Package `glmmAK`

This package implements several generalized linear (mixed) models (GLMM) where for random effects either a conventional normal distribution is assumed or a flexible model based on penalized smoothing is used for the random effect distribution. We call the second class of models as penalized Gaussian mixture (PGM) or shortly G-spline.

Models with random effects are estimated in a Bayesian way using the MCMC. The package implements also some models without random effects and these can be estimated also using maximum-likelihood. Additional information can be found in the references mentioned below and at personal webpage of Arnošt Komárek.

This overview provides a sorted list of the functions of the package and links to few more involved examples.

1. Generalized linear models (GLM)

Two functions of the package implements few instances of the GLM and their equivalents can be found also in other (standard) R packages, namely

cumlogit
fits
- a logit model for binomial response (see also glm from package stats);
- a cumulative logit model for multinomial response under the assumption of the proportional odds (see also polr from package MASS) and also without assuming proportionality of the odds.
logpoisson
fits a log-linear model for Poisson response (see also glm from package stats).

2. Generalized linear mixed models (GLMM)

The core functions related to the GLMM's with normally distributed random effects and with random effects which distribution is specified in a flexible way using the penalized Gaussian mixture (PGM) or shortly G-spline. Methodology has been described in

KOMÁREK, A. and LESAFFRE, E. (2008).
Generalized linear mixed model with a penalized Gaussian mixture as a random-effects distribution.
Computational Statistics and Data Analysis, 52(7), 3441-3458.

Main functions from the package related to this methodology

cumlogitRE
implements MCMC sampling for the random effects logit model for binary response and the cumulative logit model for multinomial response.
cumlogitRE.predict
implements computation of the posterior predictive category probabilities in models fitted using cumlogitRE.
logpoissonRE
implements MCMC sampling for the random effects log linear model for Poisson response.
logpoissonRE.predict
implements computation of the posterior predictive counts in models fitted using logpoissonRE.
summaryGspline1
provides computation of the pointwise posterior summaries (mean, quantiles) of a univariate penalized Gaussian mixture fitted as a random effect distribution using cumlogitRE or logpoissonRE. In other words, this function provides an estimate of the random effect distribution in PGM GLMM's with univariate random effects (e.g., models with random intercept).
summaryGspline2
provides computation of the pointwise posterior summaries (mean, quantiles) of a bivariate penalized Gaussian mixture fitted as a random effect distribution using cumlogitRE or logpoissonRE. In other words, this function provides an estimate of the random effect distribution in PGM GLMM's with bivariate random effects (e.g., models with random intercept and slope).

Secondary functions from the package related to this methodology

Examples

ex-Toenail.pdf - example 1 using the data set toenail. Among others, it shows in more detail use of functions cumlogitRE, summaryGspline1.
ex-Toenail.R - code for the example 1
ex-Epileptic.pdf - example 2 using the data set epilepticBC Among others, it shows in more detail use of functions logpoissonRE, summaryGspline2.
ex-Epileptic.R - code for the example 2

3. Posterior computation

There are few functions in the package for general posterior computation which either supplement the coda package or slightly modify its functions:

4. Miscellaneous

The package also contains some functions which are either simple utilities or are related to some of my secondary interests and were written mainly for testing purposes.

5. Datasets

Finally, there are some datasets, mostly taken from the literature, available in the package:

Package glmmAK