Predicting future consumer purchases in grocery retailing with the condensed Poisson lognormal model

Abstract To identify the effect of marketing actions on consumer purchasing, analysts must disentangle the dynamic component of purchasing from expected period-to-period stochastic fluctuations. This is done by comparing marketplace observations to the conditional expectation of future purchasing. Current methods of deriving the conditional expectation contain systematic bias and rely on certain unrealistic modelling assumptions. We therefore propose a new model to predict future consumer purchases in grocery retailing. The new model is a mixture of Erlang-2, Poisson and lognormal distributions or a condensed Poisson lognormal model (CPLN). Using two grocery retailing datasets from the UK, we demonstrate that the CPLN model predicts future consumer purchases well with error of 7% and 9%, respectively. Compared with the previous benchmark model, the condensed Negative Binominal Distribution (CNBD), the CPLN model reduces error by 50% (7% versus 14%) and 67% (9% versus 27%), respectively. Theoretical and practical implications for retailers are discussed.