Using Gaussian mixtures with unknown number of
components for mixed model estimation
Laurence Watier, Sylvia Richardson & Peter J. Green
Hierarchical mixed models are used to account for
dependence between correlated data, in particular
dependence created by a group structure within the sample.
In such models, the correlation between observations
is modelled by including, in the regression model,
group-indexed parameters regarded as random variables,
so called random effects.
Gaussian distributions are commonly used for the random effects.
However, this choice places a strong constraint on the
shape of the random parameter distribution.
In this presentation, we focus on misspecification in
mixed model with random intercept, a commonly used model in epidemiology.
We propose to model the prior distribution of the
random intercept by gaussian mixtures with an
unknown number of components in a Bayesian framework.
This methodology has recently been developed by
Richardson and Green (1997) to analyse heterogeneous data.
Another use of gaussian mixtures with unknown number of
components is that of density estimation.
Some keywords:
Bayesian estimation;
Gaussian mixtures; Misspecification; Mixed models.
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