• Communications for Statistical Applications and Methods
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• 제22권4호
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• pp.349-359
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• 2015

We study a semiparametric Bayesian approach to small area estimation under a nested error linear regression model with area level covariate subject to measurement error. Consideration is given to radial basis functions for the regression spline and knots on a grid of equally spaced sample quantiles of covariate with measurement errors in the nested error linear regression model setup. We conduct a hierarchical Bayesian structural measurement error model for small areas and prove the propriety of the joint posterior based on a given hierarchical Bayesian framework since some priors are defined non-informative improper priors that uses Markov Chain Monte Carlo methods to fit it. Our methodology is illustrated using numerical examples to compare possible models based on model adequacy criteria; in addition, analysis is conducted based on real data.

• Communications for Statistical Applications and Methods
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• 제17권6호
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• pp.845-852
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• 2010

The outcomes of counts commonly occur in the area of disease mapping for mortality rates or disease rates. A Poisson distribution is usually assumed as a model of disease rates in conjunction with a gamma prior. The small area typically refers to a small geographical area or demographic group for which very little information is available from the sample surveys. Under this situation the model-based estimation is very popular, in which the auxiliary variables from various administrative sources are used. The empirical Bayes estimator under Poissongamma model has been considered with its accuracy measures. An accuracy measure using a bootstrap samples adjust the underestimation incurred by the posterior variance as an estimator of true mean squared error. We explain the suggested method through a practical dataset of hitters in baseball games. We also perform a Monte Carlo study to compare the accuracy measures of mean squared error.

• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.637-645
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• 2003

Small area estimation had been studied using data-based methods such as Direct, Indirect, Synthetic methods. However recently, model-based such as based on regression or time series estimation methods are applied to the study. In this paper we investigate a model-data based small area estimation which takes into account the spatial relation among the areas. The Economic Active Population Survey in 2001 are used for analysis and the results from the model based and model-data based estimation are compared with using MSE(Mean squared error), MAE(Mean absolute error) and MB(Mean bias).

• 보건교육건강증진학회지
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• 제20권1호
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• pp.19-39
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• 2003

Purpose: Although there is a lot of secondary data available for comparing community health status and planning health policies in terms of large area such as metropolitan cities or provinces, there is restricted data for establishing community health policies of the small areas such as towns, Gun(i.e., districts), and Gu. Specifically, the problems of producing a valuable index for health promotion in small areas are three fold: First, there is not an appropriate index model for measuring a small community health status. Second, a large part of secondary data in the small areas has been produced in an irregular time interval. In addition, all valuable data can not be integrated without time consuming work. Thus this study tries to establish a health promotion index model for assisting community health promotion initiatives of local governments. Methods and materials: Literature review, community health specialist consultation and a questionnaire survey was performed. Results: Based on Dever's model, a prototype of health promotion indicators was proposed and modified by the community health specialists. 15 classification scheme of statistical yearbook reorganized into the six areas. Those six areas were comprised in 24 indicator class with 96 specific indicators. Through further modification processes by a questionnaire survey, we developed a health promotion indicator model that contains six areas with 23 indicator class encompassed by 87 specific indicators. Conclusions: This study proposed a model of health promotion indicator comprised in the six areas with 23 indicator classes for measuring small area health promotion status. However, more specific or additional data in human biology, environment, and socioeconomic data is essential for producing a stronger model for health promotion measurement.

• Journal of the Korean Data and Information Science Society
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• 제27권5호
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• pp.1433-1441
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• 2016

Small area model provides reliable and accurate estimations when the sample size is not sufficient. Our dataset has an inherent nonlinear pattern which signicantly affects our inference. In this case, we could consider semiparametric models such as truncated polynomial basis function and radial basis function. In this paper, we study four Bayesian semiparametric models for small areas to handle this point. Four small area models are based on two kinds of basis function and different knots positions. To evaluate the different estimates, four comparison measurements have been employed as criteria. In these comparison measurements, the truncated polynomial basis function with equal quantile knots has shown the best result. In Bayesian calculation, we use Gibbs sampler to solve the numerical problems.

• Journal of the Korean Data and Information Science Society
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• 제27권5호
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• pp.1423-1431
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• 2016

When the sample size in a certain domain is too small to produce adequate information, small area model with random effects is usually used. Also, if we do not consider an inherent pattern which data possess, it considerably affects inference. In this paper, we mainly focus on modeling to handle increased variation of the Current Population Survey (CPS) median income as the Internal Revenue Service (IRS) mean income increases. In a hierarchical Bayesian framework, most estimations are carried out through the Gibbs sampler while the grid method is used to generate parameters from non-standard form. Numerical study indicates that the performance of proposed model is better than that of CPS method in terms of four comparison measurements.

• Journal of the Korean Data and Information Science Society
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• 제27권2호
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• pp.531-538
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• 2016

In this paper we deal with the small area estimation for the case that the response variables take binary values. The mixed effects models have been extensively studied for the small area estimation, which treats the spatial effects as random effects. However, when the spatial information of each area is given specifically as coordinates it is popular to use the geographically weighted logistic regression to incorporate the spatial information by assuming that the regression parameters vary spatially across areas. In this paper, relaxing the linearity assumption and propose a geographically weighted kernel logistic regression for estimating small area proportions by using basic principle of kernel machine. Numerical studies have been carried out to compare the performance of proposed method with other methods in estimating small area proportion.

• Communications for Statistical Applications and Methods
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• 제29권5호
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• pp.547-559
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• 2022

For a chi-squared test, which is a statistical method used to test the independence of a contingency table of two factors, the expected frequency of each cell must be greater than 5. The percentage of cells with an expected frequency below 5 must be less than 20% of all cells. However, there are many cases in which the regional expected frequency is below 5 in general small area studies. Even in large-scale surveys, it is difficult to forecast the expected frequency to be greater than 5 when there is small area estimation with subgroup analysis. Another statistical method to test independence is to use the Bayes factor, but since there is a high ratio of data dependency due to the nature of the Bayesian approach, the low expected frequency tends to decrease the precision of the test results. To overcome these limitations, we will borrow information from areas with similar characteristics and pool the data statistically to propose a pooled Bayes test of independence in target areas. Jo et al. (2021) suggested hierarchical Bayesian pooling models for small area estimation of categorical data, and we will introduce the pooled Bayes factors calculated by expanding their restricted pooling model. We applied the pooled Bayes factors using bone mineral density and body mass index data from the Third National Health and Nutrition Examination Survey conducted in the United States and compared them with chi-squared tests often used in tests of independence.

• Journal of the Korean Data and Information Science Society
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• 제26권1호
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• pp.101-109
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• 2015

행정구역상 읍/면/동 단위의 소지역 (small area)별로 질병위험의 차이에 대한 분석을 위해, 2005년 기준 서울 행정동을 기준으로 2005년부터 2008년까지 질병, 사고, 암 사망자료에 대한 표준화 사망률 (SMR; standardized mortality rate)을 고려하였다. 소지역 단위로 질병사망률을 직접 추정하는 것은 소지역 내 표본수가 작아, 개발 소지역 단위에서의 직접 계산된 SMR은 그 추정치의 정도 (precision) 확보가 어려운 문제점이 발생한다. 따라서, 본 연구에서는 각 소지역간 효과 추정을 위해 공간적 상관성 (spatial correlation)을 가지는 다단계 일반화 선형모형 (HGLM; hierarchical generalized linear models)을 고려하였다. 이를 통해, 서울지역 동별 주요 사망원인에 따른 공변량의 효과 및 추정된 SMR을 근거로 질병지도 결과를 제시하였다.

• 응용통계연구
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• 제24권3호
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• pp.445-453
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• 2011

Almost all small area estimations are obtained by minimizing the mean squared error. Recently relative error prediction methods have been developed and adapted to small area estimation. Usually the estimators obtained by using relative error prediction is called a shrinkage estimator. Especially when data set consists of large range values, the shrinkage estimator is known as having good statistical properties and an easy interpretation. In this paper we study the shrinkage estimators based on logistic regression type estimators for small area estimation. Some simulation studies are performed and the Economically Active Population Survey data of 2005 is used for comparison.