Inferring Logit Models from Empirical Margins Using Proxy Data

We examine several approaches for inferring logit models from empirical margins of predictor covariates and conditional margins containing the means of a binary response for each covariate margin. One method is to fit proxy data to the conditional response using the beta distribution, a process we call “margin analysis.” Proxy data can obtained using three approaches: (1) implementing the iterative proportional fitting (IPF) procedure on the margin totals, (2) sampling from a larger relevant data source such as the census, and (3) enumerating, or sampling from, the combinatoric space of all possible tables constrained by the margins. The first procedure is a well-studied approach for estimating contingency tables from margins, but it does not necessarily maintain the associations between the covariates unless seeded with an initial