DSpace Collection:http://dspace.library.iitb.ac.in/jspui/handle/100/138032015-10-04T03:26:31Z2015-10-04T03:26:31ZOptimal Paired Choice Block DesignsSingh, RakhiDas, AshishChai, Feng-Shunhttp://dspace.library.iitb.ac.in/jspui/handle/100/173522015-09-16T13:09:47Z2015-09-16T00:00:00ZTitle: Optimal Paired Choice Block Designs
Authors: Singh, Rakhi; Das, Ashish; Chai, Feng-Shun
Abstract: Choice experiments mirror real world situations closely and helps manufacturers, policy-makers and other researchers in taking business decisions on their product characteristics based on its perceived utility. In a paired choice experiment, several pairs of options are shown to respondents. The respondents are asked to give their preference among the two options for each of the choice pairs shown to them. In order to conduct an experiment, a choice design is customarily used to efficiently estimate the parameters of interest which essentially consists of either the main effects only or the main plus two-factor interaction effects of the attributes. Traditionally,
every respondent is shown the same collection of choice pairs under an
untenable assumption that the respondents are alike in every respect. Also, as the
attributes or the number of levels under each attribute increases, the number of
choice pairs in an optimal paired choice design increases rapidly. To address these
concerns, under the multinomial logit model or the linear paired comparison model, we first incorporate the respondent effects and then present optimal designs for the parameters of interest. We provide optimal paired choice designs for estimating the main effects for symmetric and asymmetric multi-level attributes with smaller number of choice pairs shown to each respondent. We also provide optimal paired choice designs for estimating the main effects only and the main plus two-factor interaction effects under the main plus two-factor interaction effects model.2015-09-16T00:00:00ZOn optimal two-level supersaturated designsSingh, RakhiDas, Ashishhttp://dspace.library.iitb.ac.in/jspui/handle/100/173492015-02-04T14:24:50Z2015-02-04T00:00:00ZTitle: On optimal two-level supersaturated designs
Authors: Singh, Rakhi; Das, Ashish
Abstract: A popular measure to assess two-level supersaturated designs is the $E(s^2)$ criteria. Recently, Jones and Majumdar (2014) introduced the $\mbox{{\it UE}}(s^2)$ criteria and obtained optimal designs under the criteria. Effect-sparsity principle states that only a very small proportion of the factors have effects that are large. These factors with large effects are called {\it active} factors. Therefore, the basis of using a supersaturated design is the inherent assumption that there are very few active factors which one has to identify. Though there are only a few active factors, it is not known a priori what these active factors are. The identification of the active factors, say $k$ in number, is based on model building regression diagnostics (e.g. forward selection method) wherein one has to desirably use a supersaturated design which on an average estimates the model parameters optimally during the sequential introduction of factors in the model building process. Accordingly, to overcome possible lacuna on existing criteria of measuring the goodness of a supersaturated design, we meaningfully define the $ave(s^2_k)$ and $ave(s^2)_\rho$ criteria, where $\rho$ is the maximum number of active factors. We obtain superior $\mbox{{\it UE}}(s^2)$-optimal designs in ${\cal D}_U(m,n)$ and compare them against $E(s^2)$-optimal designs under the more meaningful criteria of $ave(s^2_k)$ and $ave(s^2)_\rho$. It is seen that $E(s^2)$-optimal designs perform fairly well or better even against superior $\mbox{{\it UE}}(s^2)$-optimal designs with respect to $ave(s^2_k)$ and $ave_d(s^2)_\rho$ criteria.2015-02-04T00:00:00ZD- and MS-optimal 2-Level Choice Designs for $N\not\equiv 0$ (mod 4)Singh, RakhiChai, Feng-ShunDas, Ashishhttp://dspace.library.iitb.ac.in/jspui/handle/100/162342014-11-22T08:11:00Z2014-11-22T00:00:00ZTitle: D- and MS-optimal 2-Level Choice Designs for $N\not\equiv 0$ (mod 4)
Authors: Singh, Rakhi; Chai, Feng-Shun; Das, Ashish
Abstract: Street and Burgess (2007) present a comprehensive exposition of designs for choice experiments till then. Our focus is on choice experiments with two-level factors and a main effects model. We consider designs for choice experiment involving $k$ attributes (factors) and all choice sets are of size $m$. We derive a simple form of the Information matrix of a choice design for estimating the factorial effects. For $N$ being the number of choice sets in the design, we obtain $D$- and $MS$-optimal designs in the class of all designs with given $N$, $k$ and $m=2$. For given $N$ and $k$, we show that in many situations $D$-optimal designs for $m=2$ are superior than the optimal design for $m=3$ and $m=5$. Also, $MS$-optimal designs with $m=2$ are always better than the best designs under the same optimality criteria for any odd $m$. Furthermore, with respect to $trace$-optimality, there is no optimal design for $m>2$ which is better than the optimal design for $m=2$.2014-11-22T00:00:00ZCharacterization and Optimal Designs for Choice ExperimentsCHAI, FENG-SHUNDAS, ASHISHMANNA, SOUMENhttp://dspace.library.iitb.ac.in/jspui/handle/100/162332014-11-21T12:37:57Z2014-11-21T00:00:00ZTitle: Characterization and Optimal Designs for Choice Experiments
Authors: CHAI, FENG-SHUN; DAS, ASHISH; MANNA, SOUMEN
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 $m$.2014-11-21T00:00:00Z