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.

## Details

### 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"