# Conjoint analysis

Conjoint analysis, also known as multiattribute compositional models, is a statistical technique that was introduced into the marketing research community by University of Pennsylvania, Wharton professor Paul Green in the late 1960s. Since then, conjoint analysis has become the most popular multiattribute choice model in marketing. It can be used as a trade-off measurement technique to determine consumer preferences and buying intentions, and to also predict how consumers might react to changes in a current product or new product introduction. Conjoint analysis is often used today in new product design and advertising.

Conjoint analysis generally implies the use of design of experiments statistical techniques to construct efficient survey designs and assess the relative importance of each attribute (and it's possible values, or "levels") that compose a product. The independent variables (factors) are the attributes set to discrete levels, and the dependent variable (output) is the consumer response: either rating, ranking, or choice among the presented set of alternatives.

## Basic Process

The basic process for a conjoint analysis is as follows:

• The product features that will be analyzed are determined.
• Potential customers are shown numerous different sets of products. Each set includes several product profiles that have multiple conjoined product features.
• For each set of products, they select (by ranking, rating, or choosing) the profiles according to some overall criterion, such as preference, acceptability, or likelihood of purchase.
• Choice simulator models such as the first choice model, average probability model, and the logit model are used to estimate the utility of each product feature.
• This information is then incorporated into a new or existing product.

## Data Collection

Instead of asking respondents what they prefer in a product directly, conjoint analysis presents to them potential product profiles that have specific combinations of attributes. These profiles can be evaluated in several ways, including:

• Rating (e.g. rating with a scale from 1-10)
• Ranking (e.g. rank best as 1st, 2nd, 3rd, etc.)
• Choice (e.g. four options, which do you choose?)

An example of a product profile using rating is shown below:

An example of a product profile using choice is shown below:

The conjoint analysis is usually done using stated choice, which is data collected using a survey that is typically developed with experimental design (aka design of experiments) techniques. A full factorial survey could be generated that tests every possible combination of attributes. However, in most cases this is not feasible due to the great amount of questions needed. It is also not even necessary, since balanced and orthogonal arrays can be used to reduce the number to a much smaller fractional factorial design. This design can be generated using a program such as SAS Institute's SAS system. The advantage of stated choice data is that it is possible to conduct a controlled experiment, which provides high-quality data. However, the task of evaluating product profiles in the survey may differ from the consumer experience in the marketplace, and survey data measures what people say and not necessarily what they do. Designing such a survey is an iterative process, and while there are no fixed rules on how to create a "good" conjoint survey, there are some best practices for designing a conjoint survey.

An alternative to stated choice data is revealed preference data. This consists of using data that is collected from actual performance in the marketplace. The advantage of this is that the data is a real measure of how consumers act. However, there are problems with multicollinearity - it is difficult to tell exactly why someone is choosing one product over another.

## Simulation Analysis

There are many different simulator models available for use in estimating the utility function of the product attributes. These include the first choice model, the average choice model, and the logit model.

### First choice model

For each respondent, the product with the highest utility is the product of choice and receives a value of 1. If there is a tie for the highest utility, both products get a value of 0.5. In the end the most votes for a product evaluated as a proportion of the number of respondents is the most desirable product.

### Average choice model

Also known as the Bradley-Terry-Luce model. The choice probability for a product is based on the utility of that product divided by the sum of all products in the simulated market.

### Random Utility Discrete Choice Models

Introduces a random error term to the measurement of utility and calculates the probability of choice as equal to the probability of the utility of one product being greater than the utility of all other products. Models vary based on the assumed distribution of the random error component and the specification of the deterministic component of utility. The most popular models are the logit model and the probit model.