relativization of predictor matrix?

[nina nikolic]

Good evening again!
Thanks for all your patience and support. Now I apologize in advance if my question is a trivial one:
is it necessary/useful to relativize the predictor matrix data in order to bring different scales of variables to equal footing?
I am doing NPMR (local mean with a gaussian weighting)...  does it have any built-in standardization, or some relativization is advised?
Thanks!

[Peter Nelson]

Hi Nina,

I don't think relativizations are necessary due to differences in
scale. However, you would want to consider transformations if you have
really skewed distributions of any of your predictors.

I'd be interested to hear other views on this.

Peter Nelson
PhD candidate
Department of Botany and Plant Pathology
Cordley Hall 2082
Oregon State University
Corvallis, Oregon 97331-2902
Phone: 541-737-1742

[Bruce McCune]

I agree, no need to relativize the predictors.
-Bruce

[nina nikolic]

Dear Peter & Prof. McCune, thank you for the answer!

Now this opens another question: why is skewness of predictors a problem in NPMR?
Yes, some of my predictors (soil parameters) are rather skewed, and I tend to think that this particular skewness is a true property of my data (i.e. not a result of undersampling or some other sampling flaw).

What is the risk of not eliminating skewness of predictors? If it is only a decrease of xR2, I could live with it, but if I would be violating some basic assumption of the method, it's important to know.

My only desire not to transform predictors might be a silly one: I very much like the direct comparability of soil predictors in a modeled response of different plant species abundances, more so since the soil predictors are in a rather extreme range.

[Bruce McCune]

You're right in thinking that a method that can handle nonlinear
shapes is more likely to make sense of skewed predictors. But still
it can be helpful to have your errors distributed relatively evenly
throughout a response surface. That's one aspect of fit that can
improve by transforming a predictor. Another is, as you suggest, that
the measure of fit, e.g. R^2 can improve.

But you give a good reason for not transforming predictors. So you
need to weigh the benefits against the drawbacks, given your study
objectives and audience.

-Bruce McCune

[nina nikolic]

[nina nikolic]

Dear prof. McCune, thanks, that is clear and very helpful.