Regressor Selection with the Analysis of Variance Method

Identication of nonlinear dynamical models of a black box nature involves both structure decisions, i.e., which regressors to use, the selection of a regressor function, and the estimation of the parameters involved. The typical approach in system identication seems to be to mix all these steps, which for example means that the selection of regressors is based on the ts that is achieved for dierent choices. Alternatively one could then interpret the regressor selection as based on hypothesis tests (F-tests) at a certain condence level that depends on the data. It would in many cases be desirable to decide which regressors to use independently of the other steps. In this paper we investigate what the well known method of analysis of variance (ANOVA) can oer for this problem. System identication applications violate many of the ideal conditions for which ANOVA was designed and we study how the method performs under such non-ideal conditions. ANOVA is much faster than a typical parametric estimation method, using e.g. neural networks. It is actually also more reliable, in our tests, in picking the correct structure even under non-ideal conditions. One reason for this may be that ANOVA requires the data set to be balanced, that is regressor value combinations in test/validation data that are very common or unusual are adjusted in order to play more equal roles when deciding their in uence on the t. Just applying tests of t for the recorded data may give improper weight to very common regressor value combinations