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Estimate or extract residual or model-based degrees of freedom from regression models.

Usage

get_df(x, ...)

# S3 method for default
get_df(x, type = "residual", verbose = TRUE, ...)

Arguments

x

A statistical model.

...

Currently not used.

type

Can be "residual", "wald", "normal", or "model". "analytical" is an alias for "residual".

• "residual" (aka "analytical") returns the residual degrees of freedom, which usually is what stats::df.residual() returns. If a model object has no method to extract residual degrees of freedom, these are calculated as n-p, i.e. the number of observations minus the number of estimated parameters. If residual degrees of freedom cannot be extracted by either approach, returns Inf.

• "wald" returns residual (aka analytical) degrees of freedom for models with t-statistic, 1 for models with Chi-squared statistic, and Inf for all other models. Also returns Inf if residual degrees of freedom cannot be extracted.

• "normal" always returns Inf.

• "model" returns model-based degrees of freedom, i.e. the number of (estimated) parameters.

• For mixed models, can also be "ml1" (approximation of degrees of freedom based on a "m-l-1" heuristic as suggested by Elff et al. 2019) or "betwithin", and for models of class merMod, type can also be "satterthwaite" or "kenward-roger". See 'Details'.

Usually, when degrees of freedom are required to calculate p-values or confidence intervals, type = "wald" is likely to be the best choice in most cases.

verbose

Toggle warnings.

Details

Degrees of freedom for mixed models

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).

m-l-1 degrees of freedom

The m-l-1 heuristic is an approach that uses a t-distribution with fewer degrees of freedom. In particular for repeated measure designs (longitudinal data analysis), the m-l-1 heuristic is likely to be more accurate than simply using the residual or infinite degrees of freedom, because get_df(type = "ml1") returns different degrees of freedom for within-cluster and between-cluster effects. Note that the "m-l-1" heuristic is not applicable (or at least less accurate) for complex multilevel designs, e.g. with cross-classified clusters. In such cases, more accurate approaches like the Kenward-Roger approximation 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.

Between-within degrees of freedom

The Between-within denominator degrees of freedom approximation is, similar to the "m-l-1" heuristic, recommended in particular for (generalized) linear mixed models with repeated measurements (longitudinal design). get_df(type = "betwithin") implements a heuristic based on the between-within approach, i.e. this type returns different degrees of freedom for within-cluster and between-cluster effects. Note that this implementation does not return exactly the same results as shown in Li and Redden 2015, but similar.

Satterthwaite and Kenward-Rogers degrees of freedom

Unlike simpler approximation heuristics like the "m-l-1" rule (type = "ml1"), the Satterthwaite or Kenward-Rogers approximation is also applicable in more complex multilevel designs. However, the "m-l-1" or "between-within" heuristics also apply 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.

• Satterthwaite FE (1946) An approximate distribution of estimates of variance components. Biometrics Bulletin 2 (6):110–4.

• 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

Examples

model <- lm(Sepal.Length ~ Petal.Length * Species, data = iris)
get_df(model) # same as df.residual(model)
#> [1] 144
get_df(model, type = "model") # same as attr(logLik(model), "df")
#> [1] 7