Evaluation of alternative model selection criteria in the analysis of unimodal response curves using CART

Journal of Applied Statistics
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Abstract

We investigated CART performance with a unimodal response curve for one continuous response and four continuous explanatory variables, where two variables were important (i.e. directly related to the response) and the other two were not. We explored performance under three relationship strengths and two explanatory variable conditions: equal importance and one variable four times as important as the other. We compared CART variable selection performance using three tree-selection rules ('minimum risk', 'minimum risk complexity', 'one standard error') to stepwise polynomial ordinary least squares (OLS) under four sample size conditions. The one-standard-error and minimum risk-complexity methods performed about as well as stepwise OLS with large sample sizes when the relationship was strong. With weaker relationships, equally important explanatory variables and larger sample sizes, the one-standard-error and minimum-risk-complexity rules performed better than stepwise OLS. With weaker relationships and explanatory variables of unequal importance, tree-structured methods did not perform as well as stepwise OLS. Comparing performance within tree-structured methods, with a strong relationship and equally important explanatory variables, the one-standard-error rule was more likely to choose the correct model than were the other tree-selection rules. The minimum-risk-complexity rule was more likely to choose the correct model than were the other tree-selection rules (1) with weaker relationships and equally important explanatory variables; and (2) under all relationship strengths when explanatory variables were of unequal importance and sample sizes were lower.

Publication type Article
Publication Subtype Journal Article
Title Evaluation of alternative model selection criteria in the analysis of unimodal response curves using CART
Series title Journal of Applied Statistics
DOI 10.1080/02664769822909
Volume 25
Issue 5
Year Published 1998
Language English
Publisher Taylor & Francis
Description 14 p.
First page 685
Last page 698
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