Selective sampling for binary choice models

Marketing problems sometimes pertain to the analysis of dichotomous dependent variables, such as "buy" and "not buy" or "respond" and "not respond." One outcome can strongly outnumber the other, such as when many households do not respond (e.g., to a direct mailing). In such situations, an efficient data-collection strategy is to sample disproportionately more from the smaller group. However, subsequent statistical analysis must account for this sampling strategy. In this article, the authors put forward the econometric method that can correct for the sample selection bias, when this method does not lead to a loss in precision. The authors illustrate the method for synthetic and real-life data and document that reductions of more than 50% in sample sizes can be obtained.