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

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