## Predicting Choice with Conjoint Analysis and Discrete Choice

### Conjoint Analysis and Discrete Choice have become popular for marketers and product managers, because they let them predict choice behavior.

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 our last blog, “Understanding Conjoint Analysis in 15 Minutes”. Because I touched only briefly on choice models in that article, I expand on that subject here using the same example. I will provide simplified examples of two of the most widely used models:

- A multi-product model (also known as a “competitive model,” because it typically seeks to include all the products in the competitive set).
- A single-product model (also known as a “likelihood of purchase” model, because it typically seeks to predict preference for a new product offered without competition).

**Multi-Product Model**

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 preference.

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 find how their preferences are split between the two balls (we will call this “preference share”).

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 re-compute 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.

Above, we have shown a very simplistic example with just two products. In use for decision-making, multi-product models allow the user to enter all the relevant competitors and see how preference is divided amongst them. In addition, one can simulate the various offerings in one’s own product line to see how preference is divided.

**Single-Product Model**

Some products do not exist within a well-defined competitive set, or are entirely new to the market. In these cases, it makes most sense to focus the conjoint analysis on a single product. In the example below, we provide a simplified look at how we predict likelihood of purchase for a single product.

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:

Technical note: The vertical scale above 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*.

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.

« Back to Blog

>> Follow us on Twitter for the latest from Sawtooth Technologies Consulting.