Optimal Paired Choice Block Designs

Abstract

Choice experiments help manufacturers, service-providers, policy-makers and other researchers in taking business decisions. Traditionally, while using designs for discrete choice experiments, every respondent is shown the same collection of choice pairs (that is, the choice design). Also, as the attributes and/or the number of levels under each attribute increases, the number of choice pairs in an optimal paired choice design increases rapidly. Moreover, in the literature under the utility-neutral setup, random subsets of the theoretically obtained optimal designs are often allocated to respondents. The question therefore is whether one can do better than a random allocation of subsets. To address these concerns, in the linear paired comparison model (or, equivalently the multinomial logit model), we first incorporate the fixed respondent effects (also referred to as the block effects) and then obtain optimal designs for the parameters of interest. Our approach is simple and theoretically tractable, unlike other approaches which are algorithmic in nature. We present several constructions of optimal block designs for estimating main effects or main plus two-factor interaction effects. Our results show when and how an optimal design for the model without blocks can be Statistica Sinica: Newly accepted Paper (accepted version subject to English editing) Optimal Paired Choice Block Designs 2 split into blocks so as to retain the optimality properties under the block model.

Optimal Paired Comparison Block Designs

“…It is worth noting that for attributes 3 ≤ K ≤ 12 each at two-levels Singh et al (2015) provided constructions of optimal paired choice block designs, which can be obtained from Theorem 3.3 and Corollary 3.3 as exhibited in Table 2 of Singh et al (2015) using the method of orthogonal array (OA) of strength two and generators (G), and having N ≡ 0 (mod 4) pairs. In their OA+G construction method when the number of blocks b = 1 the block size is given by m = N ≡ 0 (mod 4) and for b = 2 or 4 the block size can be either m ≡ 2 (mod 4) or m ≡ 0 (mod 4).…”

“…Within such classes of designs several results are known (Jacroux et al, 1983;Cheng, 1978;Mukerjee et al, 2002;SahaRay and Dutta, 2018, amongst others). Our designs are compared to that of Singh et al (2015) in Table 6 under the main effects block model.…”

“…, K each at two-levels (v k = 2). As already mentioned, here the experimental situation involve N pairs which can be generally partitioned into b blocks of size m. Here we allocate N = bm pairs among b respondents in such a way that each respondent observes m pairs (e.g., see Singh et al, 2015). Let Ξ N be the class of all such available paired comparion block designs.…”

Optimal Approximate Choice Designs for a Two-step Coffee Choice, Taste and Choice Again Experiment

“…More recently, Singh et al (2019) built optimal choice designs under the MNL model with blocks of equal size, where each block was supplied to a respondent; the authors developed their approach under the utility-neutral assumption (i.e., by assuming that the unknown parameter values in the MNL Fisher Information Matrix (FIM) are all equal to 0). Singh et al (2019) introduced an additional parameter for the block effect in the MNL model to account for a particular type of respondents' heterogeneity. Großmann (2020) extended the approach of Singh et al (2019) by considering a MNL model with main effects only, and all attributes at two levels.…”

“…Singh et al (2019) introduced an additional parameter for the block effect in the MNL model to account for a particular type of respondents' heterogeneity. Großmann (2020) extended the approach of Singh et al (2019) by considering a MNL model with main effects only, and all attributes at two levels. The author also investigated the respondents' heterogeneity as defined by Singh et al (2019), illustrating how it is substantially different with respect to its usual meaning in the choice experiment literature (Sándor & Wedel, 2002), since it relates to how the respondents' choices are affected by the order in which the alternatives are presented.…”