Kenward-Roger approximation for SEs, CIs and p-values
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)
model |
A statistical model. |
ci |
Confidence Interval (CI) level. Default to 0.95 (95%). |
dof |
Degrees of Freedom. |
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.
A data frame.
Kenward, M. G., & Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihood. Biometrics, 983-997.
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.
if (require("lme4", quietly = TRUE)) {
model <- lmer(Petal.Length ~ Sepal.Length + (1 | Species), data = iris)
p_value_kenward(model)
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