R: Generalized Linear Models with random intercept

glmmML {glmmML}

R Documentation

Generalized Linear Models with random intercept

Description

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

Usage

glmmML(formula, family = binomial, data, cluster, weights,
cluster.weights, subset, na.action, 
offset, contrasts = NULL, 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.
`contrasts`	an optional list. See the 'contrasts.arg' of 'model.matrix.default'.
`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)

G\"oran Brostr\"om

References

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

Examples

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)

[Package glmmML version 1.1.6 Index]