Combining Sample and Census Data in Small Area Estimates: Iterative Proportional Fitting with Standard Software

Abstract

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.

*Census data are Crown Copyright; the 1991 Sample of Anonymised Records (SAR) s were purchased by the U.K. Economic and Social Research Council and Joint Information Systems Committee (JISC) for academic and other research purposes. The work for this paper and its writing were supported respectively by the U.K. Economic and Social Research Council awards R000223703, “Combining aggregate and micro-data to extend census tables for local areas” and RR000271214, “Local demography and race.” Paul Norman provided helpful comments on a draft.

Key Words:

• Small areas
• iterative proportional fitting
• multilevel models

Notes

*Census data are Crown Copyright; the 1991 Sample of Anonymised Records (SAR) s were purchased by the U.K. Economic and Social Research Council and Joint Information Systems Committee (JISC) for academic and other research purposes. The work for this paper and its writing were supported respectively by the U.K. Economic and Social Research Council awards R000223703, “Combining aggregate and micro-data to extend census tables for local areas” and RR000271214, “Local demography and race.” Paul Norman provided helpful comments on a draft.

Note. IPF=Iterative Proportional Fitting.

Note. SAR=Sample of Anonymised Records.

Additional information

Notes on contributors

Ludi Simpson

Reader in Social Statistics

Mark Tranmer

A lecturer in statistics