D-optimal population designs in linear mixed effects models for multiple longitudinal data

Figures & data

Figure 1. The individual D-optimal design allocations of time points for the linear and quadratic mixed effects model (13(13) $\begin{array}{r}\{\begin{array}{l}{y}_1={\beta }_{10}+{\beta }_{11}t+b_{10}+e_1,\\ y_2={\beta }_{20}+{\beta }_{21}t+{\beta }_{22}{t}^2+b_{20}+b_{21}t+e_2.\end{array}\end{array}$(13) ) for different values of m and ${\gamma }_{12}$.

Figure 2. The individual optimal design allocations of time points for the linear and quadratic mixed effects model (13(13) $\begin{array}{r}\{\begin{array}{l}{y}_1={\beta }_{10}+{\beta }_{11}t+b_{10}+e_1,\\ y_2={\beta }_{20}+{\beta }_{21}t+{\beta }_{22}{t}^2+b_{20}+b_{21}t+e_2.\end{array}\end{array}$(13) ) for different values of m and ρ.

Figure 3. Relative efficiencies of ${\zeta }_m^{\ast }$ relative to ${\zeta }_{12}^{\ast }$ for the two-response linear mixed model (14(14) $\{\begin{array}{l}{y}_{ij1}={\beta }_{10}+{\beta }_{11}{t}_{ij}+b_{i10}+b_{i11}{t}_{ij}+e_{i1j},\\ y_{ij2}={\beta }_{20}+{\beta }_{21}{t}_{ij}+b_{i20}+b_{i21}{t}_{ij}+e_{i2j}.\end{array}$(14) ) with costs $c_1=100$ and $c_2\in \{0.01,0.1,1,2,5,20\}$.