Goodness-of-Fit Measures for Induction Trees

This paper is concerned with the goodness-of-fit of induced decision trees. Namely, we explore the possibility to measure the goodnessof-fit as it is classically done in statistical modeling. We show how Chisquare statistics and especially the Log-likelihood Ratio statistic that is abundantly used in the modeling of cross tables, can be adapted for induction trees. Not only is the Log-likelihood Ratio statistic suited for testing the goodness-of-fit. It allows also to test the significance of the fit between two nested trees. In addition, we derive from it pseudo R’s. We propose also adapted forms of the Akaike (AIC) and Bayesian (BIC) information criteria that prove useful in selecting the best compromise model between fit and complexity.