Satterthwaite approximation for SEs, CIs and p-values

An approximate F-test based on the Satterthwaite (1946) approach.

Usage

ci_satterthwaite(model, ci = 0.95, ...)

dof_satterthwaite(model)

p_value_satterthwaite(model, dof = NULL, ...)

se_satterthwaite(model)

Arguments

model

A statistical model.

ci

Confidence Interval (CI) level. Default to 0.95 (95%).

...

Additional arguments passed down to the underlying functions. E.g., arguments like vcov or vcov_args can be used to compute confidence intervals using a specific variance-covariance matrix for the standard errors.

dof

Degrees of Freedom.

Value

A data frame.

Details

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. Unlike simpler approximation heuristics like the "m-l-1" rule (dof_ml1), the Satterthwaite approximation is also applicable in more complex multilevel designs. 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.

References

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

See also

dof_satterthwaite() and se_satterthwaite() are small helper-functions to calculate approximated degrees of freedom and standard errors for model parameters, based on the Satterthwaite (1946) approach.

dof_kenward() and dof_ml1() approximate degrees of freedom based on Kenward-Roger's method or the "m-l-1" rule.

Examples

# \donttest{
if (require("lme4", quietly = TRUE)) {
  model <- lmer(Petal.Length ~ Sepal.Length + (1 | Species), data = iris)
  p_value_satterthwaite(model)
}
#>      Parameter            p
#> 1  (Intercept) 9.605145e-01
#> 2 Sepal.Length 7.882014e-29
# }