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Most applications of conjoint analysis have emphasized main-effects models, largely because fewer data points are needed to fit that type of model at the individual level. The authors suggest that such simplifications can lead to poor predictions when the underlying utility functions depart from the simplicity of a main-effects model. They also show how compromise designs, which allow orthogonal estimation of selected two-way interactions (as well as main effects), can provide a more general experimental design in cases where a specified set of two-way interactions is suspected.
Carmone et al. (Sun,) studied this question.