Modeling Ambiguity in Census Microdata Allocations to Improve Demographic Small Area Estimates

Abstract

AbstractThis article describes a methodology for allocating demographic microdata to small enumeration areas such as census tracts, in the presence of underlying ambiguities. Maximum Entropy methods impute population weights that are constrained to match a set of census tract‐level summary statistics. Once allocated, the household characteristics are summarized to revise estimates of tract‐level demographic summary statistics, and to derive measures of ambiguity. The revised summary statistics are compared with original tract summaries within a context of expected variation. Allocation ambiguity is quantified for each household as a function of the distribution of imputed sample weights over all census tracts, and by computed metrics of confusion and variety of allocation to any census tract. The process reported here allows differentiation of households with regard to inherent ambiguity in the allocation decision. Ambiguity assessment represents an important component that has been neglected in spatial allocation work to date but can be seen as important additional knowledge for demographers and users of small area estimates. For the majority of tested variables, the revised tract level summaries correlate highly with original tract summary statistics. In addition to assessments for individual households, it is also possible to compute average allocation ambiguity for individual tracts, and to associate this with demographic characteristics not utilized in the allocation process.