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Locally optimal designs for multivariate generalized linear models

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  • Idais, Osama

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.

Suggested Citation

  • Idais, Osama, 2020. "Locally optimal designs for multivariate generalized linear models," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:jmvana:v:180:y:2020:i:c:s0047259x2030244x
    DOI: 10.1016/j.jmva.2020.104663
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