Characterization and Optimal Designs for Choice Experiments
DSpace at IIT Bombay
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Title |
Characterization and Optimal Designs for Choice Experiments
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Creator |
CHAI, FENG-SHUN
DAS, ASHISH MANNA, SOUMEN |
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Subject |
choice sets
choice design factorial design main effects Hadamard matrix orthogonal array |
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Description |
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 $m$.
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Date |
2014-11-21T12:37:57Z
2014-11-21T12:37:57Z 2014-11-21 |
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Type |
Technical Report
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Identifier |
http://dspace.library.iitb.ac.in/jspui/handle/100/16233
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Language |
en
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