Pay no attention to the alternatives behind the curtain: demand forecasting with missing data

Discrete choice modeling advances abound for scenarios where we can collect data about the behaviors of individuals, and observe their ultimate choice from among the range of possible alternatives. However, particularly in competitive private sector enterprises (e.g. airlines, hotels), it is often difficult and expensive to conduct surveys of users, particularly of the customers of one's competitors. However, there is typically a huge pool of data readily available for virtually no cost about one's own customers: what, how and when they purchase, which alternatives were made available from one's own pool of alternatives, etc. We pose the question: what can we do with this data? Traditional choice based sampling tools have problems with this scenario, as the sampling rate for the choices is typically employed as a divisor, but in this case it is, for some choices, zero. But all is not lost. We propose introducing aggregate measures of demand and market share (available from government statistics and/or competitors corporate disclosures when they are publicly traded companies) to fill in the gaps in the readily available disaggregate data. This works reasonably well when the underlying model is assumed to be MNL. Whether this strategy can still be employed when the underlying model is a more general GEV model is an open question, which we are beginning to explore.