R: Ftest and degrees of freedom based on Kenward-Roger...
KenwardRoger
R Documentation
Ftest and degrees of freedom based on Kenward-Roger approximation
Description
An approximate F-test based on the Kenward-Roger
approach.
Usage
KRmodcomp(largeModel, smallModel, betaH=0, details=0)
## S3 method for class 'lmerMod'
KRmodcomp(largeModel, smallModel, betaH=0, details=0)
Arguments
largeModel
An lmer model
smallModel
An lmer model or a restriction matrix
betaH
A number or a vector of the beta of the hypothesis,
e.g. L beta=L betaH. betaH=0 if modelSmall is a model not a
restriction matrix.
details
If larger than 0 some timing details are printed.
...
Additional arguments to print function
Details
The model object must be fitted with restricted maximum
likelihood (i.e. with REML=TRUE). If the object is fitted with
maximum likelihood (i.e. with REML=FALSE) then the model is
refitted with REML=TRUE before the p-values are calculated. Put
differently, the user needs not worry about this issue.
An F test is calculated according to the approach of Kenward
and Roger (1997). The function works for linear mixed models fitted
with the lmer function of the lme4 package. Only models
where the covariance structure is a sum of known matrices can be
compared.
The largeModel may be a model fitted with lmer
either using REML=TRUE or REML=FALSE. The
smallModel can be a model fitted with lmer. It must have
the same covariance structure as largeModel. Furthermore, its
linear space of expectation must be a subspace of the space for
largeModel. The model smallModel can also be a
restriction matrix L specifying the hypothesis L β
= L β_H, where L is a k X p matrix and
β is a p column vector the same length as
fixef(largeModel).
The β_H is a p column vector.
Notice: if you want to test a hypothesis L β = c with a
k vector c, a suitable β_H is obtained via
β_H=L c where L_n is a g-inverse of L.
Notice: It cannot be guaranteed that the results agree with other
implementations of the Kenward-Roger approach!
Note
This functionality is not thoroughly tested and should be used with
care. Please do report bugs etc.
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
getKRlmervcovAdjPBmodcomp
Examples
(fmLarge <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy))
## removing Days
(fmSmall <- lmer(Reaction ~ 1 + (Days|Subject), sleepstudy))
anova(fmLarge,fmSmall)
KRmodcomp(fmLarge,fmSmall)
## The same test using a restriction matrix
L <- cbind(0,1)
KRmodcomp(fmLarge, L)
## Same example, but with independent intercept and slope effects:
m.large <- lmer(Reaction ~ Days + (1|Subject) + (0+Days|Subject), data = sleepstudy)
m.small <- lmer(Reaction ~ 1 + (1|Subject) + (0+Days|Subject), data = sleepstudy)
anova(m.large, m.small)
KRmodcomp(m.large, m.small)