Improving PRETREE's predictive capabilities

Abstract

Compared to compensatory type choice models (e.g., logit), hierarchical choice models have been used much less frequently in the real world. This has happened even though there is a lot of evidence to suggest that the hierarchical structure is closer to the actual process by which individuals make choices. In this paper, we have considered one of the original hierarchical models (PRETREE). The PRETREE model has been heavily cited in the marketing and psychometric literatures. We wish to examine PRETREE at the aggregate level making n-way (market share) predictions. A primary strength of the PRETREE model was its apparent ability to capture violations of the property of the “independence of irrelevant alternatives” (IIA). We prove that there are limitations to this argument. We suggest a method to overcome these limitations; this change resulted in substantial improvement in the predictive abilities of the model, when the modified PRETREE is applied to real world data. The predictions are at an aggregate level on a hold-out sample. The above modification to PRETREE will hopefully not only renew but also increase interest in applying a hierarchical approach to modeling real-world problems on choice.