Classification and Regression Trees

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CHAPTER 29 Classification and Regression
Trees Dean L. Urban
Tables, Figures, and Equations
From McCune, B. J. B. Grace. 2002. Analysis
of Ecological Communities. MjM Software Design,
Gleneden Beach, Oregon http//www.pcord.com
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Table 29.1. A matrix matching statistical
techniques to various applications that require
group classification or discrimination.
Applications are discussed in the Introduction,
coded here as groups defined on species
composition (SPP) or environmental variables
(ENV). Techniques are discriminant analysis
(DA), group-contrast Mantel test (GC-Mantel),
multivariate analysis of variance (MANOVA),
nonparametric MANOVA (NPMANOVA), multi-response
permutation procedures (MRPP), classification and
regression trees (CART), generalized linear
models (GLM), and generalized additive models
(GAM).
Application Appropriate Techniques
Exploratory data analysis
1a. Do SPP groups differ? CART, DA, GC-Mantel, MANOVA, NPMANOVA, MRPP
1b. On which ENV variable(s)? CART, DA, partial GC-Mantel
2a. Do ENV groups differ? ISA, CART, GC-Mantel, MRPP
2b. On which SPP? ISA, CART, partial GC-Mantel
3a. Do habitats differ? DA, CART, MANOVA, NPMANOVA, MRPP, logistic regression, GLM, GAM, etc.
3b. On which variable(s)? CART, DA, partial GC-Mantel, logistic regression, etc.
Predict group membership
1c. on SPP ISA (with some modification)
2c. on ENV CART, DA, (multinomial) logistic regression
3c. habitat variables CART, DA, logistic regression
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Table 29.3. Indicator Species Analysis for the
seven forest types identified via hierarchical
clustering. Indicator values (IV) are percentage
of perfect fidelity. Indicator values were
tested for statistical significance based on 1000
permutations (, p lt 0.001 , p lt 0.005).
Sequence order of groups in data, Identifier
group identifier, Avg Average IV, Max Maximum
IV, MaxGrp Group with highest IV.
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Figure 29.1. Upper Classification tree for 7
forest types on 15 environmental variables
(function rpart, complexity parameter (cp)
0.000001, minsplit 10, split information).
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Figure 29.1. (Lower) Pruned classification tree,
simplified by stopping the tree at the number of
nodes corresponding to the point where the
pruning curve crosses the minimum (1 S.E.) line
(Fig. 29.2).
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Table 29.4. Misclassification table for the 7
forest types, based on a pruned CART model with
11 nodes (Fig. 29.3). Rows are actual forest
types, columns are predicted forest types. Row
totals are indexed as number correct/number
misclassified. Total misclassification rate
based on jack-knifing is 39/98 (39.8).
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Figure 29.2. Cost-complexity pruning curve for
the classification tree in Figure 29.1. Error
bars are estimated from 10 cross-validation
subsets of the samples. The horizontal line is
one standard error above the minimum error rate.
Inf infinite. Relative error is calculated
by cross-validation.