Simulation and Reality

3 Relating Qualitative Domain Expertise to Statistical Evidence:
An Intelligent Market Modelling System

These attributes have no objective meaning. Examples in markets for alcoholic beverages are "special", "traditional", "imported" (though usually produced domestically), "unique". The first models reported by Moss and Edmonds [12] were based on marketing practitioners' assessments of the different reasons why agents might buy such beverages. For one such market, the reasons given were that they sought the "physiological effect" -- this was called "functional drinking" or that they were buying drink for social occasions such as parties or for self-reward or because they sought new and distinctive drinks. Moss and Edmonds devised a distribution function relating brand characteristics as specified by the marketing practitioners to the requirements of consumers in different social contexts. They were therefore called context-dependent attribute preference (CDAP) functions. The differences between CDAP functions and the utility functions used by economists is that utility functions relate to individual preferences and purport to mimic the decisions of individuals while CDAP functions describe the mean preferences, the importance of individual brand attributes and their tolerances to deviations from the ideal attributes for all consumers in particular social contexts. For example, the purchasers of beverages for a party will want something special but not very distinctive so that the beverages will be attractive to a wide range of tastes. On the other hand, the same individuals buying beverages to celebrate (say) a career advancement will either want or certainly be more tolerant of distinctiveness in their purchase since it will be primarily for their own enjoyment. Specialness will still be an important consideration. Moreover, some attributes will be more important in some circumstances than others

Fig. 1

The three functions (upper, middle and lower) relate the contribution to demand strength for the same ideal value of the brand attribute but are critical to different degrees. Because the values of the functions for each attribute of the brand are multiplied together in determining brand strength, the shallowest function is the least critical because deviations from the ideal reduce the contribution to strength by the smallest amount. The "variance is an index of how tolerant consumers in this social context will be to deviations of actual characteristic intensity from the ideal at c*

The function which captured these desiderata is given in fig. 1 where the value on the vertical axis is the contribution to the strength of demand by consumers in the particular context and the horizontal axis is the intensity of the particular attribute associated with a brand. The parameters of the CDAP functions for each brand and each attribute are obtained from the marketing practitioners who enter the values on a five-point Lickert scale. So the presence of an attribute could be taken to be "highly critical", "moderately critical", "not very critical", "hardly matters" or "does not matter". The ideal value is specified in similarly qualitative terms.

The model was constructed so that, given the various CDAP functions, including functions for the parameters "relative price" and "expensiveness", the relative attractiveness of each brand together with the extent to which each brand differed in its attributes from other brands (described as inter-brand distances) was used to determine the market share of each brand given the prices of all brands considered.

In the first generation of these models, the marketing practitioners specified the contexts (social, self-rewarding, functional, etc.) and the characteristic ideals, tolerances and criticality of each brand attribute in each context. They also specified their estimates of the proportion of demand accounted for by consumers in each context. The model incorporating these judgements and estimates was then run over a subset of the data available on prices and sales of each brand. Usually, the data was obtained from supermarket scanners for a geographical region such as the UK or metropolitan areas of the United States. A binary search algorithm was used to obtain the best fit in terms of smallest root mean squared errors (RMSEs) or minimum absolute percentage errors (MAPEs). The search algorithm changed the specified sensitivities of consumers to prices, to relative distances among brands and to the relative market strengths implied by the brand attributes relative to the CDAP functions. It then changed the proportions of demands accounted for by consumption in each context and, finally, it changed the ideal values of the various attributes in each context. The result was a set of modifications to the qualitative judgements of the domain experts together with statistical measures of the consistency of those judgements with the numerical data. The RMSEs and MAPEs obtained with these models was in every case far better at tracking market shares over the holdout set (the data not used in parameterizing the models) than were the best ordinary least-squares models.

A second generation of these market models reported by Edmonds and Moss [13] incorporated only the practitioner judgements of the important brand attributes in different markets and used a genetic programming algorithm to identify contexts, the relative importance of each context and corresponding CDAP function parameters to minimize RMSEs. The contexts were not given mnemonic names by the model but they provided an important input to the development by marketing practitioners of their own understanding of the markets that had been modelled.

Clearly, the CDAP functions are entirely procedural and there is no explicit representation of agent cognition in the model. In a model which aggregates context-dependent demands rather than agents, there is no immediate scope for representing individual agents, much less their cognitive processes. However, to extend these models to the development of new markets arising from new product introductions such as the so-called "alcopops" or the development of new classes of consumers in the developing or emerging-market economies, some representation of agent cognition would be essential to model emerging tastes and, so, demands for brand attributes in various social contexts. In such extensions to the models described here, the behaviour emerging from populations of software agents will also yield numerical simulation outputs amenable to statistical comparisons with the empirical record. In such cases, not only will we have well validated representations of cognition but also the models themselves, including their representations of qualitative phenomena, will be as well verified as statistical technique allows.

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