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.

## 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()`

.