`pbkrtest`

- at a glanceThe primary focus is on mixed effects models as implemented in the `lme4`

package. For those linear mixed models, the pbkrtest package implements

Kenward-Roger based F-tests

Parametric bootstrap based test

Satterthwaite based F-tests (! NEW !)

In addition, `pbkrtest`

also implments parametric bootstrap tests for generalized linear mixed models, for generalized linear models and for linear models.

If you publish work where pbkrtest, please do cite this paper (a latex entry is given below): *Halekoh, U., and Højsgaard, S. (2014) A Kenward-Roger Approximation and Parametric Bootstrap Methods for Tests in Linear Mixed Models - the R Package pbkrtest. J. Stat. Soft. Vol. 59, Issue 9.* pdf

Summer 2020: Satterthwaites method for computing denominator degrees of freedom has been implemented. Is in github version of package now - in experimental form.

Summer 2020: Kenward-Roger approximation for

`nlme`

and`gls`

models has been contributed. Is not in package yet.

2020: Inferens i mixed models i R - hinsides det sædvanlige likelihood ratio test. 42. Symposium i Anvendt Statistik, 27.-28. January, Aarhus, Denmark pdf

2018: Inference in mixed models in R - beyond the usual asymptotic likelihood ratio test. Nordstat conference, Tartu, Estonia, June 2018. pdf

Please see my talks page.

Calculation of the the adjusted degrees of freedom for the Kenward-Roger approximation can be computationally demanding because it requires inversion of an N ×N matrix where N is the number of observations. Possible remedies for this:

On linux (ubuntu), changing the BLAS to ATLAS-BLAS generally provides a speed-up with a factor 3-6 (compared with R’s default BLAS). That helps in some situations.

Parametric bootstrap is an alternative, and while also computationally intensive, parametric bootstrap can be parallelized (facilities exist in

`pbkrtest`

). href=“http://cran.r-project.org/web/packages/pbkrtest/index.html”>pbkrtest).Use Satterthwaites approximation instead. This method scales better higher dimensional problems.

Development versions of the package reside on github. To use the development version, PLEASE first install the package from `CRAN` to get dependencies right and then AFTERWARDS install the development version using:

`devtools::install_github("hojsgaard/pbkrtest")`

Q: Do these methods work for generalized linear mixed models ?

A: Parametric bootstrap is available for generalized linear mixed models. We are not aware of any developments for approximate F-tests in the spirit of Kenward-Roger / Satterthwaite for generalized linear models.

Q: Are these models implemented for mixed models fitted with the nlme package?

A: Yes and no. Code exists but needs to be integrated with the package.

When reporting unexpected behaviours, bugs etc. PLEASE supply:

A small reproducible example in terms of a short code fragment.

The data. The preferred way of sending the data “mydata” is to copy and paste the result from running

`dput(mydata)`.The result of running the

`sessionInfo()`function.

`citation("pbkrtest")`

```
To cite pbkrtest in publications use:
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, 59(9), 1-30.
URL http://www.jstatsoft.org/v59/i09/.
A BibTeX entry for LaTeX users is
@Article{,
title = {A Kenward-Roger Approximation and Parametric Bootstrap Methods for Tests in Linear Mixed Models -- The {R} Package {pbkrtest}},
author = {Ulrich Halekoh and S{\o}ren H{\o}jsgaard},
journal = {Journal of Statistical Software},
year = {2014},
volume = {59},
number = {9},
pages = {1--30},
url = {http://www.jstatsoft.org/v59/i09/},
}
```