This paper describes the core features of the R package geepack, which implements the generalized estimating equations (GEE) approach for fitting marginal generalized linear models to clustered data. Clustered data arise in many applications such as longitudinal data and repeated measures. The GEE approach focuses on models for the mean of the correlated observations within clusters without fully specifying the joint distribution of the observations. It has been widely used in statistical practice. This paper illustrates the application of the GEE approach with geepack through an example of clustered binary data.
When testing for reduction of the mean value structure in linear mixed models, it is common to use an asymptotic χ 2 test. Such tests can, however, be very poor for small and moderate sample sizes. The pbkrtest package implements two alternatives to such approximate χ 2 tests: The package implements (1) a Kenward-Roger approximation for performing F tests for reduction of the mean structure and (2) parametric bootstrap methods for achieving the same goal. The implementation is focused on linear mixed models with independent residual errors. In addition to describing the methods and aspects of their implementation, the paper also contains several examples and a comparison of the various methods.
We introduce new types of graphical Gaussian models by placing symmetry restrictions on the concentration or correlation matrix. The models can be represented by coloured graphs, where parameters that are associated with edges or vertices of the same colour are restricted to being identical. We study the properties of such models and derive the necessary algorithms for calculating maximum likelihood estimates. We identify conditions for restrictions on the concentration and correlation matrices being equivalent. This is for example the case when symmetries are generated by permutation of variable labels. For such models a particularly simple maximization of the likelihood function is available. Copyright (c) 2008 Royal Statistical Society.
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