glmmML (version 0.65-2)

glmmML: 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, subset, na.action, 
offset, prior = c("gaussian", "logistic", "cauchy"),
start.coef = NULL, start.sigma = NULL, fix.sigma = FALSE, 
control = list(epsilon = 1e-08, maxit = 200, trace = FALSE),
method = c("Laplace", "ghq"), n.points = 1, 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.

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?

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.

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

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 log of the standard deviation of the random effects (log(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
• 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

encoding

UTF-8

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.

References

Broström (2003). Generalized linear models with random intercepts. http://www.stat.umu.se/forskning/reports/glmmML.pdf

See Also

glmmboot, glm, optim, glmm in Lindsey's repeated package, lmer in Matrixand glmmPQL in MASS.

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)