kr-modcomp: F-test and degrees of freedom based on Kenward-Roger...

In pbkrtest: Parametric Bootstrap, Kenward-Roger and Satterthwaite Based Methods for Test in Mixed Models

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 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 smallModel is a model object and not a restriction matrix.
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 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.

Author(s)

Ulrich Halekoh [e-mail], Søren Højsgaard [e-mail]

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)

pbkrtest documentation built on Jan. 22, 2023, 1:52 a.m.