Estimating Optimal Transformations for Multiple Regression Using the ACE Algorithm

This paper introduces the alternating conditional expectation (ACE) algorithm of Breiman and Friedman (1985) for estimating the trans- formations of a response and a set of predictor variables in multiple re- gression that produce the maximum linear effect between the (transformed) independent variables and the (transformed) response variable. These trans- formations can give the data analyst insight into the relationships between these variables so that relationship between them can be best described and non-linear relationships can be uncovered. The power and usefulness of ACE guided transformation in multivariate analysis are illustrated using a simulated data set as well as a real data set. The results from these exam- ples clearly demonstrate that ACE is able to identify the correct functional forms, to reveal more accurate relationships, and to improve the model fit considerably compared to the conventional linear model.

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