kr-vcovAdj function

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

Kenward and Roger (1997) describe 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 class 'lmerMod'
vcovAdj(object, details = 0)

Arguments

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

Returns

• 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 effects

• 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.

Examples

fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
class(fm1)

## 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

## 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)

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., https://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

Author(s)

Ulrich Halekoh uhalekoh@health.sdu.dk , Søren Højsgaard sorenh@math.aau.dk