A Probit model with Structured Covariance for Similarity Effects and Source of Volume Calculations
Keywords
substitution, similarity, cannibalization, conjoint analysis, hierarchical Bayes
Abstract
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 property of independence of irrelevant alternatives, which often does not match observed substitution behavior and leads to inaccurate calculations of source of volume when new entrants are introduced. In this article, the authors 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. They find across multiple data sets 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.
Original Publication Citation
Dotson, Jeffery P., John R. Howell, Thomas Otter, Peter Lenk, Steve MacEachern, and Greg M. Allenby, "A Probit Model with Structured Covariance for Similarity Effects and Source of Volume Calculations", Journal of Marketing Research, 2018.
BYU ScholarsArchive Citation
Dotson, Jeffrey P.; Howell, John R.; Brazell, Jeff D.; Otter, Thomas; Lenk, Peter J.; MacEachern, Steve; and Allenby, Greg M., "A Probit model with Structured Covariance for Similarity Effects and Source of Volume Calculations" (2018). Faculty Publications. 8533.
https://scholarsarchive.byu.edu/facpub/8533
Document Type
Peer-Reviewed Article
Publication Date
2018
Publisher
Journal of Marketing Research
Language
English
College
Marriott School of Business
Department
Marketing
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