Modeling Qualitative Outcomes by Supplementing Participant Data with General Population Data: A Calibrated Qualitative Response Estimation Approach

Often providers of a program or service have detailed information about their clients, but only limited information about potential clients. Likewise, ecologists frequently have extensive knowledge regarding habitats where a given animal or plant species is known to be present, but they lack comparable information on habitats where they are certain not to be present. In epidemiology, comprehensive information is routinely collected about patients who have been diagnosed with a given disease; however, commensurate information may not be available for individuals who are known to be free of the disease. While it may be highly beneficial to learn about the determinants of participation (in a program or service) or presence (in a habitat or of a disease), the lack of a comparable sample of observations on subjects that are not participants (or that are non-present) precludes the application of standard qualitative response models, such as logit or probit. In this paper, we examine how one can overcome this challenge by combining a participant-only sample with a supplementary sample of covariate values from the general population. We derive some new estimators of conditional response probabilities based on this sampling scheme by exploiting the parameter restrictions implied by the relationship between the marginal and conditional response probabilities in the supplementary sample. When the prevalence rate in the population is known, we demonstrate that the choice of estimator is especially important when this rate is relatively high. Our simulation results indicate that some of our new estimators for this case rival the small sample performance of the best existing estimators. Our estimators for the case where the prevalence rate is unknown also perform comparably to the best existing estimator for this situation in our simulations. In contrast to most existing estimators, our new estimators are straightforward to apply to exogenously stratified samples (such as when the supplementary sample is drawn from a Census ...