Random Coefficient Regression Model Of Optimal Design

This paper is concerned with the optimal design for the three variables random coefficientregression models and second-order bivariate random coefficient regression models,and the robustdesign for random coefficient regression models.We are dedicated to optimal design on the unit cube design region under the three variablesrandom coefficient regression models. The result is that optimal designs can be confined at ex-treme settings of the unit cube, analytical solutions of optimal designs are obtained by matlab.The conclusion could be extended on general cube regions.Based on the central composite design, some optimal designs under the criteria of orthog-onality,rotatability, D and A for second-order bivariate random coefficient regression modelscan be obtained. It’s clear that the random effect does no business with the orthogonal design, andthe rotatable design often not exist except for the intercept coefficient is random; Also,under thecriteria of D and A,the optimal design can be got only if the value of γ is infinite.We tentatively study the robust design for random coefficient regression models. Assumethat the true model is a second-order random coefficient regression model,we fit it with a first-order random coefficient regression model. Under the predicted mean-squared error criterion, theconclusion is reached that the optimal design in some particular situations in which both varianceand bias occur is very nearly the same as would be obtained if variance were ignored completelyand the experiment design so as to minimize bias alone.