Comparison of Small Area Models in SAIPE

The ongoing Small Area Income and Poverty Estimates (SAIPE) project at the Census Bureau estimates numbers of poor school-age children by state, county, and ultimately school district, based upon Current Population Survey (CPS) and IRS data along with information from the latest decennial census. The current SAIPE county-level methodology relies on a Fay-Herriot (1979) model fitted to log-counts of related school-age children in CPS-sampled households, and discards data from those sampled counties with no sampled poor children. The present paper compares SAIPE smallarea estimation by analogous Fay-Herriot models for logarithms of county child poverty rates with a unit(i.e., individual-) level logistic regression model with county-level random effects (GLMM). This comparison is based upon several loss criteria applied to SAIPE datasets from 1994 and 1990, using CPS weighted estimates or (in 1990) decennial census data as standards of truth for the county-level child poverty rates being estimated. The GLMM is shown to fit the data better than the log-rate Fay-Herriot models, when judged by the internal evidence of the 1994 and 1990 CPS datasets. SAIPE’s Fay-Herriot fitting method for 1990 log-rates performs excellently in matching to the 1990 Census log-rate in CPS-sampled counties, but worse than GLMM in counties with no CPS sample.