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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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    1. Silvio S. Zocchi & Anthony C. Atkinson, 1999. "Optimum Experimental Designs for Multinomial Logistic Models," Biometrics, The International Biometric Society, vol. 55(2), pages 437-444, June.
    2. Holger Dette & Laura Hoyden & Sonja Kuhnt & Kirsten Schorning, 2017. "Optimal designs for thermal spraying," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 53-72, January.
    3. Imhof, Lorens, 2000. "Optimum Designs for a Multiresponse Regression Model," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 120-131, January.
    4. Krafft, Olaf & Schaefer, Martin, 1992. "D-Optimal designs for a multivariate regression model," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 130-140, July.
    5. Soumaya, Moudar & Gaffke, Norbert & Schwabe, Rainer, 2015. "Optimal design for multivariate observations in seemingly unrelated linear models," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 48-56.
    6. Yue, Rong-Xian & Liu, Xin & Chatterjee, Kashinath, 2014. "D-optimal designs for multiresponse linear models with a qualitative factor," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 57-69.
    7. Valerii V. Fedorov & Robert C. Gagnon & Sergei L. Leonov, 2002. "Design of experiments with unknown parameters in variance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 18(3), pages 207-218, July.
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