Between-within approximation for SEs, CIs and p-valuesSource:
Approximation of degrees of freedom based on a "between-within" heuristic.
ci_betwithin(model, ci = 0.95, ...) dof_betwithin(model) p_value_betwithin(model, dof = NULL, ...)
A mixed model.
Confidence Interval (CI) level. Default to
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 (see Li and Redden 2015). The
Between-within denominator degrees of freedom approximation is
recommended in particular for (generalized) linear mixed models with repeated
measurements (longitudinal design).
dof_betwithin() implements a heuristic
based on the between-within approach. Note that this implementation
does not return exactly the same results as shown in Li and Redden 2015,
In particular for repeated measure designs (longitudinal data analysis),
the between-within heuristic is likely to be more accurate than simply
using the residual or infinite degrees of freedom, because
returns different degrees of freedom for within-cluster and between-cluster
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.
Li, P., Redden, D. T. (2015). Comparing denominator degrees of freedom approximations for the generalized linear mixed model in analyzing binary outcome in small sample cluster-randomized trials. BMC Medical Research Methodology, 15(1), 38. doi:10.1186/s12874-015-0026-x
dof_betwithin() is a small helper-function to calculate approximated
degrees of freedom of model parameters, based on the "between-within" heuristic.