22
Figure 2.2: Illustration of the distribution of the latent variable vil in the model
described in (2.2)-(2.4) when the covariate takes values —1 and 1. Here we consider:
J = I type of toxicity, no patient-specific random effect ri, G = 2 components in the
mixture of normals and three, K = 2, possible ordinal outcomes. In both mixtures,
the darkly shaded, lightly shaded and white areas correspond to the probabilities πι⅛
of the ordinal outcome taking the values 0, 1 and 2, respectively.
On the other, large values of G may overparameterize the model leading to poorly
mixing Markov chains. Alternatively, using reversible jump MCMC (Green, 1995),
G could be included in the parameter vector and estimated as part of the inference.
But since the parameters of interest are the cell probabilities πj⅛, and inference on
mixture-specific parameters is not of interest we prefer the approach with fixed large
values of G. Formally implied inference on the parameters of the mixture model,
including μjg and pjg, should not be interpreted. Problems related to label switching
(arbitrary permutation of the terms in the mixture) and node duplication (replicating