Optimum Experimental Designs for Multinomial Logistic Models

Zocchi, Silvio Sandoval; Atkinson, Anthony C.

doi:10.1111/j.0006-341x.1999.00437.x

Cited by 43 publications

(27 citation statements)

References 34 publications

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“…Inequality (21) implies that lim t→∞ Φ p Σ ξ 0 +ξ S (t) (g) = −∞, which contradicts the fact that Φ p Σ ξ 0 +ξ S (t) (g) is a nonnegative function. Similar arguments can be applied to the case when K ≤ δ, in which we let α = 1.…”

Section: Appendixmentioning

confidence: 95%

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

Yang

Biedermann

Tang

2013

Journal of the American Statistical Association

121

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Deriving optimal designs for nonlinear models is challenging in general. Although some recent results allow us to focus on a simple subclass of designs for most problems, deriving a specific optimal design mainly depends on algorithmic approaches. There is need of a general and efficient algorithm which is more broadly applicable than the current state of the art methods. We present a new algorithm that can be used to find optimal designs with respect to a broad class of optimality criteria, when the model parameters or functions thereof are of interest, and for both locally optimal and multistage design strategies. We prove convergence to the desired optimal design, and show that the new algorithm outperforms the best available algorithm in various examples.

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Section: Appendixmentioning

confidence: 95%

“…Optimal designs for model (10) depend on the values of the unknown parameters (Zocchi and Atkinson, 1999). We assume that θ 1 = (1, 1, −1, 2) and θ 2 = (−1, 2, 1, −1), and let the design space X = {(6i/s, 6j/s, 6k/s), i, j, l = 0, 1, .…”

Section: Examplementioning

confidence: 99%

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

Yang

Biedermann

Tang

2013

Journal of the American Statistical Association

121

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“…Chaloner and Larntz (1989) considered determination of optimal design for experiments using logistic regression. Zocchi and Atkinson (1999) considered design for multinomial logistic models. Dey, Ghosh, and Mallick (2000) edited a collection of articles that provided Bayesian analyses for GLMs.…”

Section: Binary Regressionmentioning

confidence: 99%

Bayesian inference for categorical data analysis

Agresti

Hitchcock

2005

JISS

132

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This article surveys Bayesian methods for categorical data analysis, with primary emphasis on contingency table analysis. Early innovations were proposed by Good (1953Good ( , 1956Good ( , 1965 for smoothing proportions in contingency tables and by Lindley (1964) for inference about odds ratios. These approaches primarily used conjugate beta and Dirichlet priors. Altham (1969Altham ( , 1971 presented Bayesian analogs of small-sample frequentist tests for 2×2 tables using such priors. An alternative approach using normal priors for logits received considerable attention in the 1970s by Leonard and others (e.g., Leonard 1972). Adopted usually in a hierarchical form, the logit-normal approach allows greater flexibility and scope for generalization. The 1970s also saw considerable interest in loglinear modeling. The advent of modern computational methods since the mid-1980s has led to a growing literature on fully Bayesian analyses with models for categorical data, with main emphasis on generalized linear models such as logistic regression for binary and multi-category response variables.

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“…For multinomial data, the response may be modelled using a multivariate GLM [35], with potentially different linear predictors used to describe the probability of success in each category, together with an identifiability constraint. The design problem is then a natural generalisation of that given in Section 2, using a suitably defined information matrix [36] which will depend on the parameters from each linear predictor.…”

Section: Discussionmentioning

confidence: 99%

Robust designs for binary data: applications of simulated annealing

Woods

2010

Journal of Statistical Computation and Simulation

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When the aim of an experiment is the estimation of a Generalised Linear Model (GLM), standard designs from linear model theory may prove inadequate. This paper describes a flexible approach for finding designs for experiments to estimate GLMs through the use of D-optimality and a simulated annealing algorithm. A variety of uncertainties in the model can be incorporated into the design search, including the form of the linear predictor, through use of a robust design selection criterion and a postulated model space. New methods appropriate for screening experiments and the incorporation of correlations between possible model parameters are described through examples. An updating formula for Doptimality under a GLM is presented which improves the computational efficiency of the search.Robust designs for binary data: applications of simulated annealingSouthampton Statistical Sciences Research Institute, University of Southampton, Southampton, UK AbstractWhen the aim of an experiment is the estimation of a Generalised Linear Model (GLM), standard designs from linear model theory may prove inadequate. This paper describes a flexible approach for finding designs for experiments to estimate GLMs through the use of D-optimality and a simulated annealing algorithm. A variety of uncertainties in the model can be incorporated into the design search, including the form of the linear predictor, through use of a robust design selection criterion and a postulated model space. New methods appropriate for screening experiments and the incorporation of correlations between possible model parameters are described through examples. An updating formula for D-optimality under a GLM is presented which improves the computational efficiency of the search.

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Optimum Experimental Designs for Multinomial Logistic Models

Cited by 43 publications

References 34 publications

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

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

Bayesian inference for categorical data analysis

Robust designs for binary data: applications of simulated annealing

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