Estimating a multinomial probit model of brand choice using the method of simulated moments

The multinomial probit model of brand choice is theoretically appealing for marketing applications as it is free from the ‘independence of irrelevant alternatives’ property of the multinomial logit model. However, difficulties in estimation have restricted its widespread use in marketing. This paper presents an application of the method of simulated moments, a new methodology that enables easy estimation of probit models with a large number of alternatives in the choice set. It describes the theoretical development of the technique and using pseudo-simulated data, conducts numerical experiments to compare the method with existing techniques for estimating probit models. Using the scanner panel data on the purchases of catsup, the paper provides an empirical application of the method of simulated moments to the estimation of the parameters of a multinomial probit model. Estimating the covariance structure associated with the underlying latent variable probit model enables broad patterns of similarities across alternatives to be identified. It also enables a pairwise similarity matrix across choice alternatives to be derived, which when input into a multidimensional scaling routine provides a graphical representation of competitive structure in the catsup market. For completeness, the paper compares the substantive implications for the effects of marketing variables obtained from the multinomial probit model with those obtained from models in the extant marketing literature.