Predicting Choice
Editor's note: Joseph Curry is a vice president of Sawtooth Software, a company that writes and markets microcomputer software for marketing research. Since 1978, Curry has been involved in the development of microcomputer software systems for interactive interviewing and data analysis.
Bringing a new or reconfigured product to market involves a number of complex, interrelated decisions. Marketers must decide what features a product should have, how to price it, and whom to target. And, all of this must be done against a background of anticipated competition. Conjoint analysis has become a popular technique for making these types of decisions because it lets marketers predict choice behavior.
I described the basics of conjoint analysis in my last article, "Understanding Conjoint Analysis in 15 Minutes" (Quirk's Marketing Research Review, June/July 1989). Because I touched only briefly on choice models in that article, I expand on that subject here using the same example. I will describe three of the most widely used models: First Choice, Share of Preference, and Likelihood of Purchase.
Suppose we want to market a new golf ball and have decided that the salient features and feature alternatives are:
Also suppose we have interviewed golfers to determine their preferences for these features. For one buyer these preferences are reflected in the following "utilities:"
A utility has the property that the higher its value, the more desirable its corresponding feature. Utilities can be added to yield a total value for a combination of features.
Suppose we were considering marketing one of two golf balls:
One way to predict which ball our buyer will choose is to add up the buyer's utilities for each ball; the one with the higher total is expected to be the buyer's first choice.
Given these two choices, we'd expect our buyer to choose the Long-Life Ball. Repeating this for the 100 buyers in our hypothetical sample, we might get:
We can use this approach to answer "what-if' questions. For example, suppose we dropped the price of the Distance Ball from $ 1.50 to $ 1.25. Which ball would our buyer prefer? Let's recompute the totals and see.
This price decrease is enough to make our buyer switch. For the total sample, the results for the lower-price Distance Ball might turn out to be:
We could also look separately at market segments. For example, our sample includes 50 males and 50 females. The split, keeping the Distance Ball at the lower price, might be:
We 'd expect the Distance Ball to appeal to men and the Long-Life Ball to appeal to women.
This simple way of simulating behavior, which can be extended to any number of buyers and products, is referred to as the First Choice approach. Although conceptually and computationally simple, the First Choice model has one major drawback: it usually overstates choice for the more popular products. For this reason the Share of Preference model is often a better estimator of choice.
Unlike the First Choice model, which assigns a buyer's entire purchase to the product with the highest utility, the Share of Preference model splits the probability of purchase among all competing products according to their utilities. Why should this be better? First, it recognizes that buyers do not always purchase the product for which they have the highest utility. And second, many products represent low-involvement purchases for buyers. For these products buyers often have no clear first choice.
How does the Share of Preference model transform a buyer's utilities into product preference shares? One of the most common methods used is a logit transformation.
The logit transformation for converting a buyer's utility for Product A, (UA), into a preference share, P(A), for Product A in a market made up of two products, A and B, is:
where e equals 2.718 and b can be interpreted as a measure of the buyer's involvement in the product category (see below). The preference share for Product B is:
This expression can be generalized to any number of products by adding a term in the denominator for each additional product.
Marketers use the logit transformation because it has three intuitively desirable properties. First, the higher a product's utility, the greater is its preference share. Second, the buyer's preferences across all products sum to 1. And third, the greater the buyer's involvement in the category (i.e., the larger b becomes), the more distinct are the preference shares.
Let's apply the Share of Preference model to our buyer for the Distance (DB) and Long-Life Balls (LB) at their original prices. With UDB = 105, ULB = 110, and assuming b = 0.02
Comparing the results between the First Choice and the Share of Preference models for our buyer we get:
and for the sample of buyers:
Note that the Share of Preference estimates are more conservative than those for the First Choice model.
Although Share of Preference is more realistic than First Choice, it has a serious defect: If you add identical (or very similar) products to the model, the total preference share for those products is artificially inflated. This defect (sometimes referred to as the "red bus/blue bus" problem) can be avoided by using a Share of Preference model that corrects for similar products.
Both the First Choice and Share of Preference models predict a buyer's choice assuming that the buyer is going to purchase. Neither, however, accounts for the fact that different purchasers may be more or less likely to purchase. For this, marketers use Likelihood of Purchase models.
Anticipating the use of a Likelihood of Purchase model, we asked the buyers we surveyed their purchase likelihood for three test concepts. Here are the results for one buyer:
Note that the Concepts 1 and 3 represent the two extremes of the range we are considering, and Concept 2 is somewhere in between.
We can also calculate this buyer's utility for these concepts:
Let's plot this buyer's purchase likelihoods against the utilities, and fit a straight line through the points:
Note that the vertical scale is not linear. We have actually regressed 1n(p/1-p) rather than p, where p is the likelihood of purchase. This produces a better straight-line fit in most cases since the likelihood is in general not a linear function of the utilities and log transformations tend to straighten curves.
From this graph we can estimate this buyer's purchase likelihood for any ball. Let's do it for the Distance Ball which has a utility of 120 for this buyer.
Reading from the graph, we estimate that our buyer has about a 70% likelihood of purchasing the Distance Ball, if that ball alone were available. It is from the slope of this line that we estimate the b value (involvement) for the Share of Preference model.
Although there is valuable information contained in these models, it is important to remember that they are decision support tools and not decision makers in and of themselves. They are reliable in deciding how to best configure a new product and relatively reliable in estimating how much better one alternative is over another. These tools should be used with caution, however, when forecasting sales or market shares.