R help - Mar 2002 - Standardized Beta?

Greetings all!

Got another question for you:

When doing regression, is there a way of automatically obtaining the 
standardized correlation coefficients?

/Fredrik
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On 03/04/02 15:04, Fredrik Karlsson wrote:
>Greetings all!
>
>Got another question for you:
>
>When doing regression, is there a way of automatically obtaining the 
>standardized correlation coefficients?
>
>/Fredrik
Use scale() on all the variables, e.g.

lm(scale(y) ~ scale(x1) + scale(x2))

or else I standardize the variables first (using scale()).

Probably this is wrong, but it seems like the natural way to do
it, so, if it is wrong, it would be useful to know how to do it
correctly.

Jon Baron
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At 03:04 PM 3/4/2002 +0100, Fredrik Karlsson wrote:
>When doing regression, is there a way of automatically obtaining the
>standardized correlation coefficients?
Dear Fredrik,

I assume that you mean standardized *regression* coefficients. If so, a 
simple approach is to use the scale function to standardize the variables 
and then to perform a regression with lm; you can include -1 on the 
right-hand side of the model formula to suppress the constant; it will be 0 
within rounding error anyway.

For example, using the Duncan data frame in the car package:

         > Duncan.s <- as.data.frame(scale(Duncan[, 2:4])) # omits a
factor
in col. 1
         > lm(prestige ~ income + education - 1, data=Duncan.s)

         Call:
         lm(formula = prestige ~ income + education - 1, data = Duncan.s)

         Coefficients:
         income  education
          0.4643     0.5155

Of course, you could also compute the standardized coefficients from the 
unstandardized coefficients and the standard deviations of the variables; 
for example

         > mod <- lm(prestige ~ income + education, data=Duncan)
         > coef(mod)
         (Intercept)      income   education
          -6.0646629   0.5987328   0.5458339
         > coef(mod)[2:3]*sd(Duncan[,c('income', 
'education')])/sd(Duncan$prestige)
         income education
         0.4642947 0.5155284

Finally, it's not hard to encapsulate this in a function:

         > std.coef <- function (mod){
         +     sy <- sd(response(mod))
         +     sx <- sd(model.matrix(mod)[,-1])
         +     b <- coef(mod)[-1]
         +     b*sx/sy
         +     }

         > std.coef(mod)
         income education
         0.4642947 0.5155284

Is that what you had in mind?
   John


-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox
-----------------------------------------------------

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