Monday, January 26, 2015

Wine for Breakfast: Consumption Occasion as the Unit of Analysis

If the thought of a nice Chianti with that breakfast croissant is not that appealing, then I have made by point: occasion shapes consumption. Our tastes have been fashioned by culture and shared practice. Yet, we often ignore the context and run our analyses as if consumers were not nested within situations. Contextual effects are attributed to the person, who is treated as both the unit of observation and the unit of analysis.

Obviously, it would be difficult to interview the occasion. We need informants to learn about wine occasions. Thus, we seek out consumers to tell us when and where they drink what kinds of wines by themselves and with others. Even if one knows little about wine etiquette, the situation imposes such strong constraints that is makes sense to treat the consumption occasion as the unit of analysis. The person serves as the measuring instrument, but the focus is on the determining properties of the occasion.

Continuing with our example, there is a broad range of red and wine varietals that can be purchased in varying containers from a number of different retailers and served in various locations with a diversity of others. The list is long, and it is unlikely that we can ask for the details for more than a couple of consumption occasions before we fatigue our respondents. Yet, it is the specifics that we seek, including the benefits sought and the features considered.

Clearly, there is a self-selection process so that we would expect to find certain types of individuals in each situation. However, the consumption occasion imposes its own rules over and above any selection effect. Therefore, we would anticipate that whatever the reasons for your presence, the occasion will dictate its own norms. In the end, it is reasonable to aggregate the responses of everyone reporting on each consumption occasion and run the analysis with those aggregate responses as the rows. The columns are formed using all the data gathered about the occasion.

And It Isn't Just About Wine and Breakfast (Benefit Structure Analysis)

There are occasions when you use your smartphone to take pictures. If you were thinking about purchasing a new smartphone, you would consider camera ease of use and picture quality remembering those low-light photo that were out of focus and those sunsets where the sun is a blur. Usage occasion seems to impact almost every purchase. You pick your parents up at the airport, so you need four doors, preferably with easy access to the rear seats. Usage is so important that the website or the salesperson always  asks how you intend to use your new acquisition. Context matters whatever you buy (e.g., a washing machine, a garden hose, clothes, cosmetics, sporting equipment, and suitcases).

The goal is to uncover the major sources of variation differentiating among all the consumption occasions. Product differentiation and customer segmentation originate in the usage context. Since opportunities for increased profitability are found in the details, let's pretend we are journalists and ask who, what, where, when, why, and how. These six questions alone can generate a lot of rows, for instance, we obtain some 15,625 possible combinations when we suppose that the answers to each of the six questions could be classified into one of five categories (15,625 = 5x5x5x5x5x5). Of course, most of these rows will be empty because the responses to the six questions are not independent. Yet, 10% is still over 1500 rows, even if many of those rows will be sparse with zero or very small frequencies. Finally, the columns can contain any information collected about the consumption occasions in the rows, though one would expect inquiries concerning benefits sought and features preferred.

Now, we have a large matrix revealing the linkages between many specific occasions and a wide range of benefits and features. It might helpful to revisit the work on Benefit Structure Analysis from the 1970s in order to see how others have analyzed such a matrix. In Exhibit 5 from that Journal of Marketing article, we are presented with a matrix of 51 benefits wanted across 21 cleaning tasks. The solution was a simultaneous row and column linkage analysis, which seems similar to the biclustering that one would achieve today with nonnegative matrix factorization (NMF). As noted in the article, when cleaning furniture, the respondents desired products that removed dust, dirt and film without leaving residues or scratches. On the one hand, there appears to be a structure underlying the cleaning tasks revealed by their shared benefits, On the other hand, the benefits are clustered together by their common association with similar cleaning tasks.

Following that line of reasoning, we can simulate a data matrix by specifying a set of common latent features linking the occasions and the benefits. As outlined in a prior post, the data generating process is an additive superpositioning of building blocks formed by the occasion-benefit linkages. We can begin with some product, for example, coffee. When do we drink coffee, and why do we drink it? Even the shortest list would include starting the day (occasion) in order to jump-start the brain (benefit). Is this a building block? If there were a sizable cohort of first-of-the-day kickstarters who did not drink coffee for the same reasons at other occasions, then we would have a building block.

The data matrix tells us what benefits are sought in each occasion. Neither the occasions nor the benefits are independent. There are times and places when specialty coffee replaces our regular cup. What occasions come to mind when you think about iced or frozen blended coffees? To help us understand this process, I have reproduced a figure from an earlier post.

The associations between the ten occasions labeled A to J and the seven benefits numbered 1 to 7 are indicated by filled squares in Section a. The rows and columns are interchanged as we move from Sections b to c until we see the building blocks in Section d. The solid black and white squares do not show the shades of gray indicating the degree to which coffee drinkers demand the benefit in each occasion. Specifically, Benefit 6 is wanted in both Occasions A, C and H and Occasions D, G, I and E. However, it is likely drinkers are not equally demanding in the two sets of occasions. For example, coffee that starts the day must energize, but the coffee in the afternoon might be primarily a break or a low calorie refreshment. In both cases we are seeking stimulation, just not as much in the afternoon as the first cup of the day.

Benefit structure analysis remains a critical component in any marketing plan. Opportunity is found in the white spaces where benefits are not delivered by the current offerings. Case studies and qualitative research findings fill the business shelves of online and retail book sellers. Now, advances in statistical modeling enable us to inquire at the deep level of detail that drives consumer product purchases. The R code needed to simultaneously cluster the rows and columns of such data matrices has been provided in a series of previous posts on music, cosmetics, personality inventoriesscotch whiskey, feature usage, and the consumer purchase journey.

Sunday, January 11, 2015

Some Applications of Item Response Theory in R

The typical introduction to item response theory (IRT) positions the technique as a form of curve fitting. We believe that a latent continuous variable is responsible for the observed dichotomous or polytomous responses to a set of items (e.g., multiple choice questions on an exam or rating scales from a survey). Literally, once I know your latent score, I can predict your observed responses to all the items. Our task is to estimate that function with one, two or three parameters after determining that the latent trait is unidimensional. In the process of measuring individuals, we gather information about the items. Those one, two or three parameters are assessments of each item's difficulty, discriminability and sensitivity to noise or guessing.

All this has been translated into R by William Revelle, and as a measurement task, our work is done. We have an estimate of each individual's latent position on an underlying continuum defined as whatever determines the item responses. Along the way, we discover which items require more of the latent trait in order to achieve a favorable response (e.g., the difficulty of answering correctly or the extremity of the item and/or the response). We can measure ability with achievement items, political ideology with an opinion survey, and brand perceptions with a list of satisfaction ratings.

To be clear, these scales are meant to differentiate among individuals. For example, the R statistical programming language has an underlying structure that orders the learning process so that the more complex concepts are mastered after the simpler material. In this case, learning is shaped by the difficulty of the subject matter with the more demanding content reusing or building onto what has already been learned. When the constraints are sufficient, individuals and their mastery can be arrayed on a common scale. At one end of the continuum are complex concepts that only the more advanced students master. The easier stuff falls toward the bottom of the scale with topics that almost everyone knows. When you take an R programming achievement test, your score tells me how well you performed relative to others who answered similar questions (see normed-referenced testing).

The same reasoning applied to IRT analysis of political ideology (e.g., the R package basicspace). Opinions tend to follow a predictable path from liberal to conservative so that only a limited number of all possible configurations are actually observed. As shown below, legislative voting follows such a pattern with Senators (dark line) and Representatives (light line) separate along the liberal to conservative dimensions based on their votes in the 113th Congress. Although not shown, all the specific votes can also be placed on this same scale so that Pryor, Landrieu, Baucus and Hagan (in blue) are located toward the right because their votes on various bills and resolutions agreed more often with Republicans (in red). As with achievement testing, an order is imposed on the likely responses of objects so that the response space in p dimensions (where p equals the number of behaviors, items or votes) is reduced to a one-dimensional seriation of both votes and voters on the same scale.

My last example comes from marketing research where brand perceptions tend to organized as a pattern of strengths and weaknesses defined by the product category. In a previous post, I showed how preference for Subway fast food restaurants is associated with a specific ordering of product and service attribute ratings. Many believe that Subway offers fresh and healthy food. Fewer like the taste or feel it is filling. Fewer still are happy with the ordering or preparation, and even more dislike the menu and the seating arrangements. These perceptions have an order so that if you are satisfied with the menu then you are likely to be satisfied with the taste and the freshness/healthiness of the food. Just as issues can be ordered from liberal to conservative, brand perceptions reflect the strengths and weaknesses promised by the brand's positioning. Subway promises fresh and healthy food but not prepackaged and waiting under the heat lamp for easy bagging. The mean levels of our satisfaction ratings will be consistent with those brand priorities.

We can look at the same data from another perspective. Heatmaps summarize the triangular pattern observed in data matrices that can be modeled by IRT. In a second post analyzing the Subway data, I described the following heatmap showing the results from the 8-item checklist of features associated with the brand. Each row is a different respondent with the blue indicating that the item was checked and red telling us that the item was not checked. As one moves down the heatmap, the overall perceptions become more positive as additional attributes are endorsed. Positive brand perceptions are incremental, but the increments are not more of the same. Tasty and filling gets added to healthy and fresh. That is, greater satisfaction with Subway is reflected in the willingness to endorse additional components of the brand promise. The heatmap is triangular so that those who are happy with the menu are likely to be at least as satisfied with all the attributes to the right.