Estimating logistic regression models when the dependent variable has no variance

Abstract

We show that the binary logistic regression model can often be estimated even when the study sample is confined to observations on only one of the possible outcomes of the dependent variable. Provided that an appropriate supplementary sample can be found, the two samples may be pooled, and a simple method employed to estimate the model with a conventional statistics package. The supplementary sample must contain information on the regressors of the model, but need not contain any information on the dependent variable. Hence supplementary samples can often be found in general purpose public use surveys such as the U.S. Census.