Small Area Estimation Approach Research Articles

Vaccination coverage in India: A small area estimation approach

Information on population health indicators in India come from a number of surveys that vary in periodicity, scope and detail. In the case of immunization, the most recent coverage indicators are derived from the first round of Annual Health Survey (AHS-1, 2010-11), but these were conducted only in 9 of 35 states and union territories. The most recent national surveys of immunization coverage were conducted in 2009 (Coverage Evaluation Survey) by UNICEF. Therefore, reliable immunization coverage data for the entire country since 2009 is lacking. We used an established approach of small area estimation to predict coverage rates of several vaccinations for the remaining 26 states (not covered by AHS-1) in 2011. In our method, we considered a linear mixed model that combines data from five cross sectional surveys representing five different time points. Our model encompasses sampling error of the survey estimates, area specific random effects, autocorrelated area by time random effects and hence, borrows strength across areas and time points both. Model-based estimates for 2011 are almost identical to the AHS-1 estimates for the nine states, suggesting that our model provides reliable prediction of vaccination coverage as AHS-1 estimates are highly precise because of their large sample size. Results indicate that coverage inequality between rural and urban areas has been reduced significantly for most states in India. The National Rural Health Mission has had both supply side and demand side effects on the immunization programme in rural India. In combination, these effects may have contributed to the reduction of vaccination coverage gaps between urban and rural areas.

Small area estimation for semicontinuous skewed spatial data: An application to the grape wine production in Tuscany

Linear-mixed models are frequently used to obtain model-based estimators in small area estimation (SAE) problems. Such models, however, are not suitable when the target variable exhibits a point mass at zero, a highly skewed distribution of the nonzero values and a strong spatial structure. In this paper, a SAE approach for dealing with such variables is suggested. We propose a two-part random effects SAE model that includes a correlation structure on the area random effects that appears in the two parts and incorporates a bivariate smooth function of the geographical coordinates of units. To account for the skewness of the distribution of the positive values of the response variable, a Gamma model is adopted. To fit the model, to get small area estimates and to evaluate their precision, a hierarchical Bayesian approach is used. The study is motivated by a real SAE problem. We focus on estimation of the per-farm average grape wine production in Tuscany, at subregional level, using the Farm Structure Survey data. Results from this real data application and those obtained by a model-based simulation experiment show a satisfactory performance of the suggested SAE approach.

Understanding State Variation In Health Insurance Dynamics Can Help Tailor Enrollment Strategies For ACA Expansion

The number and types of people who become eligible for and enroll in the Affordable Care Act's (ACA's) health insurance expansions will depend in part on the factors that cause people to become uninsured for different lengths of time. We used a small-area estimation approach to estimate differences across states in percentages of adults losing health insurance and in lengths of their uninsured spells. We found that nearly 50 percent of the nonelderly adult population in Florida, Nevada, New Mexico, and Texas--but only 18 percent in Massachusetts and 22 percent in Vermont--experienced an uninsured spell between 2009 and 2012. Compared to people who lost private coverage, those with public insurance were more likely to experience an uninsured spell, but their spells of uninsurance were shorter. We categorized states based on estimated incidence of uninsured spells and the spells' duration. States should tailor their enrollment outreach and retention efforts for the ACA's coverage expansions to address their own mix of types of coverage lost and durations of uninsured spells.

Exploring spatial dependence in area-level random effect model for disaggregate-level crop yield estimation

This paper describes an application of small area estimation (SAE) techniques under area-level spatial random effect models when only area (or district or aggregated) level data are available. In particular, the SAE approach is applied to produce district-level model-based estimates of crop yield for paddy in the state of Uttar Pradesh in India using the data on crop-cutting experiments supervised under the Improvement of Crop Statistics scheme and the secondary data from the Population Census. The diagnostic measures are illustrated to examine the model assumptions as well as reliability and validity of the generated model-based small area estimates. The results show a considerable gain in precision in model-based estimates produced applying SAE. Furthermore, the model-based estimates obtained by exploiting spatial information are more efficient than the one obtained by ignoring this information. However, both of these model-based estimates are more efficient than the direct survey estimate. In many districts, there is no survey data and therefore it is not possible to produce direct survey estimates for these districts. The model-based estimates generated using SAE are still reliable for such districts. These estimates produced by using SAE will provide invaluable information to policy-analysts and decision-makers.

SPATIAL SMALL AREA ESTIMATION FOR DETERMINATION OF UNDERDEVELOPED VILLAGES IN THE PROVINCE OF YOGYAKARTA (DIY) IN 2011

Indonesia's poverty alleviation programs are implemented by two approaches target, those are the pockets (areas) of poverty and the poor households. Related with poverty alleviation programs targeting poor areas, in the Medium Term Development Plan (RPJM) 2010-2014, the government through the Development Backward Areas Ministry (KPDT) has determined the backward or underdeveloped regions at the level of district/city. There is no district/city in the province of Yogyakarta (DIY) are classified as underdeveloped region, but in 2011 the poverty rate in DIY is the highest compared with other provinces in Java and Bali. Therefore, the classifications of underdeveloped areas are not optimal if applicable only within the district, but it needs to be seen in the smaller scope, such as village. The main purpose of this study is to determine the underdeveloped villages in DIY in 2011. The average per capita household expenditure is a key indicator in measuring poverty. Susenas data can only be used to estimate the average per capita household expenditure to the level of district. Therefore, to obtain the estimated value in village level, this study used Small Area Estimation approach by combining census data (Podes 2011) and survey data (Susenas 2011). This study used Geographically Weighted Regression (GWR) with Adaptive Gaussian Kernel Bandwidth weighting function. GWR is a linear regression model that produces the local parameters in all locations. GWR parameters estimated are performed by Weighted Least Squares (WLS) method which involving spatial aspects. The results found that there were 13 underdeveloped villages in DIY. Furthermore, the Local Indicator of Spatial Association (LISA) is used to look at the tendency of cluster in underdeveloped villages. Then, maps are used to compare characteristic of underdeveloped villages among others.

Empirical Bayesian Method for the Estimation of Literacy Rate at Sub-district Level Case Study: Sumenep District of East Java Province

This paper discusses Bayesian Method of Small Area Estimation (SAE) based on Binomial response variable. SAE method being developed to estimate parameter in small area due to insufficiency of sample. The case study is literacy rate estimation at sub-district level in Sumenep district, East Java Province. Literacy rate is measured by proportion of people who are able to read and write, from the population of 10 year-old or more. In the case study we used Social Economic Survey (Susenas)data collected by BPS. The SAE approach was applied since the Susenas data is not representative enough to estimate the parameters at sub-district level because it’s designed to estimate parameters in regional area (in scope of a district/city at minimum). In this research, the response variable being used was logit function trasformation of pi (the parameter of Binomial distribution). We applied direct and indirect approach for parameter estimation, both using Empirical Bayes approach. For direct estimation we used prior distribution of Beta distribution and Normal prior distribution for logit function (pi) and to estimate parameter by using numerical method, i.e integration Monte Carlo. For indirect approach, we used auxiliary variables which are combinations of sex and age (which is divided into five categories). Penalized Quasi Likelihood (PQL) was used to get parameter estimation of SAE model and Restricted Maximum Likelihood method (REML) for MSE estimation. Instead of Bayesian approach, we are also conducting direct estimation using classical approach in order to evaluate the quality of the estimators. This research gives some findings, those are: Bayesian approach for SAE model gives the best estimation because having the lowest MSE value compares to the other methods. For the direct estimation, Bayesian approach using Beta and logit Normal prior distribution give a very similar result to the direct estimation with classical approach since the weight of is too large, which is about 0.905. It is also found that direct estimation using Bayesian approach with the Beta prior distribution gives better MSE than using logit normal prior distribution.

Small area estimation of poverty proportions under area-level time models

The unit-level small area estimation approach has no standard procedure and each case needs separate modeling when the domain parameters are not linear or the target variable is not normally distributed. Area-level linear mixed models can be generally applied to produce EBLUP estimates of linear and non linear parameters because direct estimates are weighted sums, so that the assumption of normality may be acceptable. The problem of estimating small area non linear parameters is treated, with special emphasis on the estimation of poverty proportions. Borrowing strength from time by using area-level linear time models is proposed. Four time-dependent area-level models are considered and the behavior of the two basic ones is empirically investigated. The developed model-based methodology for estimating poverty proportions is applied in the Spanish Living Conditions Survey.

MEASURING SUB‐NATIONAL INCOME POVERTY BY USING A SMALL AREA MULTIVARIATE APPROACH

The present paper proposes a statistical strategy for the analysis of regional disparities in income poverty. For the EU countries, information on individual income has been collected until now by the European Community Household Panel survey, which only yields reliable estimates for very large regions within countries. In order to obtain reliable estimates for some of the poverty indicators suggested by the Laeken Council at the sub‐national level, we suggest the adoption of a multivariate small area estimation approach which enables us to reduce estimate variability. We concentrate on Italy, the country with the lowest degree of regional cohesion within the EU. Results show that disparity cannot be reduced to the so‐called “North–South divide,” with the “poor” South separated from the “affluent” North, as both these macro‐regions display large internal differences in terms of both poverty level and income inequality. The strategy we propose could also be adopted in order to measure poverty in other European regions, using information produced by the new EU Survey on Income and Living Conditions, which is replacing the European Community Household Panel.

Non-Parametric Small Area Estimation Using Penalized Spline Regression

SummaryThe paper proposes a small area estimation approach that combines small area random effects with a smooth, non-parametrically specified trend. By using penalized splines as the representation for the non-parametric trend, it is possible to express the non-parametric small area estimation problem as a mixed effect model regression. The resulting model is readily fitted by using existing model fitting approaches such as restricted maximum likelihood. We present theoretical results on the prediction mean-squared error of the estimator proposed and on likelihood ratio tests for random effects, and we propose a simple non-parametric bootstrap approach for model inference and estimation of the small area prediction mean-squared error. The applicability of the method is demonstrated on a survey of lakes in north-eastern USA.

Welfare and Environment in Rural Uganda: Results from a Small-Area Estimation Approach

This study combines census, survey and bio-physical data to generate spatially disaggregated poverty/biomass information for rural Uganda. It makes a methodological contribution to small area welfare estimation by exploring how the inclusion of bio-physical information improves small area welfare estimates. By combining the generated poverty estimates with national bio-physical data, this study explores the contemporaneous correlation between poverty (welfare) and natural resource degradation at a level of geographic detail that has not been feasible previously. The resulting estimates of poverty measures were improved by the inclusion of bio-physical information and the poverty estimates appear to be more robust, as the standard errors show a decline of up to 40 percent in some cases. The coefficients of variation (i.e., the ratio of the standard error and the point estimate) decline in general as well. Overall, we conclude that the estimates of the poverty measures are more robust when bio-physical information is taken into account. One of the outputs of this study is a series of maps showing poverty and biomass overlays for Uganda. These maps can be used as a planning tool and for targeting purposes.

Nonparametric Small Area Estimation Using Penalized Spline Regression

We propose a new small area estimation approach that combines small area random effects with a smooth, nonparametrically specified trend. By using penalized splines as the representation for the nonparametric trend, it is possible to express the small area estimation problem as a mixed effect model regression. This model is readily fitted using existing model fitting approaches such as restricted maximum likelihood. We develop a corresponding bootstrap approach for model inference and estimation of the small area prediction mean squared error. The applicability of the method is demonstrated on a survey of lakes in the Northeastern US.