glmmML: Generalized Linear Models with random intercept

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

Fits GLMs with random intercept by Maximum Likelihood and numerical integration via Gauss-Hermite quadrature.

Usage

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glmmML(formula, family = binomial, data, cluster, weights,
cluster.weights, subset, na.action, 
offset, prior = c("gaussian", "logistic", "cauchy"),
start.coef = NULL, start.sigma = NULL, fix.sigma = FALSE, x = FALSE, 
control = list(epsilon = 1e-08, maxit = 200, trace = FALSE),
method = c("Laplace", "ghq"), n.points = 8, 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. Defaults to one.

cluster.weights

Cluster weights. Defaults to one.

subset

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

na.action

See glm.

start.coef

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

start.sigma

starting value for the mixing standard deviation. Defaults to 0.5.

fix.sigma

Should sigma be fixed at start.sigma?

x

If TRUE, the design matrix is returned (as x).

offset

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

prior

Which "prior" distribution (for the random effects)? Possible choices are "gaussian" (default), "logistic", and "cauchy".

control

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

method

There are two choices "Laplace" (default) and "ghq" (Gauss-Hermite).

n.points

Number of points in the Gauss-Hermite quadrature. If n.points == 1, the Gauss-Hermite is the same as Laplace approximation. If method is set to "Laplace", this parameter is ignored.

boot

Do you want a bootstrap estimate of cluster effect? The default is No (boot = 0). If you want to say yes, enter a positive integer here. It should be equal to the number of bootstrap samples you want to draw. A recomended absolute minimum value is boot = 2000.

Details

The integrals in the log likelihood function are evaluated by the Laplace approximation (default) or Gauss-Hermite quadrature. The latter is now fully adaptive; however, only approximate estimates of variances are available for the Gauss-Hermite (n.points > 1) method.

For the binomial families, the response can be a two-column matrix, see the help page for glm for details.

Value

The return value is a list, an object of class 'glmmML'. The components are:

boot

No. of boot replicates

converged

Logical

coefficients

Estimated regression coefficients

coef.sd

Their standard errors

sigma

The estimated random effects' standard deviation

sigma.sd

Its standard error

variance

The estimated variance-covariance matrix. The last column/row corresponds to the standard deviation of the random effects (sigma)

aic

AIC

bootP

Bootstrap p value from testing the null hypothesis of no random effect (sigma = 0)

deviance

Deviance

mixed

Logical

df.residual

Degrees of freedom

cluster.null.deviance

Deviance from a glm with no clustering. Subtracting deviance gives a test statistic for the null hypothesis of no clustering. Its asymptotic distribution is a symmetric mixture a constant at zero and a chi-squared distribution with one df. The printed p-value is based on this.

cluster.null.df

Its degrees of freedom

posterior.modes

Estimated posterior modes of the random effects

terms

The terms object

info

From hessian inversion. Should be 0. If not, no variances could be estimated. You could try fixing sigma at the estimated value and rerun.

prior

Which prior was used?

call

The function call

x

The design matrix if asked for, otherwise not present

Note

The optimization may not converge with the default value of start.sigma. In that case, try different start values for sigma. If still no convergence, consider the possibility to fix the value of sigma at several values and study the profile likelihood.

Author(s)

Göran Broström

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

glmmboot, glm, optim, lmer in Matrixand glmmPQL in MASS.

Examples

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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)
glmmML(y ~ x, data = dat, cluster = id)


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