By default, interaction effects are not estimated in ACBC's HB routines. But, you can include selected first-order interactions (interactions between two attributes) if you wish.
Most conjoint models assume a simple additive model. This implies that the effect (utility) of each attribute can be estimated and considered independent of all other attributes. Indeed, main effects tend to account for the majority of the explainable variance in the data. However, there are instances in which significant interaction effects exist and market simulators can be improved if those effects are included in the model.
Including interaction effects in CBC models is especially critical if pooled (aggregate) analysis is employed. However, it has been demonstrated that the need to model interaction effects is significantly reduced when using individual-level estimation (as is the norm for ACBC). But, that doesn't mean that one can simply ignore interaction effects if using HB. We recommend you be on the lookout for interaction effects and that you investigate including them in ACBC models. ACBC's designs appear to be as effective as standard CBC designs with respect to accommodating interaction effects.
Standard CBC gives two useful tools for identifying interaction effects that may provide improved fit to the model. CBC's Counts program reports a interaction Chi-Square test for all attributes taken two-at-a-time. This can help you identify which effects (at least when considered in a pooled model) may be significant and useful. In the CBC documentation, we have encouraged users also to use aggregate logit and the "2 Log-Likelihood" test to test the strength and significance of first-order interactions.
With Adaptive CBC designs, standard counting analysis is not appropriate (since the designs are not level balanced). But, one can perform a series of pooled logit models (using our Latent Class software with a one-group solution) to investigate potential interaction effects using the "2 Log-Likelihood" test. It is interesting to note, however, that a strong lift in likelihood due to the inclusion of an interaction effect for a pooled model may not necessarily translate into a strong lift for an individual-level model.
Many of the interactions detected with aggregate modeling in CBC over the years have been due to respondent heterogeneity. For example, if the same people who prefer convertibles also prefer the color red for automobiles, then the "convertible + red" interaction effect may be mostly accounted for simply by estimating individual-level models (with main effects). But, interaction effects may more pervasive within each individual's psyche, and in those cases interaction effects can improve individual-level model performance.
A recommended practice is to investigate all potential first-order interaction effects using aggregate logit and the "2 Log-Likelihood" test. Those interaction effects that are strongest and most critical to the aims of the study (such as brand and price, for a brand equity/pricing study) could also be investigated within HB modeling. Useful interactions can be confirmed by examining the model fit to holdouts, or by seeing if there appears to be a positive lift in RLH as reported by HB.
As noted earlier, it is quite possible that including what appears to be a strong interaction effect (from an aggregate modeling perspective) within individual-level HB models may offer no improved fit. This would suggest that the interaction is mostly due to heterogeneity rather than a more pervasive (intra-respondent) interaction effect.
Unless there is compelling evidence for including an interaction in individual-level ACBC models, we recommend omitting it to avoid overfitting.
