Most conjoint methods assume "main effects only" estimation. These are simple additive models in which the value of a product concept is equal to the simple additive sum of its parts (the attribute levels). The part-worths for each attribute are measured independently of all others. Main effects (the independent effect of each attribute) tend to capture the vast majority of variance to be explained in choice data. However, there are instances in which the presence of interactions between attributes makes the simple model not as accurate as it could be. Adding interaction terms to the main effects model, in these instances, could add important explanatory power and improve predictive accuracy.
In a Sawtooth Software conference, the following explanation of an interaction was provided, "Interactions occur when the combined effect of two attributes is different from the sum of their two main effect utilities. For example, being stranded on a deserted island is pretty bad, say it has a utility of -40. Attending a party hosted by cannibals is also a bad thing, say with a utility of -50. But attending a party hosted by cannibals on a deserted island could be altogether worse, in grisly sorts of ways (utility -250)." ("An Overview and Comparison of Design Strategies for Choice-Based Conjoint Analysis," Keith Chrzan and Bryan Orme, 2000 Sawtooth Software Conference.)
One of the strengths of CBC is its ability to estimate the effects of interactions. We think that CBC provides an excellent way to produce relatively precise results when attribute interactions are of concern.
It can be demonstrated that interaction effects can be revealed through choice simulations using main-effect models that do not directly model interaction terms, if the source of the interactions between attributes is principally due to differences in preference among groups or individuals. If Latent Class or HB are used to model main-effects, there is less need to additionally model interactions. Either way, the randomized choice designs offered in CBC are appropriate for either aggregate or disaggregate analysis; for main-effects or models that involve interactions. We recommend you be on the lookout for significant interactions--even if using disaggregate analysis.
To obtain strongest results for interactions, some level overlap should be incorporated into your CBC designs. See the section entitled CBC Questionnaires and Designs for more information.
Be careful about adding interaction terms to the model, as they come at a cost and can easily lead to overfitting. In other words, the extra parameters within the model may not be worth the amount of extra fit to the data and worse predictions may result for market simulations involving new choice scenarios. It would be a mistake to simply add all interaction terms between attributes to the model simply because the analyst wanted to ensure that if interaction effects existed that they were captured.