R: Ajusted covariance matrix for linear mixed models according...

kr-vcov {pbkrtest} | 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.

### Usage

    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.

### 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.

### Author(s)

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

### 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)

    ## 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)

[Package pbkrtest version 0.4-7 Index]