On Optimal Designs for Nonlinear Models: A General and Efficient Algorithm

Yang, Min; Biedermann, Stefanie; Tang, Elina

doi:10.1080/01621459.2013.806268

Cited by 93 publications

(132 citation statements)

References 29 publications

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“…Other interesting aims are to extend the algorithm for several design variables and adjust it to multi-stage designs. The last point may be a difficult task since the multiplicative algorithm is only defined to one-stage designs (Yang [46]). …”

Section: Discussionmentioning

confidence: 99%

Combined algorithm to compute D-optimal designs

Martín

Gutiérrez

2015

Journal of Computational and Applied Mathematics

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a b s t r a c tAlgorithmic techniques for computing optimal designs continue being a need in the optimal experimental design field. The increasing interest in finding the optimal experimental conditions makes that new methods are demanded for more complex frameworks showing more realistic situations. Numerical techniques are often the unique viable option for computing these designs since to tackle analytically the problem results impracticable in most of cases. Wynn-Fedorov algorithm, multiplicative algorithm and their modifications are the more frequently used methods in the literature for computing D-optimal designs. However, they are not always suitable and efficient to compute optimal designs since their procedures are very limited by the computational requirements. A new algorithm to obtain D-optimal designs is proposed in this paper. It is based on combining suitable strategies followed by the traditional algorithms. A proof of the convergence is provided and several numerical examples are presented to illustrate its improved results.

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Section: Discussionmentioning

confidence: 99%

Combined algorithm to compute D-optimal designs

Martín

Gutiérrez

2015

Journal of Computational and Applied Mathematics

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“…Several early versions were developed, including [30] and [28], and more recent and faster versions exist, such as [40] and [38]. The convergence properties of the original algorithm are analyzed in [21].…”

Section: Lemmamentioning

confidence: 99%

Fast algorithms for the minimum volume estimator

Ahipaşaoğlu

2014

J Glob Optim

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The minimum volume ellipsoid (MVE) estimator is an important tool in robust regression and outlier detection in statistics. We develop fast and efficient algorithms for the MVE estimator problem and discuss how they can be implemented efficiently. The novelty of our approach stems from the recent developments in the first-order algorithms for solving the related minimum volume enclosing ellipsoid problem. Comparative computational results are provided which demonstrate the strength of the algorithms.

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“…In contrast to the exact design framework where it is computationally prohibitive to do an exhaustive search over all possible designs to find a design that is globally optimal, the continuous design framework has well-established mathematical theories and tools to leverage for the fast identification of a globally optimal continuous design. In particular, we discuss in §3 the use of the general equivalence theorem (Kiefer 1974) and our extension of the optimal weight exchange algorithm by Yang et al (2013) to achieve this goal.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the continuous design framework (see, for example, Silvey 1980, Pukelsheim 1993) and recent research on optimal designs in the statistics literature (Yang et al 2013), the proposed approach makes it computationally feasible to obtain heterogeneous designs with assured high design efficiency. We show through examples that compared to efficient heterogeneous choice designs obtained from the separate search approach recommended by Sándor and Wedel (2005), designs obtained through our proposed approach achieve efficiency gains from 12.5% to 16.6% (when measured by the D-error), and at the same time take only a fraction (12% to 20%) of the computation time.…”

Section: Introductionmentioning

confidence: 99%

Construction of Heterogeneous Conjoint Choice Designs: A New Approach

Liu

Tang

2015

Marketing Science

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E xtant research on choice designs in marketing focuses on the construction of efficient homogeneous designs where all respondents get the same design. Recently marketing scholars proposed the construction of efficient heterogeneous designs where different respondents or groups of respondents get different subdesigns, and demonstrated substantial efficiency gain when such heterogeneous designs are employed. A significant hurdle in the widespread adoption of heterogeneous designs is the high computation cost, even when the number of subdesigns contained in the heterogeneous design is restricted to be small. In this paper we propose a new approach for the construction of efficient heterogeneous choice designs. In contrast to extant approaches that are based on an exact design framework where it is computationally prohibitive to do an exhaustive search to find a globally optimal design, our proposed approach is based on the continuous design framework where well-established mathematical theories can be leveraged for quick identification of a globally optimal design. The proposed approach makes it feasible to generate a highly efficient choice design that is completely heterogeneous-a unique subdesign for each individual respondent in the choice experiment. The proposed approach is the first in the marketing literature to find a completely heterogeneous choice design with assured high global design efficiency using the continuous design framework. Results from simulation and empirical studies demonstrate superior performance of the proposed approach over extant approaches in constructing efficient heterogeneous choice designs.Data, as supplemental material, are available at http://dx.

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On Optimal Designs for Nonlinear Models: A General and Efficient Algorithm

Cited by 93 publications

References 29 publications

Combined algorithm to compute D-optimal designs

Combined algorithm to compute D-optimal designs

Fast algorithms for the minimum volume estimator

Construction of Heterogeneous Conjoint Choice Designs: A New Approach

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