Approximation of degrees of freedom based on a "m-l-1" heuristic as suggested by Elff et al. (2019).
dof_ml1(model)p_value_ml1(model, dof = NULL)
se_ml1(model)
A mixed model.
Degrees of Freedom.
The p-values.
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 statitics. The m-l-1 heuristic is such an approach
that uses a t-distribution with fewer degrees of freedom (dof_ml1) to
calculate p-values (p_value_ml1), standard errors (se_ml1)
and confidence intervals (ci(method = "ml1")).
Note that the "m-l-1" heuristic is not applicable for complex
multilevel designs, e.g. with cross-classified clusters. In such cases,
more accurate approaches like the Kenward-Roger approximation (dof_kenward())
is recommended. 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.
Elff, M.; Heisig, J.P.; Schaeffer, M.; Shikano, S. (2019): Multilevel Analysis with Few Clusters: Improving Likelihood-based Methods to Provide Unbiased Estimates and Accurate Inference, British Journal of Political Science.
dof_ml1() and se_ml1() are small helper-functions
to calculate approximated degrees of freedom and standard errors of model
parameters, based on the "m-l-1" heuristic.
# NOT RUN {
library(lme4)
model <- lmer(Petal.Length ~ Sepal.Length + (1 | Species), data = iris)
p_value_ml1(model)
# }
# NOT RUN {
# }
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