Rescale standardized coefficients back to their original range after model fitting

Predictor variables are often standardized to be included in statistical models and allow comparison of the effect sizes for different predictors. This functions scales the fitted models coefficients back to the original scale of the predictors, to allow ecological interpretation.

Usage

rescale_coefficients(...)

# S3 method for class 'coxph'
rescale_coefficients(model, data, ...)

# S3 method for class 'lm'
rescale_coefficients(model, data, ...)

# S3 method for class 'glm'
rescale_coefficients(model, data, ...)

# S3 method for class 'bag'
rescale_coefficients(bag, data, tostd = TRUE, ...)

Arguments

model

[lm,glm,coxph]
Fitted model object created by a fitting function such as lm(), glm(), or coxph().

data

[data.frame]
The original data used to fit the model, in unstandardized form.

bag

[bag,list]
A bag of models, as returned by bag_models().

tostd

[logical(1)=TRUE]
Only relevant for the bag method. If TRUE (default), raw model coefficients (fitted on standardized predictors) are converted to standardized scale by multiplying by predictor SDs. If FALSE, coefficients are converted back to the original (unstandardized) scale by dividing by predictor SDs.

Value

A matrix or vector of rescaled coefficients. For lm, glm, and coxph methods, coefficients are returned in the original (unstandardized) scale. For the bag method, direction depends on tostd: standardized scale if TRUE, original scale if FALSE.

Examples

library(dplyr)

# standardize predictors
iris_std <- iris |>
  dplyr::mutate(across(2:4, ~ scale(.x)))
# fit model
m1 <- lm(Sepal.Length ~ Petal.Length + Species, data = iris_std)
summary(m1)
#> 
#> Call:
#> lm(formula = Sepal.Length ~ Petal.Length + Species, data = iris_std)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -0.75310 -0.23142 -0.00081  0.23085  1.03100 
#> 
#> Coefficients:
#>                   Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)         7.0829     0.1562  45.333  < 2e-16 ***
#> Petal.Length        1.5968     0.1144  13.962  < 2e-16 ***
#> Speciesversicolor  -1.6010     0.1935  -8.275 7.37e-14 ***
#> Speciesvirginica   -2.1177     0.2735  -7.744 1.48e-12 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.338 on 146 degrees of freedom
#> Multiple R-squared:  0.8367,	Adjusted R-squared:  0.8334 
#> F-statistic: 249.4 on 3 and 146 DF,  p-value: < 2.2e-16
#> 

# rescale coefficients
(resc_cf <- rescale_coefficients(m1, iris))
#>       (Intercept)      Petal.Length Speciesversicolor  Speciesvirginica 
#>         7.0828803         0.9045646        -1.6009717        -2.1176692 

# compare with model with no standardization of predictors
coef(lm(Sepal.Length ~ Petal.Length + Species, data = iris))
#>       (Intercept)      Petal.Length Speciesversicolor  Speciesvirginica 
#>         3.6835266         0.9045646        -1.6009717        -2.1176692