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Small Geographic Area Estimation in Winbugs with Two Approaches Prediction

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Small Geographic Area Estimation in Winbugs with Two Approaches Prediction Journal of the Faculty of Environmental Science and Technology. Okayama University Vo1.9. No.1, pp.9-17. February 2004 Small Geographic Area Estimation in WinBUGS with Two Approaches Prediction Agus SETIAWAN· and Tomoyuki TARUMf· (Received November 25, 2003) Small Area Estimation (SAE) is the process ofusing statistical models to link survey outcome variables to a set ofpredictor variables known for small domains, in order to predict domain-level estimates. The need for detailed statistics on small area is constantly increasing. Small area estimation is becoming important in survey sampling due to a growing demand for reliable small area statistics from both public and private sectors. Bayesian hierarchical models provide a convenient framework for disease mapping and geographical correlation studies. Computation may be carried out using the freely-available WinBUGS software. Two approaches prediction to estimate total patient in small area i will be presented. For the purpose ofthis paper, the small area estimation in this context use data ofIndonesia's population based on the 2000 census for the population of Jakarta and data of patient diarrhea from District Health Service ofJakarta. We interest to predict total patient of diarrhea as variable of interest and data population as auxiliary data from unsample for each small area. Key words: Auxiliary data, Population density, Sample survey, Small area estimation, WinBUGS 1. INTRODUCTION information collected on a large spatial scale to local areas within the study region. A geographic Sample surveys are widely used to provide domain (area) is regarded as "large (or major)" if estimates oftotal, mean and other parameters not the domain-specific sample is large enough to only for the total population of interest but also yield "direct estimates" of adequate precision. A for subpopulation (or domain) such as geographic domain is regarded as "small" if the domain­ area. The small area estimations are widely used specific sample is not large enough to support in practice of sample survey to provide estimates direct estimates ofadequate precision, 1.N.K. Rao parameter interest ofgeographic area. Small area (2003). typically refers to a geographic area for which The term "small area" and "local area" are very little information is obtained from surveys. commonly used to denote a small geographical What is meant by a small area? By Murdock area. Some other terms used to denote a domain and Ellis (1991), small area refer to counties and with sample size include "local area", "sub subcounty areas like cities, census tract, ZIP domain", "small subgroup", "subprovince", and (Zone Improvement Plan (US post office postal "minor domain". code system)) code areas, and even individual Interest in small area estimation methods has blocks while by J. Cuzick and P. Elliot (1992), further increased. Some other proceedings of this will depend on the context, as it relates to the conferences on small area estimation include number of cases (in this case about disease) that Platek and Singh (1986), Platek, Rao, Sarndall are observed. and Singh (1987) and J. N. K. Rao (2001). According to Ulrike' Schach (Discussion Paper, Papers on small area estimation include Noel J. 2001), the general idea ofa small area estimation Purcell (1979), Prasad, N. G. N. and Rao, 1. N. K. in its original sense is an intrapolation of (1990), Malay Ghosh and Rao J. N. K. (1994), and Malay Ghosh, Kannan Natarajan, T. W. F. ·Graduate School of Natural Science and Technology, Stroud, and Bradley P. Carlin (1998). Okayama University 3-1-1 Tsushima-Naka, Okayama, For the purpose of this paper, the small area Okayama 700-8530, Japan, [email protected] estimation in this context use data of Indonesia's or [email protected] ··Department of Environmental and Mathematical Sciences, population based on the 2000 census for the Okayama University 3-1-1 Tsushima-Naka, Okayama, population ofJakarta and data ofpatient diarrhea Okayama 700-8530, Japan, [email protected] from District Health Service of Jakarta. We 9 10 J. Fac. Environ. Sci. and Tech., Okayama Univ. 9 (1) 2004 interest to estimate total patient of diarrhea as variable of interest and data population as auxiliary data from unsample for each small area. Jakarta is the capital and largest city of the Republic ofIndonesia. Situated between 105° 49' 5" east longitude and 06° 10' 7" south latitude. The city is centrally located within Indonesia on the north-west coast of the island of Java. The city dominates Indonesia's administrative, econo­ mic and cultural activities, and is a major commercial centre and transport hub within Asia. .1481.8296 .14894°.16877 We would like to describe two approaches of _ 8323 .10595 • 17034 • 17404 estimation of total patient of diarrhea in Jakarta. EZJ 10651 .11794 .20945.24688 ·1~82 • 25091 .45771 The first approach is the predictive approach to [ill 12983 domain and the second approach is by pass Figure 1. The Population Density ofJakarta Province through approach to data individual. 2000 Census ofPopulation - Indonesia In the Table 1. is showed that the area of Jakarta is 664.12 square kilometers. The special This paper focuses on the spatial distribution of capital city region of Jakarta is divided among 5 the population density of the Jakarta Province at municipalities (kotamadya), South Jakarta, East two different levels of scale, densely and rarely Jakarta, Central Jakarta, West Jakarta, and North populated area. So that, we can see the Jakarta in Jakarta. These municipalities subdivided into spatial terms by using different scales of analysis subdistricts (kecamatan) and villages (desa/ (urban, subdistricts and province). kelurahan). Subdistricts and villages are Figure 1 shows, the most densely populated government at lower levels. The special capital area signed with the blue color, which have city region of Jakarta comprise 5 municipalities, population density between 25,091 - 45,771 43 subdistricts and 265 urban. person per Square kilometers. The most rarely populated area signed with the old brown color, Table 1. The Number ofArea, Subdistrict, Villages and 1,461 - 8,296 person per square kilometers. Population Density In Jakarta by Municipalities (2000) From Figure 1 also appear that excelsior population density on area then area will be Population Sub- Munici- Area Village Density concentrated to center of economic. Because in No. 2 dis- palities (km ) (urban) (person/ Jakarta province, the center of economic located trict 2 km ) in the middle ofJakarta. South 145.73 IO 65 12,242 Jakarta The shade of brown colors show areas have East 2 188.19 10 65 12,476 belonging population density under 12,569 Jakarta person per square kilometers, while the shade of Central 3 48.08 8 44 18,190 Jakarta green to blue colors show areas have population West ~ 4 127.1 \ 8 56 14,98\ density 12,569 person per square kilometers. Jakarta Conform by subdistrict that the highest North 5 \55.0\ 7 35 9,266 Jakarta population density (very dense) is Johar Barn Jakarta 664.12 43 265 \2,569 (45,771) and Tambara (41,834). Johar Barn with area 2,38 square kilometers is occupied 108,936 From the aforementioned data, we classified person while Tambora with area 5,48 square two kinds ofdata, 25 subdistricts have population kilometers is occupied 229,253 person. The density upper 12.569 person per km 2 and 18 lowest population density area (very rare) is 2 subdistricts under 12.569 person per km . In this Kepulauan Seribu (1,461). Kepulauan Seribu or paper, we interest to estimate total patient from the thousand islands is a group of small islands subdistrict that have population density upper scattered in the bay of Jakarta (North Jakarta), 2 12,569 person per km . From 25 subdistricts (160 actually a total of 110 islands. The population urban area) that have population density upper among one island to another is different Jakarta's population density, choosen 75 urban as significantly. In Figure 1 the Kepulauan Seribu is sample. The population of density in Jakarta not appear because the position of them are Province by subdistricts are presented in Figure 1. rather scattered. Agus SETIAWAN et al. / Small Geographic Area Estimation in WinBUGS 11 Table 2. Sample Sizes (n;). Patient ofDianhea. and Population Data at Population Density ~ 12.569 person per kIn' in Jakarta -Indonesia 2000 n k Yijk Xijk n k Yijk Xijk Xa n k Yijk Xijk Xik 2 715 3367 10676 4 28 526 3931 20156 18 4 55 253 3364 26390 685 30986 98260 946 36177 185513 294 30961 242897 523 3581 29 327 2188 56 194 2098 SOl 32962 587 20139 19313 113 2399 22467 30 352 3546 57 0 485 5106 132 22082 206786 635 32638 565 46991 4 104 1669 31 187 2265 58 397 4221 120 15361 337 20843 463 38852 o 109 1920 32 397 3621 24240 19 59 328 6543 34011 \ \26 \7668 477 33325 223105 433 6022\ 313039 o 174 3447 33 696 6251 60 0 \56 3579 202 31722 835 57539 208 32945 116 1920 34 566 5803 61 0 119 2996 135 17673 679 53407 158 27578 o 176 2575 10 35 303 1861 8683 20 4 62 300 2212 13392 \ 20S 23698 359 17127 79915 274 20355 123261 o 172 1454 14022 36 0 211 1387 63 309 2811 I 294 13384 129058 I 250 12764 1 283 25877 10 0 221 2801 II 4 37 0 188 2481 22752 64 0 260 2608 378 25783 227 22840 209416 239 24005 II 0 304 3312 38 282 4537 65 0 149 1178 519 30487 341 41760 I 136 10839 4 12 267 212\ 19121 39 0 200 3098 21 2 66 0 317 3226 39914 249 19523 175992 243 28516 368 29695 367373 13 0 314 2267 40 0 209 2878 67 0 542 5926 292 20868 253 26494 630 54542 14 291 2754 12 41 0 272 3436 7979 22 68 0 67 3205 18182 270 25352
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