Abstract
This paper is concerned with the goodness-of-fit of induced decision trees. Namely, we explore the possibility to measure the goodness-of-fit as it is classically done in statistical modeling. We show how Chi-square statistics and especially the Log-likelihood Ratio statistic that is abundantly used in the modeling of cross tables, can be adapted for induction trees. The Log-likelihood Ratio is well suited for testing the significance of the difference between two nested trees. In addition, we derive from it pseudo R 2’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.
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References
Agresti, A.: Categorical Data Analysis. Wiley, New York (1990)
Akaike, H.: Information theory and an extension of the maximum likelihood principle. In: Petrox, B.N., Caski, F. (eds.) Second International Symposium on Information Theory, Akademiai Kiado, Budapest, p. 267 (1973)
Bishop, Y.M.M., Fienberg, S.E., Holland, P.W.: Discrete Multivariate Analysis. MIT Press, Cambridge (1975)
Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J.: Classification And Regression Trees. Chapman and Hall, New York (1984)
Goodman, L.A., Kruskal, W.H.: Measures of association for cross classifications. Journal of the American Statistical Association 49, 732–764 (1954)
Goodman, L.A., Kruskal, W.H.: Measures of association for cross classifications IV: simplification of asymptotic variances. Journal of the American Statistical Association 67, 415–421 (1972)
Kass, R.E., Raftery, A.E.: Bayes factors. Journal of the American Statistical Association 90, 773–795 (1995)
Light, R.J., Margolin, B.H.: An analysis of variance for categorical data. Journal of the American Statistical Association 66, 534–544 (1971)
Olszak, M., Ritschard, G.: The behaviour of nominal and ordinal partial association measures. The Statistician 44, 195–212 (1995)
Schwarz, G.: Estimating the dimension of a model. The Annals of Statistics 6, 461–464 (1978)
Theil, H.: On the estimation of relationships involving qualitative variables. American Journal of Sociology 76, 103–154 (1970)
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© 2003 Springer-Verlag Berlin Heidelberg
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Ritschard, G., Zighed, D.A. (2003). Goodness-of-Fit Measures for Induction Trees. In: Zhong, N., Raś, Z.W., Tsumoto, S., Suzuki, E. (eds) Foundations of Intelligent Systems. ISMIS 2003. Lecture Notes in Computer Science(), vol 2871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39592-8_9
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DOI: https://doi.org/10.1007/978-3-540-39592-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20256-1
Online ISBN: 978-3-540-39592-8
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