The R package emdi enables the estimation of regionally disaggregated indicators using small area estimation methods and includes tools for processing, assessing, and presenting the results. The mean of the target variable, the quantiles of its distribution, the headcount ratio, the poverty gap, the Gini coefficient, the quintile share ratio, and customized indicators are estimated using direct and model-based estimation with the empirical best predictor (Molina and Rao 2010). The user is assisted by automatic estimation of datadriven transformation parameters. Parametric and semi-parametric, wild bootstrap for mean squared error estimation are implemented with the latter offering protection against possible misspecification of the error distribution. Tools for (a) customized parallel computing, (b) model diagnostic analyses, (c) creating high quality maps and (d) exporting the results to Excel and OpenDocument Spreadsheets are included. The functionality of the package is illustrated with example data sets for estimating the Gini coefficient and median income for districts in Austria.
We introduce a command, fayherriot, that implements the Fay– Herriot model (Fay and Herriot, 1979, Journal of the American Statistical Association 74: 269–277), which is a small-area estimation technique (Rao and Molina, 2015, Small Area Estimation), in Stata. The Fay–Herriot model improves the precision of area-level direct estimates using area-level covariates. It belongs to the class of linear mixed models with normally distributed error terms. The fayherriot command encompasses options to a) produce out-of-sample predictions, b) adjust nonpositive random-effects variance estimates, and c) deal with the violation of model assumptions.
AbstractThe transformation of area aggregates between non-hierarchical area systems (administrative areas) is a standard problem in official statistics. For this problem, we present a proposal which is based on kernel density estimates. The approach applies a modification of a stochastic expectation maximization algorithm, which was proposed in the literature for the transformation of totals on rectangular areas to kernel density estimates. As a by-product of the routine, one obtains simulated geo-coordinates for each unit. With the help of these geo-coordinates, it is possible to calculate case numbers for any area system of interest. The proposed method is evaluated in a design-based simulation based on a close-to-reality, simulated data set with known exact geo-coordinates. In the empirical part, the method is applied to student resident figures from Berlin, Germany. These are known only at the level of ZIP codes, but they are needed for smaller administrative planning districts. Results for (a) student concentration areas and (b) temporal changes in the student residential areas between 2005 and 2015 are presented and discussed.
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