If the model fits, use it: Methods and benchmarks for evaluating NBD-Dirichlet goodness-of-fit

Abstract

The Dirichlet model is an empirical generalization describing and predicting repeated choice amongst a set of competitive alternatives. With the advent of big data, there are many new potential applications for this model. Its developers emphasized one goodness-of-fit statistic, and subsequent researchers have used this along with others. There is, however, no consensus in the literature regarding which measures to use or, more importantly, benchmarks. This paper proposes a suite of six goodness-of-fit statistics developed from the literature to assess the fit of the model and develops two new measures that account for category specific factors enabling the development of benchmarks. It also provides appropriate benchmarks for all statistics derived from 54 FMCG categories in the UK.