KenwardRoger {pbkrtest} | R Documentation |
An approximate F-test based on the Kenward-Roger approach.
KRmodcomp(largeModel, smallModel, betaH=0, details=0) ## S3 method for class 'lmerMod' KRmodcomp(largeModel, smallModel, betaH=0, details=0)
largeModel |
An |
smallModel |
An |
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 |
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!
This functionality is not thoroughly tested and should be used with care. Please do report bugs etc.
Ulrich Halekoh ulrich.halekoh@agrsci.dk, Soren Hojsgaard sorenh@math.aau.dk
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.
(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)