Calculates the standardised regression coefficients for a linear model.
standardCoefs(x)A linear model object (i.e. class lm)
A matrix with the regressors as rows, and the two different regression coefficients (unstandardised and standardised) as the two columns. The columns are labeled b (unstandardised) and beta (standardised).
Calculates the standardised regression coefficients (beta-weights), namely the values of the regression coefficients that would have been observed has all regressors and the outcome variable been scaled to have mean 0 and variance 1 before fitting the regression model. Standardised coefficients are sometimes useful in some applied contexts since there is a sense in which all beta values are "on the same scale", though this is not entirely unproblematic.
# Example 1: simple linear regression
# data
X1 <- c(0.69, 0.77, 0.92, 1.72, 1.79, 2.37, 2.64, 2.69, 2.84, 3.41)
Y <- c(3.28, 4.23, 3.34, 3.73, 5.33, 6.02, 5.16, 6.49, 6.49, 6.05)
model1 <- lm( Y ~ X1 ) # run a simple linear regression
coefficients( model1 ) # extract the raw regression coefficients
#> (Intercept) X1
#> 2.717160 1.156674
standardCoefs( model1 ) # extract standardised coefficients
#> b beta
#> X1 1.156674 0.8674478
# Example 2: multiple linear regression
X2 <- c(0.19, 0.22, 0.95, 0.43, 0.51, 0.04, 0.12, 0.44, 0.38, 0.33)
model2 <- lm( Y ~ X1 + X2 ) # new model
standardCoefs( model2 ) # standardised coefficients
#> b beta
#> X1 1.1278652 0.84584304
#> X2 -0.4428046 -0.08903252
#Example 3: interaction terms
model3 <- lm( Y ~ X1 * X2 )
coefficients( model3 )
#> (Intercept) X1 X2 X1:X2
#> 3.4155302 0.7945328 -1.8409489 1.0332433
standardCoefs( model3 )
#> b beta
#> X1 0.7945328 0.5958602
#> X2 -1.8409489 -0.3701504
#> X1:X2 1.0332433 0.3562668
# Note that these beta values are equivalent to standardising all
# three regressors including the interaction term X1:X2, not merely
# standardising the two predictors X1 and X2.