lsr (version 0.1.1)

standardCoefs: Standardised regression coefficients

Description

Calculates the standardised regression coefficients for a linear model.

Usage

standardCoefs(x)

Arguments

x

A linear model object (i.e. class lm).

Value

• 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).

Warning

This function is under development - I haven't tested it completely yet, and I would like to extend it to include confidence intervals for the beta weights.

Details

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 often useful in some applied contexts since there is some sense in which all beta values are "on the same scale", though this is not entirely unproblematic.

Examples

### 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 )  # pull out the raw regression coefficients
#
# (Intercept)          X1 
#    2.717160    1.156674
#

standardCoefs( model1 ) # extract standardised coefficients
#
#           b      beta
# X1 1.156674 0.8674478
# 

# For regression models with a single predictor, the standardised 
# coefficient is identical to the Pearson correlation.  
cor(X1,Y)  
# [1] 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  1.1266313  0.84491763
# X2 -0.4481639 -0.09025427
#

### 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.