I guess this is a quite basic question, but I have been struggling with this for quite some time, so I hope someone can help me with this.
I have a model (type is not relevant for now) which includes a linear predictor (LP) that would normally be calculated as:
LP = sum(coefficient1*predictor1, coefficient2*predictor2, etc.)
However, the predictors were standardized by centering them at the mean values and rescaling them using the standard deviation (SD). Hence, the LP now looks like this:
LP = sum(coefficient1*(predictor1-mean1)/SD1, coefficient2*(predictor2-mean2)/SD2, etc.)
So far it is clear to me, but now I would like to present my models in an efficient way, so instead of writing out the mean and SD for each individual predictor I want to provide only the coefficients (see first LP) and then standardize the LP as a whole. If the LP was only centered at the mean values writing it out would look like this:
LP = sum(coefficient1*predictor1, coefficient2*predictor2, etc.)- sum(coefficient1*mean1, coefficient2*mean, etc.)
Since the latter part of this formula has fixed values I can present that as one number, which makes the whole look somewhat less complicated. However, I don’t know how to also account for the SD rescaling. Does anyone know whether this (algebraically) possible and if yes how could I do that?