Journal of Statistical Theory and Practice

, Volume 12, Issue 1, pp 82–92

# Optimal two-level choice designs for estimating main and specified two-factor interaction effects

Article

## Abstract

Under the multinomial logit model, designs for choice experiments are usually based on an a priori assumption that either only the main effects of the factors or the main effects and all two-factor interaction effects are to be estimated. However, in practice, there are situations where interest lies in the estimation of main plus some two-factor interaction effects. For example, interest on such specified two-factor interaction effects arise in situations when one or two factor(s) like price and/or brand of a product interact individually with the other factors of the product. For two-level choice experiments with n factors, we consider a model involving the main plus all two-factor interaction effects, with our interest lying in the estimation of the main effects and a specified set of two-factor interaction effects. The two-factor interaction effects of interest are either (i) one factor interacting with each of the remaining n − 1 factors or (ii) each of the two factors interacting with each of the remaining n − 2 factors. For the two models, we first characterize the information matrix and then construct universally optimal choice designs for choice set sizes 3 and 4.

## Keywords

Choice experiment choice set Hadamard matrix multinomial logit model universal optimality

62K05 05B15

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