Ordered logit analysis for selectively sampled data

When customers are classified into ordered categories, which are defined from the outset, it may happen that the majority belongs to a single category. If a market researcher is interested in the correlation between the classification and individual characteristics, the natural question is whether one needs to collect data for all customers in that particular category. We address this question for the ordered logit model. We show that there is no need to consider all those customers. All that is required is a simple modification of the log-likelihood, which is based on Bayes' rule. We illustrate our proposed method on simulated data and on data concerning risk profiles of customers of an investment bank.