Creating square root scale of the household income

[Toru Oikawa]

Hello, can anyone help me?
I Need to create a square root scale of the household income (income/square root of number of family members), but the income variable in my dataset is a categorical variable. What can I do with it? Can I just divide it directly? Or should I take the average of every category?
Thank you very much!

[FernandoRios]

Hi Toru
The simple answer is...you cant, unless you have assumptions regarding your data. You could, for example, that every household within an income bracket has the same average household income (whatever is the mean point of the range in that category). And then divide that middle point by the household size squareroot. Again. this is a very strong assumption.
Perhaps you need to ask yourself: why the need to transform your income variable?
if what you are trying to do is to account for the equivalence scale effect, you could simply use the categorical dummies for income, and control for the household size (or its squared root).
HTH
Fernando