[R-sig-eco] R-sig-ecology Digest, Vol 34, Issue 5

[Dixon, Philip M [STAT]]

Matt,

Standardization is a transformation of the X variables to mean 0 and variance 1.  You do that before you fit the regression or after by multiplying beta_i by sd(X_i).

The goal of standardization is to put all X's on the same scale.  There are other ways to do that, and (important point) you can (and should) choose the biologically/ecologically most relevant way to put X's on the same scale.  Using sd(x) is often reasonable, but there may be something more appropriate.  In particular, sd(x) is not appropriate (in my mind) when one of the X's has a very skewed distribution (e.g. mostly values from 1 to 2 and one value of 100).  

My recommendation to evaluate the "impact" of each X (considered in the usual partial sense for a multiple regression coefficient) is to define equivalent changes for each X variable.  E.g. a change in temperature of 5C might be equivalent to a change in altitude of 1000m or a change in latitude of 1degree.  Then calculate the change in Y induced by each change in X.  Those are 5*beta for temp, 1000*beta for altitude and beta for latitude.

Best wishes,
Philip Dixon