On the meaning of block effects in paired comparison choice experiments and a relationship with blocked 2K main effects plans

In the optimal design literature for paired comparison choice experiments it has been proposed that respondent heterogeneity can be modelled by introducing fixed block effects into the linear predictor of the multinomial logit model and D-optimal utility-neutral designs for the modified version of the model have been derived by orthogonally blocking D-optimal utility-neutral designs for the model without block effects. In this paper, we first discuss the proper interpretation of the block effects showing that they only explain a special and non-standard type of respondent heterogeneity which refers to the order in which the alternatives in each pair are presented. Secondly, for the special case of the choice model with block effects in which the main effects of K two-level attributes are to be estimated we show how by using a previously unnoticed relationship with blocked two-level main effects plans for the linear 2K factorial model new designs for choice experiments can be constructed. These designs are usually non-orthogonally blocked and locally D-optimal in a certain subclass of designs.