Estimating Optimal Transformations for Multiple Regression Using the Ace Algorithm

In: Computers and Technology

Submitted By Tonywu
Words 6000
Pages 24
Journal of Data Science 2(2004), 329-346

Estimating Optimal Transformations for Multiple Regression Using the ACE Algorithm
Duolao Wang1 and Michael Murphy2 School of Hygiene and Tropical Medicine and 2 London School of Economics

1 London

Abstract: This paper introduces the alternating conditional expectation (ACE) algorithm of Breiman and Friedman (1985) for estimating the transformations of a response and a set of predictor variables in multiple regression that produce the maximum linear effect between the (transformed) independent variables and the (transformed) response variable. These transformations 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 examples 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. Key words: Alternating conditional expectation (ACE) algorithm, nonparametric regression, transformation.

1. Introduction In regression analysis, we try to explain the effect of one or more independent variables (predictors or covariates) on a dependent variable (response). The initial stages of data analysis often involve exploratory analysis. Instead of imposing preconceived models, we seek insight into the nature of relationships in the data set and, if possible, the underlying phenomena that might have produced the observed data values. Unfortunately traditional multiple regression techniques are limited in this respect since they usually require a priori assumptions about the functional forms…...

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