Wald.varComp: Wald-type tests for fixed effect parameters
In varComp: Variance Component Models

Description Usage Arguments Value Author(s) References See Also Examples

satterth.varComp computes the denominator degrees of freedom for testing fixed-effect parameters under the variance component model using the Satterthwaite-type method. KR.varComp computes the denominator degrees of freedom and tests fixed-effect parameters under the variance component model using the Kenward-Roger method. These functions are most conveniently used by fixef.varComp and anova.varComp.

1 2	satterth.varComp(object, Lmat, Vbet, svd.VLbet, X, K, V, ...) KR.varComp(object, Lmat, Vbet, svd.VLbet, X, K, V, ...)

`object`	An object of class `varComp`.
`Lmat`	A matrix specifying the linear combinations of fixed effect parameters to be tested for nullity. Each row is a linear combination.
`Vbet`	An optional matrix of variance-covariance matrix of fixed-effect parameter estimates.
`svd.VLbet`	An optional singular value decomposition of `Lmat` times `Vbet`.
`X`	Optional fixed-effect design matrix
`K`	Optional list of K matrices (the same as in `varComp.test`).
`V`	Optional covariance matrix of the response variable.
`...`	Place holder, not used.

A numeric scalar of denominator degree of freedom. For satterth.varComp, the 'individual.df' attribute will contain a vector of numerator degrees of freedom for each row of Lmat. For KR.varComp, the result will contain the following attributes:

numDF: The numerator degree of freedom, i.e., the rank of Lmat.
Scale: A positive numeric scalar, to be multiplied to raw F-statistics before calculating p-values.
F value: The scaled F-statistic, after adjusting for the variance estimate of fixed effect parameter estimates, and multiplied by the scaling factor.
Pr(>F): A numeric scalar of Kenward-Roger p-value.
vcov.beta: The adjusted variance-covariance estimate of fixed effect parameter estimates.

Long Qu

Michael G. Kenward and James H. Roger (1997) Small sample inference for fixed effects from restricted maximum likelihood. Biometrics 53, 983–997

Waseem S. Alnosaier (2007) Kenward-Roger Approximate F Test for Fixed Effects in Mixed Linear Models. Oregon State University Department of Statistics Ph.D. Thesis

Fai and Cornelius (1996) Approximate F-tests of multiple degree of freedom hypotheses in generalized least squares analyses of unbalanced split-plot experiments. Journal of Statistical Computation and Simulation 54, 363-378

fixef.varComp, anova.varComp

library(nlme)
data(Oxide)
lmef = lme(Thickness~Source, Oxide, ~1|Lot/Wafer)
anova(lmef)
vcf = varComp(Thickness~Source, Oxide, ~Lot/Wafer)
KR.varComp(vcf, matrix(c(0,1), 1))  # test Source effect
satterth.varComp(vcf, matrix(c(0,1), 1))  # d.f. for testing Source effect