kr-modcomp {pbkrtest} | R Documentation |
F-test 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 |
smallModel |
An |
betaH |
A number or a vector of the beta of the hypothesis, e.g. L
beta=L betaH. betaH=0 if |
details |
If larger than 0 some timing details are printed. |
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
\beta = L \beta_H
, where L
is a k \times p
matrix and
\beta
is a p
column vector the same length as
fixef(largeModel)
.
The \beta_H
is a p
column vector.
Notice: if you want to test a hypothesis L \beta = c
with a k
vector c
, a suitable \beta_H
is obtained via \beta_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.
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., 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
, lmer
, vcovAdj
,
PBmodcomp
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)