Making Sense of Common Dirichlet Deviations

Abstract

This paper reviews the regularly recurring deviations between buyer behaviour patterns and predictions from the NBD-Dirichlet model. Previous studies have tended to look at one or two Dirichlet Deviations in isolation; the aim here is to learn more about their managerial significance by categorising them according to their behavioural indicators, summarising their incidence and extent and relating them to the implied breaches of assumptions of the model. We replicate prior research results in a single, extensive database of 62 FMCG categories and find that the Dirichlet Deviations take three forms; slight systematic variances in expected metrics across all brands in every fitting, suggesting some failure in stationarity; certain types of persistent deviation for individual brands or groups of brands that indicate partitioning; and those that capture dynamic performance. Analysis shows that consumer purchase propensities are never quite fixed or entirely independent, yet brand performance remains close to Dirichlet prediction. Managers who use this model need to be aware of the strategic options that the deviations imply, and we discuss these. Findings also contribute to the idea that deviations might be reduced by model adaptations although the managerial simplicity of the NBD-Dirichlet sets a major challenge to this.

Double Jeopardy – 50 Years On. Reviving a Forgotten Tool that Still Predicts Brand Loyalty

“…Driesener (2005), Scriven and Bound (2004) and Wright et al (2002) suggest four tests be applied to arrays of fittings to assess this; the correlations between O and T, the Mean Absolute Deviation (mean |O-T|) and the Mean Absolute Percentage Error (mean (O-T)/T), and suggest a visual test for the presence of the characteristic DJ bias in values of w between the biggest and smallest rival brands. Wright et al (2002) argued that a range of tests is required since MAD gives lower errors for smaller brands and MAPE for larger brands, while correlation is sensitive both to the number of observations and, (Scriven and Bound, 2004), low variability in the array of interest. In these prior studies acceptable values for tests of T were established to be correlations greater than r = 0.6, MADs of less than 0.9, MAPE's less than 20%, and a visible DJ characteristic.…”

Patterns of fruit and vegetable buying behaviour in the United States and India

“…The Duplication of Purchase pattern has been observed in a wide range of circumstances, including consumer goods categories (Day et al 1979; Fader & Schmittlein 1993; Scriven & Bound 2004), apparel brands (Dawes 2009), product variants (Singh et al 2008), leisure activities (Scriven et al 2014), modelling brand competition for new brands (Ehrenberg 1991a), and has recently described cross-category consumer sharing (Tanusondjaja et al 2016). Given the range of contexts in which the Duplication of Purchase pattern has been found to apply, it is a valid tool for describing the buying behaviour of fruits and vegetables.…”

If the Model Fits, Use It: Methods and Benchmarks for Evaluating NBD-Dirichlet Goodness-of-Fit

“…The benchmarks in the literature are therefore implicit rather than explicit. Scriven and Bound (2004) and Wright (1999) suggest correlations for penetration should be 'high', of over 0.9, and those for purchase frequency somewhat 'lower', of at least 0.6. These authors 1 The average is used to address the scale problem identified by Wright et al (2002).…”

“…The natural approach is to assess the fit of the model's estimates with the observed data. The standard method of fit assessment for the Dirichlet model is based on individual brand deviations calculated as the difference between observed values and model estimates (Fader and Schmittlein, 1993; Goodhardt et al, 1984; Scriven and Bound, 2004; Wright, 1999; Wright et al, 2002). An assessment of fit, however, is not determined by how well the model estimates match the observed metrics for a single brand, but rather the match over all brands (Fader and Schmittlein, 1993); that is how well the model fits the category as a whole (Scriven and Bound, 2004).…”

“…Equation 1 provides the formula for the comparison of averages method for g brands where O and T are the observed values and model estimates of the metric respectively (Scriven and Bound, 2004; Sharp and Driesener, 2000; Uncles and Kwok, 2009; Wright, 1999; Wright et al, 2002). To illustrate this method, Table 1 shows observed values (O) and model estimates (T) for the toothpaste category in the UK, along with their averages.…”