Faculty of Economics and Business Administration Publications Database

A Probit Model with Structured Covariance for Similarity Effects and Source of Volume Calculations

Dotson, Jeffrey P.
Howell, John R.
Brazell, Jeff D.
Lenk, Peter J.
MacEachern, Steven
Allenby, Greg M.
Volume: 55
Number: 1
Pages: 35 - 47
Month: February
ISSN-Print: 0022-2437
Link External Source: Online Version
Year: 2018
Keywords: Substitution; Similarity; Cannibalization; Conjoint Analysis; Hierarchical Bayes

Distributional assumptions for random utility models play an important role in relating observed product attributes to choice probabilities. Choice probabilities derived with independent errors have the IIA property, which often does not match observed substitution behavior and leads to inaccurate source of volume (SOV) calculations when new entrants are introduced. In this paper, we parameterize the covariance matrix for a probit model so that similar brands in the preference space have higher correlation than dissimilar brands, resulting in higher rates of substitution. We find across multiple datasets that similarity based on overall utility, not just attributes, defines products as similar with heightened rates of substitution. The proposed model results in better in-sample and predictive fits to the data and more realistic measures of substitution for a new product introduction.