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

31 Pages Posted: 4 May 2009 Last revised: 9 Apr 2015

See all articles by Jeffrey Dotson

Jeffrey Dotson

Brigham Young University - Marriott School

Jeff D. Brazell

The Modellers, LLC

John R. Howell

Brigham Young University - Marriott School of Business

Peter Lenk

University of Michigan, Stephen M. Ross School of Business

Thomas Otter

Goethe University Frankfurt - Department of Marketing

Steven N. MacEachern

Ohio State University (OSU)

Greg M. Allenby

Ohio State University (OSU) - Department of Marketing and Logistics

Date Written: April 1, 2015

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 IIA property, which often does not match consumer behavior and leads to inaccurate source of volume predictions. Correlated errors, such as in the correlated probit model, give more realistic results. However, the source of the correlation among the utility functions for different alternatives is often not well studied. In practice, covariance matrices are frequently associated with presentation order or brands in conjoint studies. However, other structures allow richer specifications of substitution patterns. In this paper, we parameterize the covariance matrix for probit models so that similar brands in the preference space have higher correlation than dissimilar brands, resulting in higher rates of substitution. We investigate alternative measures of similarity in the context of a conjoint model, and compare the resulting substitution patterns to those of standard choice models. The proposed model fits the data better and results in more realistic measures of substitution for a product line extension. The structured covariance matrix approach allows marketing managers to predict the substitution pattern for product profiles not included in the conjoint analysis.

Keywords: Hierarchical Bayes, Choice Model, Substitution

JEL Classification: C11, C25, M31

Suggested Citation

Dotson, Jeffrey and Brazell, Jeff D. and Howell, John R. and Lenk, Peter and Otter, Thomas and MacEachern, Steven N. and Allenby, Greg M., A Probit Model with Structured Covariance for Similarity Effects and Source of Volume Calculations (April 1, 2015). Available at SSRN: https://ssrn.com/abstract=1396232 or http://dx.doi.org/10.2139/ssrn.1396232

Jeffrey Dotson

Brigham Young University - Marriott School ( email )

United States

Jeff D. Brazell

The Modellers, LLC ( email )

6995 Union Park Center
Ste 300
Salt Lake City, UT 84047
United States
8018846688 (Phone)

HOME PAGE: http://www.themodellers.com

John R. Howell

Brigham Young University - Marriott School of Business ( email )

Provo, UT 84602
United States

Peter Lenk

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

Thomas Otter

Goethe University Frankfurt - Department of Marketing ( email )

Frankfurt
Germany
++49.69.798.34646 (Phone)

HOME PAGE: http://www.marketing.uni-frankfurt.de/index.php?id=97?&L=1

Steven N. MacEachern

Ohio State University (OSU) ( email )

Blankenship Hall-2010
901 Woody Hayes Drive
Columbus, OH OH 43210
United States

Greg M. Allenby (Contact Author)

Ohio State University (OSU) - Department of Marketing and Logistics ( email )

Fisher Hall 524
2100 Neil Ave
Columbus, OH 43210
United States

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