D-optimal design for a model with interaction between a qualitative and a quantitative factor in the presence of random block effects

What is it about?

Optimal experimental designs are developed for linear regression models with both qualitative and quantitative factors of influence. In particular, we generate a characterization of optimal designs for random blocked regression experiments where under few assumptions, this characterization allows to find the weights of the optimal design analytically by means of convex optimization. It is worth-while noting that the optimal weights depend on the ratio of the variance components. However, in this context, we show that in practical applications limiting optimal designs show a high efficiency when the variance ratio approaches zero or infinity.

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