Statistics and Data Science Seminar
Abhyuday Mandal
University of Georgia
Small area estimation with uncertain random effects
Abstract: Random effects models play an important role in model-based
small area
estimation. Random effects account for any lack of fit of a regression
model for the population means of small areas on a set of explanatory
variables. In a recent paper, Datta, Hall and Mandal (2011, J. Amer.
Statist. Assoc.) showed that if the random effects to account for a lack
of fit of a regression model can be dispensed with through a statistical
test, then the model parameters and the small area means can be estimated
with substantially higher accuracy. The work of Datta et al. (2011) is
most useful when the number of small areas, m, is moderately large. For
large m, the null hypothesis of no random effects will likely be rejected.
Rejection of null hypothesis is usually caused by a few large residuals
signifying a departure of the direct estimator (Yi) from the synthetic
regression estimator. As a flexible alternative to the Fay-Herriot random
effects model and the approach in Datta et al. (2011), in this paper we
consider a mixture model for random effects. It is reasonably expected
that small areas with population means explained adequately by covariates
have little model error, and the other areas with means not adequately
explained by covariates will require a random component added to the
regression model. This model is a flexible alternative to the usual random
effects model and the data determine the extent of lack of fit of the
regression model for a particular small area, and include a random effect
if needed. Unlike the Datta et al. (2011) approach which recommends
excluding random effects from all small areas if a test of null hypothesis
of no random effects is not rejected, the present model is less
restrictive. We used this mixture model to estimate poverty ratios for 5-
to 17-year old related children for the 50 U.S. states and Washington, DC.
This application is motivated by the SAIPE project of the US Census
Bureau. We empirically evaluated the accuracy of the direct estimates and
the estimates obtained from our mixture model and the Fay-Herriot random
effects model. These empirical evaluations and a simulation study, in
conjunction with a measure of uncertainty of the new estimates show that
they are more accurate than the frequentist and the Bayes estimates
resulting from the standard Fay-Herriot model.
Wednesday August 13, 2014 at 11:00 AM in SEO 612