A comparison of some linear and nonlinear discrimination methods (Q1965928)

Let \(Y\) be a response variable and \(X_1,\dots,X_k\) be predictor variables. The alternating conditional expectations (ACE) algorithm finds nonparametric functions \(\theta(Y)\) and \(\varphi_j (X)\) which minimize the expression \( E[\theta(Y)-\sum_{j=1}^k\varphi_j(X_j)]^2/E[\theta(Y)]^2. \) ACE may be considered as a nonlinear generalization of linear regression [\textit{L. Breiman} and \textit{J.H. Friedman}, J. Am. Stat. Assoc. 80, 580-619 (1985; Zbl 0594.62044)]. An analogous generalization for canonical correlations (OVERALS algorithm) is that one made by \textit{E. van der Burg, J. de Leeuw} and \textit{R. Verdegaal} [Psychometrika 53, No. 2, 177-197 (1988; Zbl 0718.62143)]. In this article these two nonlinear algorithms are compared with classical linear regression and canonical correlation methods to analyse the results of arthropod selectivity to pest trials. The transformations of variables determined by OVERALS were quite similar to the important transformations of ACE and were presumed to be reasonable.