Can I standardize data twice? Creating a composite covariate in regression I am running a regression analyses with several covariates, and my goal is to examine the relative influence of each covariate on the dependent variable. Therefore, I have taken the approach of standardizing each predictor (demeaned and scaled to unit variance) in my model so that the regression coefficients can be compared against one another. However, one of my covariates is built from several different datasets, with the data in each measured on a different scale. I will use the example of relative cloud cover here. Dataset (1) is measured on scale from 1 - 4 (low to high cloud cover), dataset (2) on a scale from 1 - 5 (low to high cloud cover), and dataset (3) in percentages (0% - 100%). Prior to combining the 3 cloud cover datasets, I standardized each independently so that they are all on the same scale. Once combined, the mean and variance of the covariate are not exactly at 0, and 1, respectively (although close), and so to be able to compare this covariate against others in the regression model, my inclination would be to standardize the entire composite covariate (i.e. across all observations).
However, do I need to standardize a second time (i.e. across all observations of the composite covariate), because the mean/variance are not exactly at 0 and 1? Are there any implications for understanding the relative effect of the twice standardized covariate on the response variable?

You can standardize the composite score variable. The interpretation of the coefficient will be in terms of standard deviations of the composite score. It'd be difficult to break down the coefficient further for the underlying scales, though it doesn't look like that's a priority for your interpretation.
