Journal of Data Science 2(2004), 125-147 A State Duration Model for Brand Choice and Inter-Purchase Time Lynn Kuo 1 and Zhen Chen 2 1 University of Connecticut and 2 University of Pennsylvania Abstract: A new approach for analyzing state duration data in brand-choice studies is explored. This approach not only incorporates the correlation among repeated purchases for a subject, it also models the purchase timing and the brand decision jointly. The former is accomplished by applying transition model approaches from longitudinal studies while the latter is done by conditioning on the brand choice variable. Then mixed multinomial logit models and Cox proportional hazards models are employed to model the marginal densities of the brand choice and the conditional densities of the interpurchase time given the brand choice. We illustrate the approach using a Nielsen household scanner panel data set. Key words: Cox proportional hazards model, longitudinal analysis, multi- nomial logit model, state duration model. 1. Introduction In brand-choice studies, factors influencing both the brand-switching patterns and purchase-timing decisions are usually of interest. Often, data are collected from n households on their purchase behavior over a period of time. The collected panel data consist of the inter-purchase times and brands chosen, as well as a list of covariates that may include characteristics of the consumers (chooser-specific) and attributes of the brands (choice-specific) at each purchase occasion. For example, the choice-specific explanatory variables may include the price of each brand and an indicator of a special in-store display for each brand; the chooser- specific variables may contain household income and size. Most of the existing approaches to analyzing these multiple-spell and multiple- destination data are restricted to marginal approaches where attention is given either to the state-space part (brand choice) or to the inter-purchase time part. The former includes the discrete brand-choice models of McFadden (1974) and Jain, Vilcassim, and Chintagunta (1994); the latter includes the proportional haz- ards model (Cox 1972) for the inter-purchase time studied by Jain and Vilcassim (1991).