Marginal-Preserving Imputation of Three-Way Array Data in Nested Structures, with Application to Small Areal Units

Geospatial population data are typically organized into nested hierarchies of areal units, in which each unit is a union of units at the next lower level. There is increasing interest in analyses at fine geographic detail, but these lowest rungs of the areal unit hierarchy are often incompletely tabulated because of cost, privacy, or other considerations. Here, the authors introduce a novel algorithm to impute crosstabs of up to three dimensions (e.g., race, ethnicity, and gender) from marginal data combined with data at higher levels of aggregation. This method exactly preserves the observed fine-grained marginals, while approximating higher-order correlations observed in more complete higher level data. The authors show how this approach can be used with U.S. census data via a case study involving differences in exposure to crime across demographic groups, showing that the imputation process introduces very little error into downstream analysis, while depicting social process at the more fine-grained level.