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Choice Models Adjusted to Non-Available Items and Network Effects

Discrete choice modeling is one of the main tools of estimation utilities and preference probabilities among multiple alternatives in economics, psychology, social sciences, and marketing research. One of popular DCM tools is the Best-Worst Scaling, also known as Maximum Difference. Data for such modeling is given by respondents presented with several items, and each respondent chooses the best alternative. Estimation of utilities is usually performed in a multinomial-logit modeling which produces utilities and choice probabilities. This article describes how to obtain probability estimation adjusted to possible absence of items in actual purchasing. We apply Markov chain modeling in the form of Chapman-Kolmogorov equations and its steady-state solution for stochastic matrix can be obtained analytically. An adjustment to choice probability with network effects is also considered. Numerical example by marketing research data is used.