Using z-scores in regression modelling. Is it correct?

[Gianfranco Di Gennaro]

Dear all,

thank you in advance for your time.

I am currently conducting a logistic regression analysis with the outcome variable being the presence or absence of a particular pathology. The predictors I am using are as follows:

Sex
Muscle mass
BMI
Subcutaneous fat
and others

However, I have encountered an issue regarding collinearity among my predictors, particularly with sex. Specifically, muscle mass and subcutaneous fat exhibit significant differences between men and women.

In my review of relevant literature, I have noticed similar situations where predictors are transformed into z-scores calculated separately within each sex category. For instance, in women, muscle mass is z-transformed using the mean and standard deviation specific to women, and the same procedure is applied for men.

Subsequently, these z-scores are incorporated into the regression model in place of the original variables. In my case, the model would look like this:

p(pathology)=a + b1(Sex) + b2(Zmusclemass) + b3(Zsubcutaneousfat)....+ e
and so on.

Do you believe this approach is reasonable?

Thank you very much!

Gianfranco

[Leonardo Guizzetti]

Specifically, muscle mass and subcutaneous fat exhibit significant differences between men and women.

This is prime territory for an interaction with sex, not to rescale the predictors.

Mathematically, there’s nothing wrong with converting continuous variables to standard scores, in the sense that the machinery works all the same. The big caveats are whether you can credibly assume a normal distribution reasonably approximates the marginal distribution of the predictor. There are also situations where you can create misleading results by standardizing across groups, such as you had described here. It may not be advantageous to rescale when the units of the predictor have concrete and understandable differences. In this case rescaling can cloud interpretation. More can be said on the topic but that’s a superficial view of some important concerns as it pertains to your situation.