An approximate F-test based on the Kenward-Roger (1997) approach.

```
ci_kenward(model, ci = 0.95)
dof_kenward(model)
p_value_kenward(model, dof = NULL)
se_kenward(model)
```

## Arguments

model |
A statistical model. |

ci |
Confidence Interval (CI) level. Default to `0.95` (`95%` ). |

dof |
Degrees of Freedom. |

## Value

A data frame.

## Details

Inferential statistics (like p-values, confidence intervals and
standard errors) may be biased in mixed models when the number of clusters
is small (even if the sample size of level-1 units is high). In such cases
it is recommended to approximate a more accurate number of degrees of freedom
for such inferential statistics. Unlike simpler approximation heuristics
like the "m-l-1" rule (`dof_ml1`

), the Kenward-Roger approximation is
also applicable in more complex multilevel designs, e.g. with cross-classified
clusters. However, the "m-l-1" heuristic also applies to generalized
mixed models, while approaches like Kenward-Roger or Satterthwaite are limited
to linear mixed models only.

## References

Kenward, M. G., & Roger, J. H. (1997). Small sample inference for
fixed effects from restricted maximum likelihood. Biometrics, 983-997.

## See also

`dof_kenward()`

and `se_kenward()`

are small helper-functions
to calculate approximated degrees of freedom and standard errors for model
parameters, based on the Kenward-Roger (1997) approach.

`dof_satterthwaite()`

and
`dof_ml1()`

approximate degrees
of freedom based on Satterthwaite's method or the "m-l-1" rule.

## Examples

```
# \donttest{
if (require("lme4", quietly = TRUE)) {
model <- lmer(Petal.Length ~ Sepal.Length + (1 | Species), data = iris)
p_value_kenward(model)
}
#> Parameter p
#> 1 (Intercept) 9.605137e-01
#> 2 Sepal.Length 8.598429e-29
# }
```