Designs for generalized linear models with random block effects via information matrix approximations

Waite, Timothy W.; Woods, David C.

doi:10.1093/biomet/asv005

Cited by 19 publications

(25 citation statements)

References 27 publications

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“…Without loss of generality, we assume the first n blocks in the design corresponding to ζ 1 ,…, ζ n , with the remaining b − n blocks being replicates. We relax the assumption that bw i is the integer to find the so‐called approximate or continuous designs; see also the works of Cheng and Waite and Woods . Let Ξ denote the space of all possible designs of this form.…”

Section: Designs For Copula‐based Marginal Modelsmentioning

confidence: 99%

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Copula‐based robust optimal block designs

Rappold

Müller

Woods

2019

Appl Stoch Models Bus & Ind

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Blocking is often used to reduce known variability in designed experiments by collecting together homogeneous experimental units. A common modeling assumption for such experiments is that responses from units within a block are dependent. Accounting for such dependencies in both the design of the experiment and the modeling of the resulting data when the response is not normally distributed can be challenging, particularly in terms of the computation required to find an optimal design. The application of copulas and marginal modeling provides a computationally efficient approach for estimating population‐average treatment effects. Motivated by an experiment from materials testing, we develop and demonstrate designs with blocks of size two using copula models. Such designs are also important in applications ranging from microarray experiments to experiments on human eyes or limbs with naturally occurring blocks of size two. We present a methodology for design selection, make comparisons to existing approaches in the literature, and assess the robustness of the designs to modeling assumptions.

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Section: Designs For Copula‐based Marginal Modelsmentioning

confidence: 99%

“…We relax the assumption that bw i is the integer to find the so-called approximate or continuous designs; see also the works of Cheng 26 and Waite and Woods. 8 Let Ξ denote the space of all possible designs of this form. Denote the vector of responses from the ith block as…”

Section: Design Of Experiments For Copula Modelsmentioning

confidence: 99%

Copula‐based robust optimal block designs

Rappold

Müller

Woods

2019

Appl Stoch Models Bus & Ind

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“…Santner, Williams and Notz (2003, Ch.7)). A similar method was used by Waite and Woods (2015) to visualize the efficiency profile of Bayesian designs for logistic models with random effects.…”

Section: )mentioning

confidence: 99%

Singular prior distributions in Bayesian D-optimal design for nonlinear models

Waite¹

2018

STAT SINICA

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For Bayesian D-optimal design, we define a singular prior distribution for the model parameters as a prior distribution such that the determinant of the Fisher information matrix has a prior geometric mean of zero for all designs. For such a prior distribution, the Bayesian D-optimality criterion fails to select a design. For the exponential decay model, we characterize singularity of the prior distribution in terms of the expectations of a few elementary transformations of the parameter. For a compartmental model and several multi-parameter generalized linear models, we establish sufficient conditions for singularity of a prior distribution. For the generalized linear models we also obtain sufficient conditions for non-singularity.In the existing literature, weakly informative prior distributions are commonly recommended as a default choice for inference in logistic regression. Here it is shown that some of the recommended prior distributions are singular, and hence should not be used for Bayesian D-optimal design. Additionally, methods are developed to derive and assess Bayesian D-efficient designs when numerical evaluation of the objective function fails due to ill-conditioning, as often occurs for heavy-tailed prior distributions. These numerical methods are illustrated for logistic regression.

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“…Also based on generalized estimating equations inference, but more general in terms of the distribution of the responses, is the approach presented by Woods and van de Ven [4]. For likelihood estimation of general GLMM with random intercepts, FIM approximations have been presented and evaluated in detail by Waite and Woods using marginal quasi-likelihood (MQL), penalized quasi-likelihood (PQL) or new complete enumeration-based methods, as well as Monte Carlo (MC) approximations thereof [5,6].…”

Section: Introductionmentioning

confidence: 99%

A new method for evaluation of the Fisher information matrix for discrete mixed effect models using Monte Carlo sampling and adaptive Gaussian quadrature

Ueckert

2017

Computational Statistics & Data Analysis

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International audienceThe design of experiments for discrete mixed effect models is challenging due to the unavailability of a closed-form expression for the Fisher information matrix (FIM), on which most optimality criteria depend. Existing approaches for the computation of the FIM for those models are all based on approximations of the likelihood. A new method is presented which is based on derivatives of the exact conditional likelihood and which uses Monte Carlo (MC) simulations as well as adaptive Gaussian quadrature (AGQ) to integrate those derivatives over the data and random effects. The method is implemented in R and evaluated with respect to the influence of the tuning parameter, the accuracy of the FIM approximation, and computational complexity. The accuracy evaluation is performed by comparing the expected relative standard errors (RSE) from the MC/AGQ FIM with RSE obtained in a simulation study with four different discrete data models (two binary, one count and one repeated time-to-event model) and three different estimation algorithms. Additionally, the results from the MC/AGQ FIM are compared with expected RSE from a marginal quasi-likelihood (MQL) approximated FIM. The comparison resulted in close agreement between the MC/AGQ-based RSE and empirical RSE for all models investigated, and better performance of MC/AGQ than the MQL approximated FIM for variance parameters. The MC/AGQ method also proved to be well suited to calculate the expected power to detect a group effect for a model with binary outcomes

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Designs for generalized linear models with random block effects via information matrix approximations

Cited by 19 publications

References 27 publications

Copula‐based robust optimal block designs

Copula‐based robust optimal block designs

Singular prior distributions in Bayesian D-optimal design for nonlinear models

A new method for evaluation of the Fisher information matrix for discrete mixed effect models using Monte Carlo sampling and adaptive Gaussian quadrature

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