Multicollinearity: A tale of two nonparametric regressions
نویسندگان
چکیده
The most popular form of arti cial neural network, feedforward networks with sigmoidal activation functions, and a new statistical technique, multivariate adaptive regression splines (MARS) can both be classi ed as nonlinear, nonparametric function estimation techniques, and both show great promise for tting general nonlinear multivariate functions. In comparing the two methods on a variety of test problems, we nd that MARS is in many cases both more accurate and much faster than neural networks. In addition, MARS is interpretable due to the choice of basic functions which make up the nal predictive equation. This suggests that MARS could be used on many of the applications where neural networks are currently being used. However, MARS exhibits problems in choosing among predictor variables when multicollinearity is present. Due to their redundant architecture, neural networks, however, do not share this problem, and are better able to predict in this situation. To improve the ability of MARS to deal with multicollinearity, we rst use principal components to reduce the dimensionality of the input variables before invoking MARS. Using data from a polymer production run, we nd that the resulting model retains the interpretability and improves the accuracy of MARS in the multicollinear setting.
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