Attention is on mixed effects models (as implemented in the ‘lme4’ package). For linear mixed models, ‘pbkrtest’ implements (1) a parametric bootstrap test, (2) a Kenward-Roger-type F-test and (3) a Satterthwaite-type F-test. The parametric bootstrap test is also implemented for generalized linear mixed models (as implemented in ‘lme4’) and for generalized linear models. The facilities of the package are documented in the paper by Halehoh and Højsgaard, (2012, ).

Please see ‘citation(“pbkrtest”)’ for information about citing the paper and the package. If you use the package in your work, please do cite the 2012-paper. There are other packages that use ‘pbkrtest’ under the hood. If you use one of those packages, please do also cite our 2012 paper.

Documents:

  1. Halekoh and Højsgaard (2012) A Kenward-Roger Approximation and Parametric Bootstrap Methods for Tests in Linear Mixed Models The R Package pbkrtest
  2. Vignette: introduction to ‘pbkrtest’
  3. Webpage for the package

Installation

pbkrtest is available on CRAN and can be installed as usual:

install.packages('pbkrtest')

To build and install from Github with vignettes run this command from within R (please install remotes first if not already installed):

# install.packages('remotes')
remotes::install_github("hojsgaard/pbkrtest", build_vignettes = TRUE)

You can also install the package without vignettes if needed as follows:

remotes::install_github("hojsgaard/pbkrtest", build_vignettes = FALSE)

Online documentation

See https://hojsgaard.github.io/pbkrtest/.

Brief introduction

library(pbkrtest)
library(ggplot2)

ggplot(sleepstudy) + geom_line(aes(Days, Reaction, group=Subject, color=Subject))


fm0 <- lmer(Reaction ~ Days + (Days|Subject), data=sleepstudy)
fm1 <- update(fm0, .~. - Days)

p0 <- anova(fm0, fm1)
p1 <- PBmodcomp(fm0, fm1)
p2 <- KRmodcomp(fm0, fm1)
p3 <- SATmodcomp(fm0, fm1)

p0
#> Data: sleepstudy
#> Models:
#> fm1: Reaction ~ (Days | Subject)
#> fm0: Reaction ~ Days + (Days | Subject)
#>     npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)    
#> fm1    5 1785.5 1801.4 -887.74   1775.5                         
#> fm0    6 1763.9 1783.1 -875.97   1751.9 23.537  1  1.226e-06 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
p1
#> Bootstrap test; time: 8.58 sec; samples: 1000; extremes: 0;
#> Requested samples: 1000 Used samples: 994 Extremes: 0
#> large : Reaction ~ Days + (Days | Subject)
#> Reaction ~ (Days | Subject)
#>          stat df   p.value    
#> LRT    23.516  1 1.239e-06 ***
#> PBtest 23.516     0.001005 ** 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
p2
#> large : Reaction ~ Days + (Days | Subject)
#> small : Reaction ~ (Days | Subject)
#>         stat    ndf    ddf F.scaling   p.value    
#> Ftest 45.853  1.000 17.000         1 3.264e-06 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
p3
#> large : Reaction ~ Days + (Days | Subject)
#> small (restriction matrix) : 
#>     
#>  0 1
#>      statistic    ndf ddf   p.value    
#> [1,]    45.853  1.000  17 3.264e-06 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

tidy(p0)
#> Warning in tidy.anova(p0): The following column names in ANOVA output were not
#> recognized or transformed: npar
#> # A tibble: 2 x 9
#>   term   npar   AIC   BIC logLik deviance statistic    df     p.value
#>   <chr> <dbl> <dbl> <dbl>  <dbl>    <dbl>     <dbl> <dbl>       <dbl>
#> 1 fm1       5 1785. 1801.  -888.    1775.      NA      NA NA         
#> 2 fm0       6 1764. 1783.  -876.    1752.      23.5     1  0.00000123
tidy(p1)
#> # A tibble: 2 x 4
#>   type    stat    df    p.value
#>   <chr>  <dbl> <dbl>      <dbl>
#> 1 LRT     23.5     1 0.00000124
#> 2 PBtest  23.5    NA 0.00101
tidy(p2)
#> # A tibble: 2 x 6
#>   type    stat   ndf   ddf F.scaling    p.value
#>   <chr>  <dbl> <int> <dbl>     <dbl>      <dbl>
#> 1 Ftest   45.9     1   17.         1 0.00000326
#> 2 FtestU  45.9     1   17.        NA 0.00000326
tidy(p3)
#> # A tibble: 1 x 5
#>   type  statistic   ndf   ddf    p.value
#>   <chr>     <dbl> <int> <dbl>      <dbl>
#> 1 Ftest      45.9     1  17.0 0.00000326

Please find more examples in the other vignettes available at https://hojsgaard.github.io/pbkrtest/.