Re-fit a model with standardized data

Performs a standardization of data (z-scoring) using standardize() and then re-fits the model to the standardized data.

Standardization is done by completely refitting the model on the standardized data. Hence, this approach is equal to standardizing the variables before fitting the model and will return a new model object. This method is particularly recommended for complex models that include interactions or transformations (e.g., polynomial or spline terms). The robust (default to FALSE) argument enables a robust standardization of data, based on the median and the MAD instead of the mean and the SD.

Usage

# Default S3 method
standardize(
  x,
  robust = FALSE,
  two_sd = FALSE,
  weights = TRUE,
  verbose = TRUE,
  include_response = TRUE,
  ...
)

Arguments

x

A statistical model.

robust

Logical, if TRUE, centering is done by subtracting the median from the variables and dividing it by the median absolute deviation (MAD). If FALSE, variables are standardized by subtracting the mean and dividing it by the standard deviation (SD).

two_sd

If TRUE, the variables are scaled by two times the deviation (SD or MAD depending on robust). This method can be useful to obtain model coefficients of continuous parameters comparable to coefficients related to binary predictors, when applied to the predictors (not the outcome) (Gelman, 2008).

weights

If TRUE (default), a weighted-standardization is carried out.

verbose

Toggle warnings and messages on or off.

include_response

If TRUE (default), the response value will also be standardized. If FALSE, only the predictors will be standardized.

Note that for GLMs and models with non-linear link functions, the response value will not be standardized, to make re-fitting the model work.
If the model contains an stats::offset(), the offset variable(s) will be standardized only if the response is standardized. If two_sd = TRUE, offsets are standardized by one-sd (similar to the response).
(For mediate models, the include_response refers to the outcome in the y model; m model's response will always be standardized when possible).

...

Arguments passed to or from other methods.

Value

A statistical model fitted on standardized data

Generalized Linear Models

Standardization for generalized linear models (GLM, GLMM, etc) is done only with respect to the predictors (while the outcome remains as-is, unstandardized) - maintaining the interpretability of the coefficients (e.g., in a binomial model: the exponent of the standardized parameter is the OR of a change of 1 SD in the predictor, etc.)

Dealing with Factors

standardize(model) or standardize_parameters(model, method = "refit") do not standardize categorical predictors (i.e. factors) / their dummy-variables, which may be a different behaviour compared to other R packages (such as lm.beta) or other software packages (like SPSS). To mimic such behaviours, either use standardize_parameters(model, method = "basic") to obtain post-hoc standardized parameters, or standardize the data with standardize(data, force = TRUE) before fitting the model.

Transformed Variables

When the model's formula contains transformations (e.g. y ~ exp(X)) the transformation effectively takes place after standardization (e.g., exp(scale(X))). Since some transformations are undefined for none positive values, such as log() and sqrt(), the relevel variables are shifted (post standardization) by Z - min(Z) + 1 or Z - min(Z) (respectively).

Examples

model <- lm(Infant.Mortality ~ Education * Fertility, data = swiss)
coef(standardize(model))
#>         (Intercept)           Education           Fertility Education:Fertility 
#>          0.06386069          0.47482848          0.63270919          0.09829777