Ajusted covariance matrix for linear mixed models according to Kenward and Roger

Kenward and Roger (1997) describbe an improved small sample approximation to the covariance matrix estimate of the fixed parameters in a linear mixed model.

vcovAdj(object, details = 0)

# S3 method for lmerMod
vcovAdj(object, details = 0)

# S3 method for mer
vcovAdj(object, details = 0)

Arguments

object	An lmer model
details	If larger than 0 some timing details are printed.

Value

phiA

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.

References

Ulrich Halekoh, Søren Højsgaard (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

getKR, KRmodcomp, lmer, PBmodcomp, vcovAdj

Examples

fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
class(fm1)
#> [1] "lmerMod"
#> attr(,"package")
#> [1] "lme4"

## Here the adjusted and unadjusted covariance matrices are identical,
## but that is not generally the case:

v1 <- vcov(fm1)
v2 <- vcovAdj(fm1, details=0)
v2 / v1
#> 2 x 2 Matrix of class "dgeMatrix"
#>             (Intercept) Days
#> (Intercept)           1    1
#> Days                  1    1

## For comparison, an alternative estimate of the variance-covariance
## matrix is based on parametric bootstrap (and this is easily
## parallelized): 

if (FALSE) {
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
}