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I am currently trying to make a non-cognitive index using questions/variables. However there are following problems;

(a) The scales of the questions/variables vary, so I have a scale from 1 to 4 and some with 1 to 5

(b) I also have dummy variables that have been coded as 0 and 1 (yes/no)

The strategy I have in mind is to find the athematic mean of the scales that are similar and then calculate a weighted geometric mean. Do you think this is correct? Plus because of the dummy variable would it be correct to recode it as 1 and 2 so as to prevent my weighted geometric mean from going to zero?

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