Locally optimal designs for multivariate generalized linear models

JOURNAL OF MULTIVARIATE ANALYSIS

卷:180

Article

Idais, Osama¹ 

[1] Otto von Guericke Univ, Inst Math Stochast, PF 4120, D-39016 Magdeburg, Germany

关键词: Correlation matrix;    Generalized linear model;    Locally optimal design;    Multivariate response;    Saturated design;   

DOI  :  10.1016/j.jmva.2020.104663

来源: Elsevier

【 摘 要 】

The multivariate generalized linear model is considered. Each univariate response follows a generalized linear model. In this situation, the linear predictors and the link functions are not necessarily the same. The quasi-Fisher information matrix is obtained by using the method of generalized estimating equations. Then locally optimal designs for multivariate generalized linear models are investigated under the D- and A-optimality criteria. It turns out that under certain assumptions the optimality problem can be reduced to the marginal models. More precisely, a locally optimal saturated design for the univariate generalized linear models remains optimal for the multivariate structure in the set of all saturated designs. Moreover, the general equivalence theorem provides a necessary and sufficient condition under which the saturated design is locally D-optimal in the set of all designs. The results are applied for multivariate models with gamma-distributed responses. Furthermore, we consider a multivariate model with univariate gamma models having seemingly unrelated linear predictors. Under this constraint, locally D- and A-optimal designs are found as product of all D- and A-optimal designs, respectively for the marginal counterparts. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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