Get residual standard deviation from models

Returns sigma, which corresponds the estimated standard deviation of the residuals. This function extends the sigma() base R generic for models that don't have implemented it. It also computes the confidence interval (CI), which is stored as an attribute.

Sigma is a key-component of regression models, and part of the so-called auxiliary parameters that are estimated. Indeed, linear models for instance assume that the residuals comes from a normal distribution with mean 0 and standard deviation sigma. See the details section below for more information about its interpretation and calculation.

Usage

get_sigma(x, ci = NULL, verbose = TRUE)

Arguments

x: A model.
ci: Scalar, the CI level. The default (NULL) returns no CI.
verbose: Toggle messages and warnings.

Value

The residual standard deviation (sigma), or NULL if this information could not be accessed.

Interpretation of Sigma

The residual standard deviation, σ, indicates that the predicted outcome will be within +/- σ units of the linear predictor for approximately 68% of the data points (Gelman, Hill & Vehtari 2020, p.84). In other words, the residual standard deviation indicates the accuracy for a model to predict scores, thus it can be thought of as "a measure of the average distance each observation falls from its prediction from the model" (Gelman, Hill & Vehtari 2020, p.168). σ can be considered as a measure of the unexplained variation in the data, or of the precision of inferences about regression coefficients.

Calculation of Sigma

By default, get_sigma() tries to extract sigma by calling stats::sigma(). If the model-object has no sigma() method, the next step is calculating sigma as square-root of the model-deviance divided by the residual degrees of freedom. Finally, if even this approach fails, and x is a mixed model, the residual standard deviation is accessed using the square-root from get_variance_residual().

References

Gelman, A., Hill, J., & Vehtari, A. (2020). Regression and Other Stories. Cambridge University Press.

Examples

data(mtcars)
m <- lm(mpg ~ wt + cyl + vs, data = mtcars)
get_sigma(m)
#> [1] 2.608133
#> attr(,"class")
#> [1] "insight_aux" "numeric"