Return on Investment (ROI) is management’s bottom line. Consequently, everything must be separated and assigned a row with associated costs and profits. Will we make more by adding another product to our line? Will we lose sales by limiting the features or services included with the product?

The assumption is that consumers see and value the same products and features that management lists as line items on their balance sheets. It simply makes data collection and analysis so easy that the most popular techniques never question this assumption. For example, in my last post about TURF Analysis, I discussed the ice cream flavors problem. How many and what flavors of ice cream should you offer given limited freezer space?

A typical data collection would present each flavor separately and ask about purchase intent, either a binary buy or no buy or an ordered rating scale that is split into a buy-or-not-buy dichotomy using a cutoff score. Even if we assume that our client only sells ice cream in grocery stores, we still do not know anything about the context triggering this purchase. Was it bought for an individual or household? Will adults or children or both be eating it for snacks or after dinner? How will the ice cream be served (e.g., cones, bowls, or with something else like pie or cake)?

Had we started with a list of usage occasions, we could have asked about flavor choices for each occasion. In addition, we could have obtained some proportional allocation of how much each occasion contributed to total ice cream consumption. Obviously, we have multiplied the number of observations from every respondent since we ask about flavor selection for every usage occasion. Much of the data matrix will be empty since individuals are likely to buy only a few flavors over a limited set of occasions.

The typical TURF Analysis, on the other hand, strips away context. By removing the “why” for the purchase, we have induced a bias toward focusing on the flavor without any context. Technically, this was the goal of the research design in the first place. Management knows the costs associated with offering the flavor, it needs to know the profit, but that it has failed to measure. In fact, it is unclear what is being measured. Does the respondent provide their own context by thinking of the most common purchase occasion, or do they report personal preferences as they might in any social gathering when asked about their favorite flavor of ice cream? Nonetheless, we still cannot calculate profit for that would require a weighted average of selections over purchase occasions with the weights reflecting volume.

Contextualized measurement yields high-dimensional sparse data that create problems for most optimization routines. Yet, we can analyze such data by searching for low-dimensional subspaces defined by benefits delivered and affordances provided. Purchases are made to deliver benefits. Flavors are but affordances. Someone in the household likes chocolate, so the ice cream must contain some minimal level of chocolate. Flavor has an underlying structure, and the substitution pattern reflects that structure. However, chocolate may not be desirable when the ice cream is served with cake or pie. Moreover, those “buy a second at a discount” sales change everything, as do special occasions when guests are invited and ice cream is served. Customers are likely to be acquired or lost at the margins, that is, in less common usage occasions where habit does not prevail. These will never be measured when we ask for preference “out of context” because they are simply not remembered without a specific purchase occasion probe.

Deconstructing Consumption

We start by identifying the situations where ice cream is the answer. Preference construction is triggered by situational need, and the consumer relies on situational constraints to assist in the purchase process. Situations tend to be separated by time and place (e.g., after dinner in the kitchen or dining area and late night snack in front of TV) and consequently can be modeled as additive effects. Each consumer can be profiled as some weighted combination of these recurring situations.

Moreover, we make sense of individual consumption by grouping together others displaying similar patterns. We can think of this as a type of collaborative filtering. Here again, we see additive effects where the total markets can be decomposed into clusters of consumers with similar preferences. In order to capture such additive effects, I have suggested the use of nonnegative matrix factorization (NMF) in a previous post. The nonnegative restrictions help uncover additive effects, in this case, the additive effects of situations within consumers and decomposition of the total market into additive consumer segments.

You can find the details covering how to use and interpret the R package NMF in a series of posts on this blog published in July, August and September 2014. R provides an easy-to-use interface to NMF, and the output is no more difficult to understand than that produced by factor and cluster analyses. In this post I have focused on one specific application in order to make explicit the correspondence between a matrix factorization and the decomposition of a product category into its components reflecting both situational variation and consumer heterogeneity.

Bradley Efron partitions the history of statistics into three centuries with each defined by the problems that occupied its attention. The 21st century focuses on large data sets and complex questions (e.g., gene expression or data mining). Such high-dimensional data present special problems that must be faced by both statistics and people engaging in everyday life. Modeling consumption from this new perspective, we hope to achieve some insight into the purchase process and measures that will reflect what the consumer will and will not buy when they actually go shopping.