R: Ajusted covariance matrix for linear mixed models according...
vcovAdj
R Documentation
Ajusted covariance matrix for linear mixed models according to Kenward
and Roger
Description
Kenward and Roger (1997) describbe an improved small sample approximation to
the covariance matrix estimate of the fixed parameters in a linear mixed model.
the estimated covariance matrix, this has attributed P, a
list of matrices used in KR_adjust and the estimated matrix W
of the variances of the covariance parameters of the random effetcs
SigmaG
list: Sigma: the covariance matrix of Y; G: the G
matrices that sum up to Sigma; n.ggamma: the number (called M in the
article) of G matrices)
Note
If $N$ is the number of observations, then the vcovAdj()
function involves inversion of an $N x N$ matrix, so the
computations can be relatively slow.
Ulrich Halekoh, S<c3><b8>ren H<c3><b8>jsgaard (2014).,
A Kenward-Roger Approximation and Parametric Bootstrap Methods for
Tests in Linear Mixed Models - The R Package pbkrtest.,
Journal of Statistical Software, 58(10), 1-30., http://www.jstatsoft.org/v59/i09/
Kenward, M. G. and Roger, J. H. (1997), Small Sample Inference
for Fixed Effects from Restricted Maximum Likelihood, Biometrics
53: 983-997.
See Also
getKRKRmodcomplmerPBmodcompvcovAdj
Examples
fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
## Here the adjusted and unadjusted covariance matrices are identical,
## but that is not generally the case
v1 <- vcov(fm1)
v2 <- vcovAdj(fm1,detail=0)
v2 / v1
## For comparison, an alternative estimate of the variance-covariance
## matrix is based on parametric bootstrap (and this is easily
## parallelized):
## Not run:
nsim <- 100
sim <- simulate(fm.ml, nsim)
B <- lapply(sim, function(newy) try(fixef(refit(fm.ml, newresp=newy))))
B <- do.call(rbind, B)
v3 <- cov.wt(B)$cov
v2/v1
v3/v1
## End(Not run)