Why? You might ask … We are currently developing an index with several socioeconomic indicators (e.g., income, education, employment, etc.). The basic idea is to conduct a regression analysis for each indicator with geography (e.g., province) as a key independent variable. Then we want to take the average across all indicator scores (e.g., standardized betas) and rank-order these scores according to geography (e.g., 1 to 10 scale for ten provinces).
The issue we encounter is that some of our regression analysis are based on linear scales (i.e., income) whereas other measures are based on binary scales (e.g., unemployed or employed). We would use linear regression for income and logistic regression for employment status. Thus the results are interpreted differently (coefficients vs. odds ratios) and are on different scales. Prior to averaging these scores across indicators, we want to transform the values to all be on the same scale. We can do this using the min-max normalization procedure so that all indicators values fall on the same scale (0,1). But is this appropriate? Is there a better alternative?
You could dichotomise your continuous predictors using an appropriate cut off (eg are the existing ones based on 50:50 or 25:75, all choices are arbitrary but influential!) and then have odds for all the predictors. This is usually frowned on as you are losing statistical power by dichotomizing, but you have need of comparability.
What about standardised coefficients in logistic regression?
I would also try linear regressions for those dichotomous variables to get standardised coefficients.
Anyway each of these suggestions would have their own cons.
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