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.

## Arguments

- x
A model.

- ci
Scalar, the CI level. The default (

`NULL`

) returns no CI.- verbose
Toggle messages and warnings.

## 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()`

.