The `pbkrtest`

package: Parametric Bootstrap, Kenward-Roger and Satterthwaite Based Methods for Tests in Mixed Models ================

`pbkrtest`

do for you?
Hypothesis test of fixed effects in mixed models (also called random effects models, hierarchical models etc) is most commonly based on large sample asymptotics: When the amount of information becomes large, a test can be based an a -approximation. In small sample cases, this approximation can be very unreliable. The `pbkrtest`

provides alternatives to this approximation. To be specific: For linear mixed models (as implemented in the `lme4`

package), `pbkrtest`

implements the following tests for fixed effects:

- a parametric bootstrap test,
- a Kenward-Roger-type F-test and
- a Satterthwaite-type F-test.

Moreover, for generalized linear mixed models (as implemented in `lme4`

) and for generalized linear models, `pbkrtest`

also implements a parametric bootstrap test

The facilities of the package are documented in the paper by [Halekoh and Højsgaard 2014)] (https://www.jstatsoft.org/htaccess.php?volume=059&type=i&issue=09&filename=paper) Please see `citation("pbkrtest")`

for information about citing the paper and the package. If you use the package in your work, please do cite this paper. Please notice: There are other packages that use `pbkrtest`

under the hood. If you use one of those packages, please do also cite our paper.

We also refer to the Webpage for the package

```
library(pbkrtest)
library(ggplot2)
## Sugar beets: Does suger content depend on harvest time?
beets |> ggplot(aes(x=sow, y=sugpct, group=harvest)) +
geom_jitter(aes(color=harvest), width=0)
```

```
fm0 <- lmer(sugpct ~ block + sow + harvest + (1|block:harvest), data=beets)
fm1 <- update(fm0, .~. -harvest)
## Is there an effect of harvest time?
an <- anova(fm0, fm1)
pb <- PBmodcomp(fm0, fm1)
kr <- KRmodcomp(fm0, fm1)
sa <- SATmodcomp(fm0, fm1)
tidy(an)
#> # A tibble: 2 × 9
#> term npar AIC BIC logLik deviance statistic df p.value
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 fm1 9 -69.1 -56.5 43.5 -87.1 NA NA NA
#> 2 fm0 10 -80.0 -66.0 50.0 -100. 12.9 1 0.000326
tidy(pb)
#> # A tibble: 2 × 4
#> type stat df p.value
#> <chr> <dbl> <dbl> <dbl>
#> 1 LRT 12.9 1 0.000326
#> 2 PBtest 12.9 NA 0.0300
tidy(kr)
#> # A tibble: 1 × 6
#> type stat ndf ddf F.scaling p.value
#> <chr> <dbl> <int> <dbl> <dbl> <dbl>
#> 1 Ftest 15.2 1 2.00 1 0.0599
tidy(sa)
#> # A tibble: 1 × 5
#> type statistic ndf ddf p.value
#> <chr> <dbl> <int> <dbl> <dbl>
#> 1 Ftest 15.2 1 2.00 0.0599
```

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