Variable selection for market basket analysis

Abstract

Results on cross category effects obtained by explanatory market basket analyses may be biased as studies typically investigate only a small fraction of the retail assortment (Chib et al. in Advances in econometrics, vol 16. Econometric models in marketing. JAI, Amsterdam, pp 57–92, 2002). We use Bayesian variable selection techniques to determine significant cross category effects in a multivariate logit model. Hence, we achieve a reduction of coefficients to be estimated which decreases computation time heavily and thus allows to consider more product categories than most previous studies. Next to the extension of numbers of categories, the second purpose of this paper is to learn about the capabilities of different variable selection algorithms in the context of market basket analysis. We present three different approaches to variable selection and find that an adaptation of a technique by Geweke (Contemporary Bayesian econometrics and statistics. Wiley, Hoboken, 2005) meets the requirements of market basket analysis best, namely high numbers of observations and cross category effects. For a real data set, we show (1) that only a moderate fraction of possible cross category effects are significantly different from zero (one third for our data), (2) that most of these effects indicate complementarity and (3) that the number of considered product categories influences significances of cross category effects.