CEA - Cross Effects Analysis

> CEA - Cross Effects Analysis

Problem

In the common approach to estimation of product utilities each product is taken as an isolated entity. Utility of a product is understood as a fixed value independent from other products in the choice set. Only differences between utilities of the products in a choice set determine the choice probability of each product. A more realistic approach assumes that the decision is made in a stepwise manner along a hierarchical tree made of available product branches. The decision maker moves from the root of the category along the stem and excludes unacceptable branches of products until only a branch carrying the most acceptable products is found. These products, often being close substitutes, fall in the consideration scope the final consideration set is selected from. In order to build an efficient experimental design the branching should be known or guessed prior an experimental exercise.

The above approach can be easily applied when the branching nodes are well defined, e.g., in transportation problems with branches of private and public, rail and road and/or standard and luxury transportation means. The problem leads to a nested logit model. A correct nesting is hard to predict in a product category where personal tastes dominate the choice. This concerns namely CPG/FMCG products with many close substitutes. Utilities of such products are usually obtained with CBC - Choice Based Conjoint methodology. A single value of the product utility may not sufficiently describe the choice from a number of similar products.

Solution

The idea of "clout" and "vulnerability" of a product in a pair with another one was introduced by Anderson and Willey and Lazari and Anderson as an application of psychometric methods in marketing. It is also known as "availability" or "cross-effects" model. Utility of a product is understood as differing in presence or absence of another product in the choice set. In analogy to similar problems in psychometry, the conflict is reconciled by adding parameters that absorb the influences of the competing products in the choice set, with the parameters estimated as first-order (pair-wise) interactions.

A study of cross effects between products leads to a substantial increase in number of parameters that must be estimated. For N products the additional number of pairwise cross effects is ((N-1)N/2). In a realistic case of 26 products we would have additional 325 parameters. Such a number would lead to an inestimable, heavily oversaturated system, for an individual. Therefore, originally aggregated approach had been suggested. With Bayes hierarchical estimation methods, an individual approach is possible under certain conditions. The conditions can be achieved by introducing reasonable restrictions in the model such as excluding some of the cross effects from estimation. This is possible for products with negligible shares, little interest in, or those that are known as non-interacting with other products.

Properties

Estimation of cross effects is expected to be useful in CPC/FMCG product categories where personal tastes play a dominant role. In our experience, the fit between estimated and observed choices is increased not only "visibly" but also based on Bayes or Akaike information criterion, i.e. taking into account the increased number of estimated parameters. The cross-effects model seems to pin-point the current or potential direct competitors that main-effect based utilities cannot provide. It may be useful in cutting into the cannibalization problem. Another use is possible for study of inventory availability effects, outlet type selection, etc.

As aside

A simpler approach to cannibalization is to use estimation of maximal possible cannibalization in a pair of products. The method relies on utilities obtained from a CBC using the standard multinomial logit model.

The influence of a cross-effect on shares of the products involved in the effect is highest when both products have the same main-effect utilities, i.e. about the same shares. The higher the difference in utilities the lower the cross-effect is.

The typical outputs from the method are preference share simulations with different scenarios. A direct comparison of clout and vulnerability in logit units for each of the product pairs of interest seems to be even more illustrative since the cross-effects are often obscured by the main effects that usually dominate. However, the direct comparison of cross-effects requires that the sample or sub-sample is as homogeneous as possible. LCA - Latent Class Analysis may be used for finding such sub-samples.

A marked disadvantage of the method is size of the sample required to estimate the large number of parameters. The minimum is about 400 respondents in a medium size project of about 20 brands.

As aside

The method is an application of an heuristic approach to psychology of purchase behavior rather than implementation of an econometric theory.
If price sensitivity is not the aim of a study, MXD - Maximum Difference Scaling is a usable interviewing method. The SCE - Sequential Choice Exercise cannot be used.
We suggest the cross-effect approach might be useful in interpretation of the market scanner data provided the model is extended, namely completed with the consumption quantities.

Example: Cigarette packs

The objective of the study were price elasticities of cigarette brands available on the local market. For purpose of CEA analysis, all prices have been set at their market values. Clouts of the tested brands in respect to two selected domestic brands, SPB and PEW, are shown below.

CEA: Clout over SPB CEA: Clout over PEW

[ Note: If you do not see the pictures above side by side please make the browser window wider. ]

Cross-effect profiles of the two domestic brands were clearly different. The only common property was that both were loosing against imported brand variants MG1 and MG2. Utility of brand PAG as an isolated (stand-alone) product was about 1 logit lower than that of brand PEW. In presence of the latter, the former one looses another 4 logit units and becomes virtually unmarketable.