Standardized coefficients with multiple linear regression
Hi,
When performing multiple linear regression with continouous and categorical predictors, JASP says standardized coefficients can only be computed for continouous predictors. I was wondering why that is? Since other programs (like R) do allow computing this for categorical predictors as well.
Thanks!
Comments
the reason is they're not really meaningful with categorical predictors. A standardized coefficient is the effect of x on y when both x and y have been standardized, which means they each have had the mean subtracted from their values, and divided by their standard deviation. The problem is that for categorical variables, both the mean and the standard deviation don't make sense (after all they are parameters of a normal distribution).
say you have gender coded 0 1 (or -.5 +.5 or any two values), the standardized coefficient is computed as the regression with gender being recoded [gender - mean(gender)]/sd(gender), the mean is the proportion of gender 1 in the sample, the standard deviation is whatever (????), and you still get two separate values for each gender, but the regression coefficient becomes the difference between two genders that are one standard deviation apart on the gender scale (which is not an observed gender in the sample).
Anyway, I hope this makes sense. A standardized coefficient is interpreted as the change in y in standard deviation units when x increases by 1 standard deviation, but increasing a categorical variable by 1 standard deviation is meaningless, and lands on an impossible value for that variable.