I have to add 2 variables (for 60 organisations) to get a composite score based on those two variables. One is the age of the organisation (measured in number of years) and the other is the number of products it manufactures.
Method 1: I calculated z scores for each variable, weighted them ( on the basis of a certain criteria) and added the weighted z score to get the composite z square.
Method 2: I divided the range of values for each variable into 5 equidistant classes. and gave them a score ranging from 1 to 5 based on the class to which the given value of a particular variable belonged; weighted them (according to a criteria) and added the weighted scores.
If I have to use the composite score as an independent variable in a regression analysis, which method will be better?
Can you suggest any other method to combine the above two variables.
Thank you.
If the aim is to use the variables in regression analysis, why trying to create a score with several arbitraty choices, and not directly use the two variables as covariates in the regression analysis?
If the aim is to use the variables in regression analysis, why trying to create a score with several arbitraty choices, and not directly use the two variables as covariates in the regression analysis?
Dr. Chris: Thank you very much for your response. I would want to use a composite score, as I intend to order the organisations based on the composite score, provided the composite variable is significant. Infact, I have nine such variables to combine, but for simplicity, I just mentioned two in the original question.
Dr. Yarnold: Thank you very much for introducing me to paradoxical confounding, and providing links to interesting research papers. I would definitely go through these papers and will come back to you in case of query or need for discussion.
It depends on what the principal purpose for the composite score would be. Note that either of your methods will give equal (method 1) or near-equal (method 2) weight to each individual constituent of the composite (in a linear composite, weights are proportional to variable SDs). If the chief purpose is as an indicator for ranking/rating your cases (organizations), then the weights should reflect some empirical or rationally identified criterion. Since that appears to be your goal, then the challenge is to justify the scheme, and that's more a policy issue than a statistical issue.
If you're trying to maximize explanatory power, you might be better served by trying the nine constituent scores as separate predictors. Since that's a lot of IVs relative to the sample size you mention (N=60), it might make more sense to use principal components to reduce the number of variates, but retain the majority of the information they carry.
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