Institute of Mathematical Statistics Lecture Notes - Monograph Series

Regression tree models for designed experiments

Wei-Yin Loh

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Although regression trees were originally designed for large datasets, they can profitably be used on small datasets as well, including those from replicated or unreplicated complete factorial experiments. We show that in the latter situations, regression tree models can provide simpler and more intuitive interpretations of interaction effects as differences between conditional main effects. We present simulation results to verify that the models can yield lower prediction mean squared errors than the traditional techniques. The tree models span a wide range of sophistication, from piecewise constant to piecewise simple and multiple linear, and from least squares to Poisson and logistic regression.

Chapter information

Javier Rojo, ed., Optimality: The Second Erich L. Lehmann Symposium (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 210-228

First available in Project Euclid: 28 November 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K15: Factorial designs 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 62G08: Nonparametric regression

AIC ANOVA factorial interaction logistic Poisson

Copyright © 2006, Institute of Mathematical Statistics


Loh, Wei-Yin. Regression tree models for designed experiments. Optimality, 210--228, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000464.

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