As discussed in Chapter 2, a linear model for the decomposition of the utility of a prole may include main effects, two-way, and higher-order interactions. The full factorial design may be modeled as
= + + = =
∑ ∑µ α α + + + =
where yx x xm1 2 ... is the response or transformed response of the prole ( , ,..., )x x xm1 2 ; µ is the general mean; αAixi is the effect of factor Ai at xi level; αAixi Ajxj is the effect of factors Ai and Aj at xi and xj levels, respectively; … ; and ex x xm1 2 ... is the random error. In practice, subsets of terms are modeled in DCE (discrete choice experimentation) and CA (conjoint analysis). This chapter illustrates four types of models widely used in traditional DCE/CA. The four categories of models most widely assumed are models that include only brand effects, only attribute main effects, brand and attribute main effects, and brand and attribute main effects with selected two-way interactions. Illustrations of generic questions and experimental plans are provided. The last section that deals with brand and attribute main effects with selected two-way interactions illustrates estimation and hypothesis testing using simulated data.