lme4 (version 1.1-36)

vcov.merMod: Covariance matrix of estimated parameters

Description

Compute the variance-covariance matrix of estimated paramers. Optionally also computes correlations, or the full (joint) covariance matrix of the fixed-effect coefficients and the conditional modes of the random effects.

Usage

# S3 method for merMod
vcov(object, correlation = TRUE, sigm = sigma(object),
    use.hessian = NULL, full = FALSE, ...)

Value

a covariance matrix (sparse when full=TRUE)

Arguments

object

an R object of class merMod, i.e., as resulting from lmer(), or glmer(), etc.

correlation

(logical) indicates whether the correlation matrix as well as the variance-covariance matrix is desired

sigm

the residual standard error; by default sigma(object).

use.hessian

(logical) indicates whether to use the finite-difference Hessian of the deviance function to compute standard errors of the fixed effects. See Details.

full

return the 'full' covariance matrix, i.e. the joint covariance matrix of the conditional distribution of conditional modes (as in getME(., "b")) and fixed-effect parameters. (correlation and use.hessian are ignored in this case.)

Note that this option may be slow for models with large numbers of random-effect levels!

...

extra arguments for method compatibility (ignored)

Details

When use.hessian = FALSE, the code estimates the covariance matrix based on internal information about the inverse of the model matrix (see getME(.,"RX")). This is exact for linear mixed models, but approximate for GLMMs. The default is to use the Hessian whenever the fixed effect parameters are arguments to the deviance function (i.e. for GLMMs with nAGQ>0), and to use getME(.,"RX") whenever the fixed effect parameters are profiled out (i.e. for GLMMs with nAGQ==0 or LMMs).

use.hessian=FALSE is backward-compatible with older versions of lme4, but may give less accurate SE estimates when the estimates of the fixed-effect (see getME(.,"beta")) and random-effect (see getME(.,"theta")) parameters are correlated.

However, use.hessian=TRUE is not always more accurate: for some numerically unstable fits, the approximation using RX is actually more reliable (because the Hessian has to be computed by a finite difference approximation, which is also error-prone): see e.g. https://github.com/lme4/lme4/issues/720

Examples

fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
gm1 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
             data = cbpp, family = binomial)
(v1 <- vcov(fm1))
v2 <- vcov(fm1, correlation = TRUE)
# extract the hidden 'correlation' entry in @factors
as(v2, "corMatrix")
v3 <- vcov(gm1)
v3X <- vcov(gm1, use.hessian  = FALSE)
all.equal(v3, v3X)
## full correlatiom matrix
cv <- vcov(fm1, full = TRUE)
image(cv, xlab = "", ylab = "",
      scales = list(y = list(labels = rownames(cv)),
                    at = seq(nrow(cv)),
                    x = list(labels = NULL)))