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

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 factors or (ii) each of the two factors interacting with each of the remaining 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

AMS SUBJECT CLASSIFICATION:

• 62K05
• 05B15

Acknowledgments

The authors are thankful to the two referees and an associate editor for their suggestions, which greatly improved the presentation of the article.

Funding

Ashish Das’s work is partially supported by the Science and Engineering Research Board, India.

Additional information

Funding

Ashish Das’s work is partially supported by the Science and Engineering Research Board, India.