Direct construction of globally D‐optimal designs for factors at two levels and main effects models

Abstract

In developing screening experiments for two‐level factors, practitioners typically are familiar with regular fractional factorial designs, which are orthogonal, globally D‐optimal (ie, 100% D‐efficient), and exist if N is a power of two. In addition, nonregular D‐optimal orthogonal designs can be generated for almost any N a multiple of four, the most notable being the family of Plackett and Burman1 designs. If resource constraints dictate that N is not a multiple of four, while an orthogonal design for two‐level factors does not exist, one can still consider a D‐optimal design. Exchange algorithms are available in commercial computer software for creating highly D‐efficient designs. However, as the number of factors increases, computer searches eventually fail to find the globally optimal design for any N or require impractical search times. In this article, we compile state‐of‐the‐art direct construction methods from the literature for producing globally D‐optimal designs for virtually any number of two‐level factors as well as any N greater than the number of factors. We summarize the known methods as well as areas for continued research, with the intention of catalyzing research in extending these construction methods.

Discrete choice experiments: An overview on constructing D-optimal and near-optimal choice sets

“…Others argue that there is a need to construct designs with for practical applications. In paper [17] the authors pointed out that “the whole field of optimal design theory is predicated on the belief that experimental designs should tailor to the needs of the practitioner and not the other way around”, which means practitioners should not be forced to fall into the case. Another potential criticism from researchers may be that it is easy to generate the required choice sets, with , as there is software that is able to do so using sophisticated search algorithms, such as SAS macros and Ngene.…”

“…We have chosen the MNL model because it is the most commonly used model to analyze choice data [15] , [16] , allowing for an arbitrary choice set size and the only model used to evaluate the optimality of combinatorially generated designs; (ii) All interactions are negligible because our interest is only for the main effects; (iii) While there are multiple criteria for assessing optimal designs, for example, D -optimal, A -optimal, or E -optimal designs, the focus will be under the D -optimality criterion using the SB approach. D -optimality criterion is commonly used in practice and in literature due to its robustness against reparameterizations [17] and can be readily updated in cases where choice sets are added or removed from a DCE, which frequently occurs in algorithmic constructions [18] ; (iv) All attributes are generic, i.e., partworth utilities are constant across all alternatives, and the choice sets are to be presented to respondents one at a time and they must choose one of the alternatives in each choice set. This approach in the literature is called Generic Forced-Choice Experiments [18] ; (v) The attribute levels are not ordered in any way that would lead to the possibility of dominated alternatives, since orthogonal designs do not account for dominant alternatives.…”

Experimental Design in Polymer Chemistry—A Guide towards True Optimization of a RAFT Polymerization Using Design of Experiments (DoE)

“…Obviously, a system other than a thermally initiated RAFT polymerization will require different factors, new setting of factor levels, and perhaps even utilization of a better suited design geometry than an FC-CCD. Here, the so-called computer-generated optimal designs have especially received attention due to their great flexibility and often optimal compromise of prediction accuracy and experimental effort [ 49 , 50 , 51 ].…”

Construction of symmetric paired choice experiments: minimising runs and maximising efficiency

“…; Goethals and Seidel (1967) extended the work of Williamson (1944) in the construction of a Hadamard matrix of order 4r using cyclic (or "circular") convolution. Details on how to construct the Goethals-Seidel construction for Hadamard matrices can be found in King et al (2020).…”

“…The formulations of the weighing design matrices included in this article are original contributions from King et al (2020).…”