pbkrtest (version 0.4-6)

KenwardRoger: 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)
"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 $L \beta = L \beta_H$, where $L$ is a $k X p$ 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!

References

Ulrich Halekoh, Sren Hjsgaard (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

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)