A Nonparametric Model of Attribute Based Inter-Product Competition
Sudhir Voleti1, Pulak Ghosh2, Praveen Kopalle3
1Marketing, Indian School of Business (ISB), Hyderabad, Andhra Pradesh, India; 2Statistics, Indian Institute of Management, Bangalore, Karnataka, India; 3Marketing, Tuck school, Darthmouth, Hanover, NH, United States

We propose a way to assess attribute based inter-product competition that employs a novel nonparametric statistical method, the nested Dirichlet Process (nDP), to effect a hierarchical clustering of our units of analysis – brands and SKUs. Our method exploits the information content in both the observed and the latent attributes in the data to induce a pattern of dependence that groups 'similar' (and hence, more substitutable) brands into similar-brand clusters and, simultaneously, groups similar SKUs within the similar-brand clusters into similar-SKU clusters. Subsequently, linear programming methods yield attribute weights that best discriminate between each pair of similar-unit clusters. These attribute weights feed into a comprehensive competition measure that easily finds place in most generalized linear models of sales or market response.

Our approach bears several advantages over extant methods - it is parsimonious, flexible, avoids distributional assumptions on model terms, avoids the model selection problem by endogenously determining the appropriate number of similarity clusters, allows inference on the clusters obtained, uses both observed and latent attributes in the clustering process, is able to accommodate restrictions defined a priori based on category structure, uses readily available secondary data on aggregate sales and product attributes, accommodates the possibility of asymmetric competitive effects between pairs of products, and yields realistic cross-product substitution effects, intuitive marginal effects as well as own- and cross-attribute elasticities.

We find that the competition measure proposed improves fit, explained variance and prediction in generalized linear models of demand based on aggregate data.

Keywords: Attribute based product competition; Nested Dirichlet process

Biography: Dr. Sudhir Voleti, Assistant Professor in Marketing at the Indian School of Business, Hyderabad, India.

PhD on Management from the University of Rochester in 2009, MBA from IIM Calcutta in 2001 and a Bachelor of Engineering from the Birla Institute, Ranchi in 1998.

The paper presented is co-authored with Dr Pulak Ghosh of IIM Bangalore and Prof. Praveen Kopalle of the Tuck school, Darthmouth.