Relevance of dynamic variables in multicategory choice models - Harald Hruschka (OR Spectrum, 2022)
We investigate the relevance of dynamic variables that reflect the purchase history of a household as independent variables in multicategory choice models. To this end, we estimate both homogeneous and finite mixture variants of the multivariate logit model. We consider two types of dynamic variables. Variables of the first type, which previous publications on multicategory choice models have ignored, are exponentially smoothed category purchases, which we simply call category loyalties. Variables of the second type are log-transformed times since the last purchase of any category. Our results clearly show that adding dynamic variables improves statistical model performance with category loyalties being more important than log-transformed times. The majority of coefficients of marketing variables (features, displays, and price reductions), pairwise category interactions, and cross-category relations differ between models either including or excluding dynamic variables. We also measure the effect of marketing variables on purchase probabilities of the same category (own effects) and on purchase probabilities of other categories (cross effects). This exercise demonstrates that the model without dynamic variables tends to overestimate own effects of marketing variables in many product categories. This positive omitted variable bias provides another explanation for the well-known problem of "overpromotion" in retailing.
Keywords: 650; Multicategory choice; Market basket analysis; Multivariate logit model; Purchase history