Interactions

As discussed in The Assumptions of Choice-Based Conjoint, an assumption of choice-based conjoint is that the appeal of a product is the sum of the utility of its attribute levels.

It’s not hard to think of situations where this assumption is a poor one. For example, in the ice cream market, chocolate and mint go together magically, and we may expect that the effect of chocolate and mint is greater than the sum of the separate effects of chocolate and mint. In theory, it is possible to empirically test for such interaction effects when conducting the statistical analysis. However, most experimental designs implicitly assume that such interactions do not exist in the data, making such testing impossible. 

There are four main approaches to dealing with interactions when creating the experiment:

1. Ignore the problem
2. Creating designs with interactions
3. Superattributes
4. Randomized algorithms with a large number of versions

Ignore the problem

It's actually exceedingly rare that interactions are found when analyzing conjoint. Consequently, it is common to ignore the problem. The reasons that interactions are rarely discovered are that:

• Most experimental design software will, by default, generate designs that assume that there are no interactions. This is because such an assumption allows smaller sample sizes and fewer questions, which leads to cheaper research and better quality data due to lower levels of fatigue.
• You need 16 times the sample size to estimate an interaction than to estimate a main effect.
• In the early days of choice-based conjoint, it was common to fit interactions. However, this was because the early analyses used simple models that did not directly consider differences between people, and the fitting of interactions compensated for this. More modern analysis techniques, such as hierarchical Bayes, automatically address differences between people.
• Even when discovered, they are difficult to explain to the end audience, and it is often the case that the added confusion created by the explanation just reduces the usefulness of the study as a whole.

Creating designs with interactions

Some experimental design software allows the user to create designs with specified interactions. For example, if one attribute is Chocolate and another is Nuts, you choose to create a design that includes interaction between Chocolate and Nuts.

Superattributes

Superattributes combine two or more attributes into a single attribute. For example, if one attribute has levels of Milk and Dark, and another has levels of Almonds and Hazelnuts, then the superattribute is:

• Milk chocolate with almonds
• Milk chocolate with hazelnuts
• Dark chocolate with almonds
• Dark chocolate with hazelnuts

Randomized algorithms with a large number of versions

Designs with interactions and superattributes require you to work out what interactions you anticipate at the time of creating the design. This is often difficult. An alternative approach is to use a randomized algorithm that generates the choice questions entirely randomly and gives each respondent a different set of questions (i.e., has one version per respondent).

There are two aspects to this:

• If interactions do exist in the data, when a randomized algorithm is used, the estimates of the utilities will represent the average appeal of the attribute levels. By contrast, when a more efficient algorithm is used, the estimates of utility may in truth be estimates of a non-intended interaction (e.g., perhaps chocolate ice cream coincidentally often appears with mint, so that the estimate of chocolate includes some aspect of chocolate + mint).
• When using a randomized algorithm it is possible to estimate interaction effects when performing analysis. The easiest way to do this is to manually modify the experimental design so that it contains superattributes (e.g., if flavor has chocolate and vanilla, and mint is a binary attribute, creating a new attribute with levels of chocolate no mint, chocolate mint, vanilla no mint, vanilla mint).

As discussed above in Ignore the problem, typically interactions won't be found.