### Department of Biostatistics Seminar/Workshop Series

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

## Jeff Dotson, PhD

### Assistant Professor of Marketing, Vanderbilt Owen Graduate School of Management

### Wednesday, November 4, 1:30-2:30pm, MRBIII Conference Room 1220

### Intended Audience: Persons interested in applied statistics, statistical theory, epidemiology, health services research, clinical trials methodology, statistical computing, statistical graphics, R users or potential users

Discrete choice experiments (e.g., conjoint analysis) and random utility models are used extensively in a variety of disciplines (including marketing, transportations, and healthcare) to elicit and infer consumer preferences for various product offerings. Although these techniques have proven useful in practice, it is well known that common assumptions about the error distribution in random utility models can result in anomalies in prediction. In particular, if the random components for the options within a choice set are assumed to be independent, then the independence of irrelevant alternatives (IIA) can result in unrealistic predictions (e.g., market share forecasts). This talk presents a parsimonious model for the error covariance based upon a subject’s perceived distance among alternatives. The value of the proposed model is demonstrated using data from a commercial conjoint study for coffee creamers. We show that assumptions about the error term in a random utility model do have a substantial impact on prediction and that the proposed structured covariance probit model can flexibly accommodate correlated errors, thus yielding more realistic patterns of substitution.