Description Usage Arguments Details Note Author(s) References See Also Examples

An approximate F-test based on the Kenward-Roger approach.

1 2 3 4 5 6 7 |

`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 [email protected], S<c3><b8>ren H<c3><b8>jsgaard [email protected]

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.

`getKR`

, `lmer`

, `vcovAdj`

,
`PBmodcomp`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
(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)
``` |

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