Institute of Mathematical Statistics Lecture Notes - Monograph Series

Regression tree models for designed experiments

Wei-Yin Loh

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196283962

Digital Object Identifier
doi:10.1214/074921706000000464

Mathematical Reviews number (MathSciNet)
MR2337836

Zentralblatt MATH identifier
1268.62090

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

Keywords
AIC ANOVA factorial interaction logistic Poisson

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

Loh, Wei-Yin. Regression tree models for designed experiments. Optimality, 210--228, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000464. https://projecteuclid.org/euclid.lnms/1196283962


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