I am working on an analysis in which I have been asked by colleagues to supply "standardised" coefficients, by which they mean on a comparable scale for ease of interpretation (I am aware that it doesn't necessarily make interpretation easy, but that is nevertheless the rationale). My question is what the best/most robust approach to standardising this particular data would be. In particular, the issue of skew in predictor variables is confusing me.

The dataset relates variables describing the local physical and socioeconomic environment to measures of population health; I am using negative binomial GLMs. An offset and some quadratic terms are included. The predictors are all continuous but with scales differing over orders of magnitude; some have inherently meaningful units while others are indices. They include both heavily left- and right-skewed variables. The model diagnostics are fine without any variable transformation or standardisation. Some of the skewed variables would be amenable to transformation to eliminate skew, but others would not; and transformation prior to standardisation would be counter-productive for interpretability.

My colleagues' preferred method of standardisation is min-max scaling, and for most of the variables involved a scale of 0-1 would make intuitive sense.

However, from my reading (e.g. here, here, here) it is my understanding that centering on the mean and dividing by the standard deviation is the recommended approach to standardisation when quadratic terms are involved - although is this still the case when using orthogonal polynomials?

Mean-centering and SD-scaling would normally achieve comparable scales for the coefficients, but given the skew in some of the predictors I'm not certain whether this is strictly correct. On the other hand, min-max scaling ignores skew and doesn't do anything about the excess high or low values, also reducing comparability. Which would be the better choice in this case - or is there another option that I'm not aware of?

Thank you.


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