Record Details

DSpace at IIT Bombay

View Archive Info
 

Metadata

 
Field Value
 
Title Characterization and Optimal Designs for Choice Experiments
 
Names CHAI, FENG-SHUN
DAS, ASHISH
MANNA, SOUMEN
Date Issued 2014-11-21 (iso8601)
Abstract Street and Burgess (2007) present a comprehensive exposition of designs for choice experiments till then. The choice design involves $n$ attributes (factors) with $i$-th attribute at $l_i$ level, and all choice sets are of size $m$. A choice design comprises $N$ such choice sets. Recently, Demirkale, Donovan and Street (2013) considered the setup of symmetric factorials ($l_i=l$) and obtained $D$-optimal choice designs under main effects model. They provide some sufficient conditions for a designs to be $D$-optimal. In this paper, we first derive a slightly modified Information matrix of a choice design for estimating the factorial effects of a $l_1 \times l_2 \times \cdots \times l_n$ choice experiment. It is seen that such a modification gives the Information matrix the desired additive property and thus, overcomes the existing shortcoming of situations where, with addition of a choice set the information content of the design decreases. While comparing designs with different $N$, we see that one needs to work with the modified information matrix. For a $2^n$ choice experiment, under the main effects model, we give a simple necessary and sufficient condition for the Information matrix to be diagonal. Furthermore, we characterize the structure of the choice sets which gives maximum $trace$ of the Information matrix. Our characterization of such an Information matrix facilitates construction of universally optimal designs with minimal number of choice sets and gives more flexibility for choosing $m$. Finally, we provide universally optimal choice designs for estimating main effects, which are optimal in the class of all designs with given $N$, $n$ and $m$.
Genre Technical Report
Topic Choice Sets
Identifier http://dspace.library.iitb.ac.in/jspui/handle/100/16233