On Some Aspects of Small Area Estimation with Bayesian Approach Utilizing SAS and R Software

The demand for reliable small area estimates derived from survey data has increased greatly in recent years due to their growing use in formulating policies and programs, allocation of government funds, regional planning, small area business decisions and other applications. Traditional direct estimates may not provide acceptable precision for small areas because sample sizes are seldom large enough in many small areas of interest. This makes it necessary to borrow information across related areas through indirect estimation based on models, using auxiliary information such as recent census data and current administrative data. Methods based on models are now widely accepted. The indirect estimates, obtained using implicit/explicit models, are usually more reliable than the direct survey estimates. To draw inferences from these models, one can use Bayesian or frequentist approach. Moreover, in almost all situations, the posterior moments involve multi-dimensional integration and consequently closed form expressions cannot be obtained. To overcome the computational difficulties one needs to apply computer intensive Monte Carlo Markov Chain (MCMC) methods. This work deals on some aspects of small area estimation with Bayesian approach using SAS and R-software’s. Direct, synthetic and composite estimators are obtained on real agricultural data set and results obtained from these estimators are compared in terms of average relative bias, average squared relative bias, average absolute bias, average squared deviation as well as the empirical mean square error. It has been found that composite estimator worked better than direct and synthetic estimators. Area level and unit level models are used to draw inferences for small areas when the variable of interest is continuous. New prior distributions are proposed and evaluated for both the models for the variance component. Laplace approximation is used to obtain accurate approximations to the posterior moments. Results from the two models are compared in terms of average relative bias, average squared relative bias and average absolute bias and numerical results obtained on a real agricultural data set highlight the superiority of using the proposed prior over the uniform prior. Also the basic linear mixed effects model is extended to allow heteroscedastic correlated within group errors. lme() function of nlme() library is used to fit the extended linear mixed effects model and its various capabilities are illustrated through examples. It has been shown that the estimation and computational methods of simple linear mixed effect models can be applied to the extended model and decomposition of variance, covariance structure of within group errors into two independent components: a variance structure and a correlation structure. The above discussed methods are illustrated practically with the help of SAS and R software on the basis of newly developed functions piest(), composite(), relativebias(), absolute bias(), Area.model.HBll(). Two functions were also developed in SAS to obtain the EBLUP and HB estimate of area level and unit level models. Both the functions consists of number of statements in SAS, utilizing number of SAS procedures viz PROC MIXED, PROC IML, PROC RANDOM, PROC MCMC, PROC PRINT. The lme() function of nlme library of R-software is used to fit the extended linear mixed effects models illustrating its various capabilities through examples on real data set. All these functions are run on real agricultural apple production data set obtained through pilot survey project in District Baramulla.