I am building a cost model with cubic root transformation of the cost. Hence dependent variable is (cost)^(1/3). Now, am at a stage where i need to re-transform the predicted value to the actual cost. But while re-transforming, i have read that we need to apply a smearing factor rather than directly taking the cube of the predicted value. Have a 2 part question:
- Smear factor is calculated as mean(g(residual)), where g() is the anti-transformation function. How are the residuals calculated here? Are these taken from the development data or the holdout data?
- Browsed through various websites, all had the calculation explained for log transformation function. In that case, smear factor is calculated as D1=mean(exp(residual)) and this value is multiplied by the predicted value as y1=D1.exp(XBETA). Now, how to get and implement the same logic for cubic root transformation? Following the same methodology, I could calculate the factor as D2=mean(residual^3). Now applying this factor seems a concern. I could consider y1 as exp{XBETA+log[mean(exp(residual))]}. On the same lines, can I consider y2 = {XBETA+D2^(1/3)}^3, i.e, {XBETA+[(mean(residual^3))^(1/3)]}^3. Does this makes sense?
Hope the questions are clear.
