficients of variation of the EBLUP provincial prevalence estimates of school-aged children.

11 Table 13. Distribution of coefficient of variation of the EBLUP provincial estimates of the prevalence of underweight children 6-10 years old Coefficient of Variation Count > Total Results also showed that only 7% of the provinces are reliable or with coefficients at most 10%. About 28% of the provinces have coefficients between 10 to 20% and the rest of the provinces have coefficients greater than 20%. D. Comparison of the Estimates Comparing the results of the three estimates based on ranking as shown in Table 14, all the provinces belonging to the top 10 underweight prevalence in direct estimates are also the provinces in the top 10 based on EBLUP estimates except for Kalinga. However, for regression-synthetic estimates, not all the provinces belonging to the top ten are the same as in the direct or EBLUP estimates. Table 14. Ranking of the direct, regression-synthetic and EBLUP estimates. Rank Based on Rank Based Regression- Region Province Name on Direct Synthetic Estimates Estimates Rank Based on EBLUP Estimates 6 Aklan Western Samar Catanduanes Eastern Samar CAR Kalinga Ilocos Sur Masbate CAR Apayao Antique 8-9 ARMM Basilan B Oriental Mindoro Note: Provinces ranking in the regression-synthetic that are not included in the list are: Sarangani (6 th ), Negros Oriental (8 th ), Leyte (9 th ) and Capiz (10 th ). Figures 1, 2 and 3 show the comparison of the three methods in the distribution of prevalence estimates, mean square errors and coefficients of variation of the estimates. In Figure 1, large percentage of the estimates is within the range of 20 to 30 for all the three estimators. The regression-synthetic and the EBLUP method produced almost the same number of estimates falling within the range of 10 to 20.

12 Figure 2 presents the distribution of mean square errors of the three sets of the estimates. The regression-synthetic estimates have the most number of accurate and precise estimates as compared to the other sets Direct Regression-synthetic eblup >40.00 Prevalence of underweight Figure 1. Comparison of the distribution of provincial estimates of the proportion of underweight children 6-10 years old using direct, regression-synthetic, and EBLUP estimation methods Direct Regression-synthetic eblup > Mean Square Error Figure 2. Comparison of the distribution of mean square errors of the provincial proportion of underweight 6-10 year old children using direct, regression-synthetic, and EBLUP estimation methods

13 Figure 3 shows the distribution of coefficients of variation of the estimates derived from the three estimators. The set of estimates from the regression-synthetic estimator is the most reliable. It shows that about 36% are falling within the 0-10% range of the coefficients while the direct and EBLUP estimator produced almost same number of estimates falling at most 10%. The rest of the coefficients of variation of the estimates of the direct and EBLUP are way too large to be reliable Direct Regression-synthetic eblup >30.00 Coefficient of Variation Figure 3. Comparison of the distribution of the coefficient of variation of the provincial proportion of underweight children 6-10 years old using direct, regression-synthetic, and EBLUP estimation methods IV. CONCLUSION The anthropometric data produced by the FNRI coming from the National Nutrition Survey conducted every 5 years is not designed to produce estimates at the regional or provincial level. Hence, there is the need to come up with estimation procedure to generate reliable statistics at that level. Three estimation procedures were employed and the results were compared. The direct estimates resulted to high mean square errors and coefficients of variation, hence, the estimates are less precise and accurate and not reliable. The regression-synthetic estimates showed lower mean square errors and coefficients of variation and therefore more precise and accurate and reliable. On the other hand, the EBLUP estimates though, it is a combination of the direct and regression-synthetic estimates, generated more or less similar

14 results with the direct estimates. Based on the findings, the regression-synthetic estimation procedure is considered to be the best estimator for the provincial prevalence of underweight children aged 6-10 years old. The use of small area estimation technique proved to be a useful method in generating sub-national estimates wherein the survey is not designed to have reliable estimates at such disaggregation. By combining the survey data with the administrativebased records such estimation process is possible. However, the success of the small area estimation method relies heavily on the quality of administrative records collected by the local government units and at the central agencies designated to collect such data.

15 References ALBACEA, ZITA VJ. C. (2004) Small Area Estimation of Sub-National Poverty Incidence. August 3, CAS TILLO, E.V. et al. (2005) Reliability of National and Regional Estimates of Nutritional Status Using the Anthropometric Indicators, Philippines Unpublished Report. Food and Nutrition Research Institute-DOST. FOOD AND NUTRITION RESEARCH INSTITUTE-DOST (2005) Sixth National Nutrition Survey: Philippines, NANAK CHAND AND CHARLES H. ALEXANDER. Using Administrative Records for Small Area Estimation in the American Community Survey September 14, NATIONAL NUTRITION COUNCIL. Has the nutrition situation improved?. August 3, RAO, J.N.K. (2000). Statistical Methodology for Indirect Estimations in Small Areas. Instituto Vaseo de Estadistica. EUSTAT. SOTTO, JENNIFER C. (2006) Estimating the Proportion of Underweight Children Aged 0 to 5 Years at the Provincial Level in the Philippines, Unpublished Special Problem, University of the Philippines at Los Baños.

16 Appendix Table 1. Direct provincial estimates of the prevalence of underweight children 6-10 years old Region/ Province Underweight Prevalence Estimate Standard Error Mean Square Error Coefficient of Variation Region 1 Ilocos Norte Ilocos Sur La Union Pangasinan Region 2 Cagayan Isabela Nueva Vizcaya Quirino Region 3 Bataan Bulacan Nueva Ecija Pampanga Tarlac Zambales Aurora Region 4A Batangas Cavite Laguna Quezon Rizal Region 4B Marinduque Occidental Mindoro Oriental Mindoro Palawan Romblon Region 5 Albay Camarines Norte Camarines Sur Catanduanes Masbate Sorsogon Region 6 Aklan Antique Capiz Iloilo Negros Occidental Guimaras Region 7 Bohol Cebu Negros Oriental Siquijor

17 (Con d) Appendix Table 1. Direct provincial estimates of the prevalence of underweight children 6-10 years old Region 8 Region/ Province Underweight Prevalence Estimate Standard Error Mean Square Error Coefficient of Variation E. Samar Leyte N. Samar W. Samar So. Leyte Biliran Region 9 Zambo del Norte Zambo del Sur Zambo Sibugay Isabela City Region 10 Bukidnon Camiguin Lanao del Norte Misamis Occ Misamis Or Region 11 Davao del Norte Davao del Sur Davao Oriental Compostela Region 12 N. Cotabato S. Cotabato Sultan Kudarat Sarangani Cotabato City NCR Manila Mandaluyong Marikina Pasig Quezon City San Juan Caloocan Malabon Navotas Valenzuela Las Pinas Makati Muntinlupa Paranaque Pasay Pateros Taguig

18 (Cont d) Appendix Table 1. Direct provincial estimates of the prevalence of underweight children 6-10 years old CAR Region/ Province Underweight Prevalence Estimate Standard Error Mean Square Error Coefficient of Variation Abra Benguet Baguio Ifugao Kalinga Mt. Province Apayao ARMM Basilan Lanao del Sur Maguindanao Sulu Tawi -tawi CARAGA Agusan Norte Agusan Sur Surigao Norte Surigao Sur