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)

se_betwithin(model)

## Arguments

model A mixed model. Confidence Interval (CI) level. Default to 0.95 (95%). Degrees of Freedom.

A data frame.

## Details

### Small Sample Cluster corrected 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, but similar.

### Degrees of Freedom for Longitudinal Designs (Repeated Measures)

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 dof_betwithin() returns different degrees of freedom for within-cluster and between-cluster effects.

## References

• 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

## See also

dof_betwithin() and se_betwithin() are small helper-functions to calculate approximated degrees of freedom and standard errors of model parameters, based on the "between-within" heuristic.

## Examples

# \donttest{
if (require("lme4")) {
data(sleepstudy)
model <- lmer(Reaction ~ Days + (1 + Days | Subject), data = sleepstudy)
dof_betwithin(model)
p_value_betwithin(model)
}
#>     Parameter            p
#> 1 (Intercept) 9.306054e-80
#> 2        Days 6.290140e-06
# }