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.
get_sigma(x, ci = NULL, verbose = TRUE)The residual standard deviation (sigma), or NULL if this
information could not be accessed.
A model.
Scalar, the CI level. The default (NULL) returns no CI.
Toggle messages and warnings.
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.
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().
Gelman, A., Hill, J., & Vehtari, A. (2020). Regression and Other Stories. Cambridge University Press.
data(mtcars)
m <- lm(mpg ~ wt + cyl + vs, data = mtcars)
get_sigma(m)
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