Combining Sample and Census Data in Small Area Estimates: Iterative Proportional Fitting with Standard Software
The combination of detailed sample data with less detailed but fully enumerated marginal subtotals is the focus of a wide range of research. In this article we advocate careful modeling of sample data, followed by Iterative Proportional Fitting (IPF). The modeling aims to estimate accurately the interaction or odds ratios of complex tables, which is information not contained in the marginal subtotals. IPF ensures consistency with the subtotals. We advance this work in three practical ways. First, we show that detailed small-area estimates of both counts and proportional distributions usually gain accuracy by combining data for larger areas containing the small areas, and we illustrate the multilevel framework to achieve these estimates. Second, we find that a general classification or socioeconomic typology of the small areas is even more associated with the within-area interactions than is membership of the larger area. Third, we show how the Statistical Package for the Social Sciences (SPSS) can be used for IPF in any number of dimensions and with any structure of constraining marginal subtotals. Throughout, we use an example taken from the 1991 U.K. Census. These data allow us to evaluate various methods combining 100 percent tabulations and the Samples of Anonymised Records.