Optimal design for linear regression models in the presence of heteroscedasticity caused by random coefficients

Optimal Designs for the Prediction of Individual Parameters in Hierarchical Models

“…If additionally the dispersion matrix remains invariant under the transformation, then optimal designs can be obtained from the class of invariant designs. This holds for the problem of estimating the population parameters β (see Graßhoff et al (2012)) and similarly for the present problem of prediction of the individual parameters β i or the individual responses μ i . For this we may consider only transformations which are compatible with the regression function: consider a one-to-one transformation g : X → X 1 of the experimental region X onto its image X 1 = g.X /.…”

“…This holds for the problem of estimating the population parameters β (see Graßhoff et al . ()) and similarly for the present problem of prediction of the individual parameters or the individual responses .…”

Optimal Time Plan in Accelerated Degradation Testing

“…Denote by σ 2 ptq " f 2 ptq T Σ γ f 2 ptq `σ2 ε ą 0 the variance function for measurements at time t, VarpY i q " σ 2 pt i q. Also here an identifiability condition has to be imposed on the variance parameters ς to distinguish between the variance σ 2 ε of the measurement error and the variance σ 2 1 of the random intercept, see [4]. The information matrix M β for the location parameter β can be written as…”

“…[1] considered the problem of constructing D-optimal designs for linear and nonlinear random effect models with applications in population pharmacokinetics. [4] presented D-optimal designs for random coefficient regression models in the basis of geometrical arguments when only one observation is available per unit, i.e. a situation which occurs in destructive testing.…”

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

“…A natural question that arises is to find optimal experimental designs for these models with respect to some optimality criterion. Graßhoff et al determined D-optimal designs that maximize the determinant of the corresponding information matrix, for a couple of different covariance structures in [6] and [5]. They found that in contrast to fixed effects models for multiple linear regression optimal settings may, surprisingly, occur in the interior of the design region under certain conditions on the covariance structure of the random coefficients.…”