# Investigating consumers' store-choice behavior via hierarchical variable selection

## TL;DR

This paper introduces a hierarchical variable selection method using mixed-integer optimization to improve store-choice models, revealing key consumer preferences across store types based on actual data.

## Contribution

It develops two novel MIO models for hierarchical variable selection, enhancing model reliability and computational efficiency in consumer store-choice analysis.

## Key findings

- Convenience stores are chosen mainly for accessibility.
- Drugstores are selected for low-price specific products.
- Grocery supermarkets are preferred for health foods by women with families.

## Abstract

This paper is concerned with a store-choice model for investigating consumers' store-choice behavior based on scanner panel data. Our store-choice model enables us to evaluate the effects of the consumer/product attributes not only on the consumer's store choice but also on his/her purchase quantity. Moreover, we adopt a mixed-integer optimization (MIO) approach to selecting the best set of explanatory variables with which to construct a store-choice model. We devise two MIO models for hierarchical variable selection in which the hierarchical structure of product categories is used to enhance the reliability and computational efficiency of the variable selection. We assess the effectiveness of our MIO models through computational experiments on actual scanner panel data. These experiments are focused on the consumer's choice among three types of stores in Japan: convenience stores, drugstores, and grocery supermarkets. The computational results demonstrate that our method has several advantages over the common methods for variable selection, namely, the stepwise method and $L_1$-regularized regression. Furthermore, our analysis reveals that convenience stores tend to be chosen because of accessibility, drugstores are chosen for the purchase of specific products at low prices, and grocery supermarkets are chosen for health food products by women with families.