Worth the effort? Comparison of different MCMC algorithms for estimating the Pareto/NBD model

The Pareto/NBD model is one of the best-known models in customer base analysis. Extant literature has brought up three different Markov Chain Monte Carlo (MCMC) procedures for parameter estimation of this model. Nevertheless, three main research gaps remain. Firstly, the issue of hyper parameter sensitivity for these procedures has been disregarded even though this is crucial when dealing with small sample sizes. Secondly, present research lacks a performance comparison between the different MCMC procedures as well as with Maximum Likelihood Estimates (MLE). Thirdly, existing minimal data set requirements for this model neglect MCMC estimation procedures as they only refer to MLE. To tackle these gaps, we perform two extensive simulation studies. We demonstrate that the algorithms differ in their sensitivity towards the hyper distributions and identify one algorithm that outperforms the other procedures in all respects. In addition, we provide deeper insights into individual level forecasts when using MCMC and enhance extant data set limitation guidelines by considering not only the cohort size but also the length of the calibration period.

COMPARATIVE MODELS IN CUSTOMER BASE ANALYSIS: PARAMETRIC MODEL AND OBSERVATION-DRIVEN MODEL

This study conducts a dynamic rolling comparison between the Pareto/NBD model (parametric model) and machine learning algorithms (observation-driven models) in customer base analysis, which the literature has not comprehensively investigated before. The aim is to find the comparative edge of these two approaches under customer base analysis and to define the implementation timing of these two paradigms. This research utilizes Pareto/NBD (Abe) as representative of Buy-Till-You-Die (BTYD) models in order to compete with machine learning algorithms and presents the following results. (1) The parametric model wins in transaction frequency prediction, whereas it loses in inactivity prediction. (2) The BTYD model outperforms machine learning in inactivity prediction when the customer base is active, performs better in an inactive customer base when competing with Poisson regression, and wins in a short-term active customer base when competing with a neural network algorithm in transaction frequency prediction. (3) The parametric model benefits more from a short calibration length and a long holdout/target period, which exhibit uncertainty. (4) The covariate effect helps Pareto/NBD (Abe) gain a better predictive result. These findings assist in defining the comparative edge and implementation timing of these two approaches and are useful for modeling and business decision making.

Systematic response errors in self-reported category buying frequencies

Purpose Despite the growing availability of scanner-panel data, surveys remain the most common and inexpensive method of gathering marketing metrics. The purpose of this paper is to explore the size, direction and correction of response errors in retrospective reports of category buying. Design/methodology/approach Self-reported purchase frequency data were validated using British household panel records and the negative binomial distribution (NBD) in six packaged goods categories. The log likelihood theory and the fit of the NBD model were used to test an approach to adjusting the errors post-data collection. Findings The authors found variations in systematic response errors according to buyer type. Specifically, lighter buyers tend to forward telescope their buying episodes. Heavier buyers tend either to over-use a rate-based estimation of once-a-month buying and over-report purchases at multiples of six or to use round numbers. These errors lead to overestimates of penetration and average purchase frequency. Adjusting the aggregate data for the NBD, however, improves the accuracy of these metrics. Practical implications In light of the importance of purchase data for decision making, the authors describe the inaccuracy problem in frequency reports and offer practical suggestions regarding the correction of survey data. Originality/value Two novel contributions are offered here: an investigation of errors in different buyer groups and use of the NBD in survey accuracy research.

Can the negative binomial distribution predict industrial purchases?

Purpose This paper aims to extend the known boundary conditions of the negative binomial distribution (NBD) model, and to test the applicability of conditional trend analysis (CTA) – a key method to identify whether changes in overall sales are accounted for by previous non-buyers, light buyers or heavy buyers – in industrial purchasing situations. Design/methodology/approach The study tested the NBD model and CTA in an industrial marketing context using a 12-month data set of purchases from an Australian supplier of a range of industrial plastic resins. Findings The purchase data displayed a good NBD fit; the study therefore extends the known boundary conditions of the model. The application of CTA provided second-period purchasing frequency estimates showing no significant difference from actual data, indicating the applicability of this method to industrial purchasing. Research limitations/implications Data relate to just one supplier. Further research across several industries is required to confirm the generalizability and robustness of NBD and CTA to industrial markets. Practical implications Marketing decisions can be improved through appropriate analysis of customer purchasing data. However, without access to equivalent competitor data, industrial marketers are constrained in benchmarking the purchasing patterns of their own customers. The results indicate that use of the NBD model enables valid benchmarking for industrial products, while CTA would enable appropriate analysis of purchases by different classes of customer. Originality/value This paper extends the known boundary conditions of the NBD model and provides the first published results, indicating the appropriateness of CTA to predict purchasing frequencies of different industrial customer classes.