Generalized Linear Models with fixed effects grouping

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Description

Fits grouped GLMs with fixed group effects. The significance of the grouping is tested by simulation, with a bootstrap approach.

Usage

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glmmboot(formula, family = binomial, data, cluster, weights, subset, na.action,
offset, start.coef = NULL,
control = list(epsilon = 1e-08, maxit = 200, trace = FALSE), boot = 0)

Arguments

formula

a symbolic description of the model to be fit. The details of model specification are given below.

family

Currently, the only valid values are binomial and poisson. The binomial family allows for the logit and cloglog links.

data

an optional data frame containing the variables in the model. By default the variables are taken from ‘environment(formula)’, typically the environment from which ‘glmmML’ is called.

cluster

Factor indicating which items are correlated.

weights

Case weights.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

na.action

See glm.

offset

this can be used to specify an a priori known component to be included in the linear predictor during fitting.

start.coef

starting values for the parameters in the linear predictor. Defaults to zero.

control

Controls the convergence criteria. See glm.control for details.

boot

number of bootstrap replicates. If equal to zero, no test of significance of the grouping factor is performed.

Details

The simulation is performed by simulating new response vectors from the fitted probabilities without clustering, and comparing the maximized log likelihoods. The maximizations are performed by profiling out the grouping factor. It is a very fast procedure, compared to glm, when the grouping factor has many levels.

Value

The return value is a list, an object of class 'glmmboot'.

coefficients

Estimated regression coefficients

logLik

the max log likelihood

cluster.null.deviance

Deviance without the clustering

frail

The estimated cluster effects

bootLog

The logLik values from the bootstrap samples

bootP

Bootstrap p value

variance

Variance covariance matrix

sd

Standard error of regression parameters

boot_rep

No. of bootstrap replicates

mixed

Logical

deviance

Deviance

df.residual

Its degrees of freedom

aic

AIC

boot

Logical

call

The function call

Note

There is no overall intercept for this model; each cluster has its own intercept. See frail

Author(s)

Göran Broström and Henrik Holmberg

References

Broström, G. and Holmberg, H. (2011). Generalized linear models with clustered data: Fixed and random effects models. Computational Statistics and Data Analysis 55:3123-3134.

See Also

link{glmmML}, optim, lmer in Matrix, and glmmPQL in MASS.

Examples

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## Not run:
id <- factor(rep(1:20, rep(5, 20)))
y <- rbinom(100, prob = rep(runif(20), rep(5, 20)), size = 1)
x <- rnorm(100)
dat <- data.frame(y = y, x = x, id = id)
res <- glmmboot(y ~ x, cluster = id, data = dat, boot = 5000)
## End(Not run)
##system.time(res.glm <- glm(y ~ x + id, family = binomial))