get_df: Extract degrees of freedom

In easystats/insight: Easy Access to Model Information for Various Model Objects

Extract degrees of freedom

Description

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

Usage

get_df(x, ...)

## Default S3 method:
get_df(x, type = "residual", verbose = TRUE, ...)

Arguments

x	A statistical model.
...	Currently not used.
type	Type of approximation for the degrees of freedom. Can be one of the following: "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" (or "m-l-1", approximation of degrees of freedom based on a "m-l-1" heuristic as suggested by Elff et al. 2019) or "between-within" (or "betwithin"). For mixed models of class merMod, type can also be "satterthwaite" or "kenward-roger" (or "kenward"). 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)
get_df(model, type = "model") # same as attr(logLik(model), "df")

easystats/insight documentation built on Dec. 14, 2024, 12:34 p.m.