I would like to create a new variable using 4 different measures: hIndex (range: 1-47), # of publications (range: 0-111), and 2 other measures (range: 1-7). I changed all of these variables into z-scores, but now I'm not sure if I'm supposed to use the average, sum, or product of the z-scores to create my new variable.
You should probably make an average, but if you want to test interactions between your variables on a separate outcome, you should multiply them and the product will constitute thw interaction
If you are trying to create a single index, then you should definitely sum or average them. Note the sum and the average will be perfectly correlated because you are dividing by a constant, but the average may be more interpretable.
Dear Denise Lucia Reyes ,
If you already have collected some data then, rather than assuming that these four variables should be combined and that the average of the z scores is necessarily the best way to combine them, I would recommend carrying out a Principal Component Analysis to test how strong their first component is and saving the regression scores. Please refer to my study guide on scale reliability.
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