Locally optimal designs for multivariate generalized linear models

Osama Idais

Journal of Multivariate Analysis, 2020, vol. 180, issue C

Abstract: 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.

Keywords: Correlation matrix; Generalized linear model; Locally optimal design; Multivariate response; Saturated design (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.jmva.2020.104663

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