The ACE algorithm for optimal transformations in multiple

Abstract

We employed the Alternating Conditional Expectations (ACE) technique (Breiman & Friedman, 1985) to relax the assumption of model linearity. By generating non-restrictive transformations for both the dependent and independent variables, ACE develops regression models that can provide much better model fits compared to models produced by standard linear techniques such as Ordinary Least Squares. The ACE transformations can reveal new information and insights on the relationship between the independent and dependent variables. The objective of fiilly exploring and explaining the effect of covariates on a response variable in regression analysis is facilitated by properly transforming the independent variables. A number of parametric transformations for continuous variables in regression analysis have been suggested (Box and Tidwell, 1962;Kruskal, 1965; Mosteller and Tukey, 1977; Cook and Weisberg, 1982; Carroll and Ruppert, 1988; Royston, 2000). In this paper, we introduce the ACE algorithm for estimating optimal transformations for both response and independent variables in regression and correlation analysis, and illustrate through two examples that usefulness of ACE guided transformation in multivariate analysis. The power of the ACE approach lies in its ability to recover the functional forms of variables and to uncover complicated relationships.