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Identifying Nonlinear Relationships in Regression using the ACE Algorithm

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  • Duolao Wang
  • Michael Murphy

Abstract

This paper introduces an alternating conditional expectation (ACE) algorithm: a non-parametric approach for estimating the transformations that lead to the maximal multiple correlation of a response and a set of independent variables in regression and correlation analysis. These transformations can give the data analyst insight into the relationships between these variables so that this can be best described and non-linear relationships uncovered. Using the Bayesian information criterion (BIC), we show how to find the best closed-form approximations for the optimal ACE transformations. By means of ACE and BIC, the model fit can be considerably improved compared with the conventional linear model as demonstrated in the two simulated and two real datasets in this paper.

Suggested Citation

  • Duolao Wang & Michael Murphy, 2005. "Identifying Nonlinear Relationships in Regression using the ACE Algorithm," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(3), pages 243-258.
    • Handle: RePEc:taf:japsta:v:32:y:2005:i:3:p:243-258
    DOI: 10.1080/02664760500054517
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    References listed on IDEAS

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    1. Patrick Royston & Douglas G. Altman, 1994. "Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(3), pages 429-453, September.
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    Cited by:

    1. Atkinson, Anthony C. & Riani, Marco & Corbellini, Aldo, 2021. "The box-cox transformation: review and extensions," LSE Research Online Documents on Economics 103537, London School of Economics and Political Science, LSE Library.
    2. Jian Zhou, 2010. "Testing for Cointegration between House Prices and Economic Fundamentals," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 38(4), pages 599-632, Winter.

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