Conjoint Analysis Technical Notes III

Conjoint analysis is a technique for measuring, analyzing, and predicting customers’ responses to new products and to new features of existing products. It enables companies to decompose customers’ preferences for products and services (typically provided as descriptions or visual images) into “part-worth” (or utilities) associated with each level of each attribute of the product. They can then recombine the part-worths to predict customers’ preferences for any possible combination of attribute levels, and the likely market share or revenue that a new product is likely to achieve when introduced into a market in which other competing products may already be available. They can also use conjoint analysis to determine the optimal product concept or to identify market segments that value a particular product concept highly.

There are three stages in a typical conjoint study:

(1) Design of a data collecting instrument,

(2) Collecting data from consumers, and

(3) Analyzing the data and simulating market response.

Transforming preferences to choices

To complete the simulation design we must specify a choice rule to transform part-worths into the product choices that customers are most likely to make. The three most common choice rules are maximum utility, share of utility, and logit.

Maximum utility rule

Under this rule we assume that each customer chooses from the available alternatives the product that provides the highest utility value, including a new product concept under consideration. This choice rule is most appropriate for high-involvement purchases such as cars, VCR's, and other durables that customers purchase infrequently.

We can compute the market share for a product by counting the number of customers for whom that product offers the highest utility and dividing this figure by the number of customers in the study. In computing overall market shares it may sometimes be necessary to weight each customer’s probability of purchasing each alternative by the relative volume of purchases that the customer makes in the product category:

I = number of customers participating in the study;

J = the number of product alternatives available for the customer to choose from, including the new product concept;

mj = market share of product j;

wi = the relative volume of purchases made by customer i, with the average volume across all customers indexed to the value 1; and

pij = proportion of purchases that customer i makes of product j (or equivalently, the probability that customer i will choose product j on a single purchase occasion).

Share of utility rule

This rule is based on the notion that the higher the utility of a product to a customer, the greater the probability that he or she will choose that product. Thus each product gets a share of a customer’s purchases in proportion to its share of the customer’s preferences:

where uij is the estimated utility of product j to customer i.We then obtain the market share for product i by averaging pij across customers. This choice rule is particularly relevant for low-involvement, frequently purchased products, such as consumer packaged goods.

Logit choice rule

This rule is similar to the share-of-utility rule, except that the underlying theoretical rationale is different. To apply the share-of- utility model, we assume that the utility functions are basically accurate— but an element of randomness occurs in translating utilities into choice. In applying the logit choice rule we assume that the computed utility values are mean realizations of a random process, so that the brand with the maximum utility varies randomly, say from one purchase situation to the next. The choice rule then gives the proportion of times that product j will have the maximum utility:

Both the share-of-utility and the traditional logit rules share a questionable property known as IIA (independence from irrelevant alternatives). The choice probabilities from any subset of alternatives depend only on the alternatives included in the set and are independent of any alternatives not included. This property implies that if, for example, you prefer light beers to regular beers, then adding a new regular beer (an irrelevant alternative) to your choice set would nevertheless lower your probability of choosing a light beer, a counterintuitive result.

The maximum utility rule (also called the first choice rule) is simple and elegant, and choices predicted by using this rule are not affected by positive linear transformations to the utility function. This rule is particularly relevant for high-ticket items and in product categories where customers are highly involved in the purchase decisions. However, this rule predicts more extreme market shares, i.e., it has a tendency to produce market shares closer to zero and one than the other choice rules. Also, it is less robust—small changes in utility values of products can drastically change their market shares. On the other hand, the market share predictions made by the share-of-preference and logit choice rules are sensitive to the scale range on which utility is measured. The market share predictions of the share-of-utility rule will change if one adds a constant value to the computed utility of each product, but they are unaltered if all utility values are multiplied by a constant. Market share predictions of the logit choice rule are not altered if one adds a constant to the utilities, but will change if one multiplies all utilities by a constant. Thus, each rule has its advantages and limitations.

One way to choose among these three rules is this: First, for each rule, compute the predicted market shares of just the existing products. Then use the choice rule that produces market shares that are closest (in the sense of least squares) to the actual market shares of these products (this assumes that we are using a representative sample of customers for the study). This approach can be formalized using yet another choice rule, called the alpha rule.

Alpha rule

This rule is a weighted combination of the maximum utility rule and the share-of-preference rule, where the weight is chosen to ensure that the market shares computed in the simulation are as close as possible to the actual market shares of the existing products. Specifically, we choose an alpha (a) in the following formula to maximally recover the observed market shares of existing products:

To determine the best value of a, we minimize the “entropy” representing the extent of departures of computed markets shares of existing products from their actual observations:

where j is an index to represent an existing product, mj is the actual market share for product j, and mˆ j is the computed market share of product j for any given α.

#ConjointAnalysis #MarketingAnalytics #Marketing