glmmPQL: PQL Estimation of Generalized Linear Mixed Models
In BradleyTerry2: Bradley-Terry Models

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

Fits GLMMs with simple random effects structure via Breslow and Clayton's PQL algorithm. The GLMM is assumed to be of the form g(μ) = Xβ + Ze where g is the link function, μ is the vector of means and X, Z are design matrices for the fixed effects β and random effects e respectively. Furthermore the random effects are assumed to be i.i.d. N(0, σ²).

glmmPQL(
  fixed,
  random = NULL,
  family = "binomial",
  data = NULL,
  subset = NULL,
  weights = NULL,
  offset = NULL,
  na.action = NULL,
  start = NULL,
  etastart = NULL,
  mustart = NULL,
  control = glmmPQL.control(...),
  sigma = 0.1,
  sigma.fixed = FALSE,
  model = TRUE,
  x = FALSE,
  contrasts = NULL,
  ...
)

`fixed`	a formula for the fixed effects.
`random`	a design matrix for the random effects, with number of rows equal to the length of variables in `formula`.
`family`	a description of the error distribution and link function to be used in the model. This can be a character string naming a family function, a family function or the result of a call to a family function. (See `family()` for details of family functions.)
`data`	an optional data frame, list or environment (or object coercible by `as.data.frame()` to a data frame) containing the variables in the model. If not found in `data`, the variables are taken from `environment(formula)`, typically the environment from which `glmmPQL` called.
`subset`	an optional logical or numeric vector specifying a subset of observations to be used in the fitting process.
`weights`	an optional vector of ‘prior weights’ to be used in the fitting process.
`offset`	an optional numeric vector to be added to the linear predictor during fitting. One or more `offset` terms can be included in the formula instead or as well, and if more than one is specified their sum is used. See `model.offset()`.
`na.action`	a function which indicates what should happen when the data contain `NA`s. The default is set by the `na.action` setting of `options()`, and is `na.fail()` if that is unset.
`start`	starting values for the parameters in the linear predictor.
`etastart`	starting values for the linear predictor.
`mustart`	starting values for the vector of means.
`control`	a list of parameters for controlling the fitting process. See the `glmmPQL.control()` for details.
`sigma`	a starting value for the standard deviation of the random effects.
`sigma.fixed`	logical: whether or not the standard deviation of the random effects should be fixed at its starting value.
`model`	logical: whether or not the model frame should be returned.
`x`	logical: whether or not the design matrix for the fixed effects should be returned.
`contrasts`	an optional list. See the `contrasts.arg` argument of `model.matrix()`.
`...`	arguments to be passed to `glmmPQL.control()`.

An object of class "BTglmmPQL" which inherits from "glm" and "lm":

`coefficients`	a named vector of coefficients, with a `"random"` attribute giving the estimated random effects.
`residuals`	the working residuals from the final iteration of the IWLS loop.
`random`	the design matrix for the random effects.
`fitted.values`	the fitted mean values, obtained by transforming the linear predictors by the inverse of the link function.
`rank`	the numeric rank of the fitted linear model.
`family`	the `family` object used.
`linear.predictors`	the linear fit on link scale.
`deviance`	up to a constant, minus twice the maximized log-likelihood.
`aic`	a version of Akaike's An Information Criterion, minus twice the maximized log-likelihood plus twice the number of parameters, computed by the `aic` component of the family.
`null.deviance`	the deviance for the null model, comparable with `deviance`.
`iter`	the numer of iterations of the PQL algorithm.
`weights`	the working weights, that is the weights in the final iteration of the IWLS loop.
`prior.weights`	the weights initially supplied, a vector of `1`'s if none were.
`df.residual`	the residual degrees of freedom.
`df.null`	the residual degrees of freedom for the null model.
`y`	if requested (the default) the `y` vector used. (It is a vector even for a binomial model.)
`x`	if requested, the model matrix.
`model`	if requested (the default), the model frame.
`converged`	logical. Was the PQL algorithm judged to have converged?
`call`	the matched call.
`formula`	the formula supplied.
`terms`	the `terms` object used.
`data`	the `data` argument used.
`offset`	the offset vector used.
`control`	the value of the `control` argument used.
`contrasts`	(where relevant) the contrasts used.
`xlevels`	(where relevant) a record of the levels of the factors used in fitting.
`na.action`	(where relevant) information returned by `model.frame` on the special handling of `NA`s.
`sigma`	the estimated standard deviation of the random effects
`sigma.fixed`	logical: whether or not `sigma` was fixed
`varFix`	the variance-covariance matrix of the fixed effects
`varSigma`	the variance of `sigma`

Heather Turner

Breslow, N. E. and Clayton, D. G. (1993) Approximate inference in Generalized Linear Mixed Models. Journal of the American Statistical Association 88(421), 9–25.

Harville, D. A. (1977) Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association 72(358), 320–338.

predict.BTglmmPQL(),glmmPQL.control(),BTm()

###############################################
## Crowder seeds example from Breslow & Clayton
###############################################

summary(glmmPQL(cbind(r, n - r) ~ seed + extract,
        random = diag(nrow(seeds)),
        family = "binomial", data = seeds))

summary(glmmPQL(cbind(r, n - r) ~ seed*extract,
                random = diag(nrow(seeds)),
                family = "binomial", data = seeds))