Optimality regions for designs in multiple linear regression models with correlated random coefficients

Ulrike Graßhoff; Heinz Holling; Frank Röttger; Rainer Schwabe

doi:10.1016/j.jspi.2020.04.004

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arXiv · 1911.05538

Optimality regions for designs in multiple linear regression models with correlated random coefficients

Ulrike Graßhoff·Heinz Holling·Frank Röttger·Rainer Schwabe

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Abstract

This paper studies optimal designs for linear regression models with correlated effects for single responses. We introduce the concept of rhombic design to reduce the computational complexity and find a semi-algebraic description for the D-optimality of a rhombic design via the Kiefer-Wolfowitz equivalence theorem. Subsequently, we show that the structure of an optimal rhombic design depends directly on the correlation structure of the random coefficients.

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Ulrike Graßhoff, Heinz Holling, Frank Röttger, Rainer Schwabe. 2019-11-13. Optimality regions for designs in multiple linear regression models with correlated random coefficients. https://doi.org/10.1016/j.jspi.2020.04.004

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