416 – A Tour of Statistical Innovations in Marketing Research
MaxDiff Adjusted to Items Non-Availability and Network Effects
Stan Lipovetsky
GfK North America
W. Michael Conklin
GfK North America
MaxDiff, or Maximum Difference, aka Best-Worst Scaling, is a discrete choice method widely used for finding utilities and choice probabilities among multiple alternatives. Data for such modeling is given by respondents who are presented with several items and chooses the best and worst alternatives. Estimation of utilities is usually performed in a multinomial-logit (MNL) modeling technique which produces utilities and choice probabilities of the compared items. This paper describes how to obtain the robust probability estimation adjusted to possible absence of items in actual purchasing. For this aim we apply Markov chain modeling in form of Chapman-Kolmogorov system of differential equations and its steady-state solution which can be reduced to eigenproblem by a stochastic matrix and solved analytically. The obtained closed-form solution suggests a robust modification of choice probabilities with accounted cases of items non-availability. Adjustment to choice probability with network effects is also considered. Numerical example by marketing research data is used and the results are discussed. This approach is useful for theoretical descriptions and practical applications.