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Discriminant analysis using a MLMM with a normal mixture 159
Figure 2. Dutch PBC Study. Estimates of selected pairwise densities from the joint distribution of the
random effects in the model in Group1 for K=1 (left panel) abd K=2 (right panel). The upper panel shows
the estimated distribution of (b i,3 , b i,4 )’(random intercept and time effect in the model for albumin), the
lower panel shows the estimated distribution of (b i,3 , b i,6 )’(random intercept in the model for albumin
and the random time effect in the model for log(alkaline phosphatase)).
used π0 =0.8, π1 =0.2 which approximately correspond to the relative sizes of the
prognostic groups in the training data set. All three prediction approaches described
in Section ’Discrimination procedure’ have been used for models with K =1and
K = 2 mixture components. The random effects prediction with K =2showedthe
best results, as will be illustrated.
The evolution of the cross-validated values of P1,i(τ), i.e. probabilities at time τ
that the subject i encounters serious disease progression by T = 10 years obtained
from the random effects prediction is shown in Figure 3. Note that for a perfect