Highly Efficient Designs to Handle the Incorrect Specification of Linear Mixed Models

We apply a maximin criterion to examine the relative-efficiency (RE) of several Dq-optimal designs for a family of linear-mixed models. Incorrect specifications of the polynomial degree, size of the autocorrelation parameter, number of random parameters, and the correlation between random intercept and random slope are investigated. We found that the maximin Dq-optimal design encountered is highly efficient; the effect of the autocorrelation parameter on the RE's of Dq-optimal designs is the largest for first-degree polynomials; and the RE of the equidistant design is lower than that of the maximin-value. Note: The following files were submitted by the author for peer review, but cannot be converted to PDF. You must view these files (e.g. movies) online. Summary. We apply a maximin criterion to examine the relative efficiency of several D q-optimal designs for a family of linear mixed models. Incorrect specifications of the order of the polynomial, size of the autocorrelation parameter , number of random parameters, and the correlation between random intercept and random slope are investigated. The results of our study allow us to draw the following conclusions: 1) the maximin D q-optimal design encountered appears to be highly efficient;2) the variation of the minimum relative efficiencies of D q-optimal designs of the family of linear mixed models that were studied, decreases as the order of the polynomial increases; 3) the effect of the autocorrelation parameter on the relative efficiencies of D q-optimal designs is the largest for first-degree polynomials; and 4) the relative efficiency of the equidistant design is lower than that of the maximin value and also lower than the reference value 0.85.