Can I test for correlation between variables before standardize them?

What I want to do is to construct GLMM’s to evaluate resource selection, and I have a set of variables (some representing distances and others representing % of land cover).

Can I test for correlation between variables before standardize them? I am not quite sure what should I do first.

Answer

Can I test for correlation between variables before standardize them? I am not quite sure what should I do first.

Correlation will be the same regardless whether you calculate it before or after standardization. To see this, it is enough to know that correlation is invariant to scale. Take bR and a>0, then

Corr(aXb,Y)=Cov(aXb,Y)Var(aXb)(Var(Y)=Cov(aX,Y)Var(aX)Var(Y)=aCov(X,Y)a2Var(X)Var(Y)=aCov(X,Y)aVar(X)Var(Y)=Cov(X,Y)Var(X)Var(Y)=Corr(X,Y)

The first equality is a definition.
The second uses the property that covariance as well as variance are invariant to location shifts.
The third uses the properties of covariance and variance with respect to multiplication by a constant.
The fourth uses the fact that a>0.
The fifth just cancels out the multipliers.
The sixth is again a definition.

This covers standardization, which is subtracting the mean and dividing by the standard deviation (a positive number).

Attribution
Source : Link , Question Author : mtao , Answer Author : Richard Hardy

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