ERIC ED385582: Instability in a Tree Approach pdf

ERIC ED385582: Instability in a Tree Approach

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One of the major problems that a tree-approach to data analysis often encounters is the instability of tree-structures. The instability issue must be dealt with before data can be interpreted by this method. Examining instability at a node of a tree provides insight into the instability of the whole tree, because the same theory of instability applies to all the nodes. This paper deals with the instability issue at a single node of a tree. It is assumed that the data are from a regression model, and the factors in that model that affect the instability are examined. Squared-error loss is considered as a criterion for tree-construction (the “ls” criterion in the CART program). The selection rate of a regressor variable at a node of a tree is used as a measure of instability. The selection rate mainly depends on: (1) regression coefficients; (2) (conditional) variance-covariance structure of the regressor variables; (3) the sample size; and (4) noise in the response variable.

Simulation results are reported that show patterns of instability for several different settings of regression models. Three figures and six tables illustrate the analysis. (Contains 10 references.) (SLD

• Creator/s: ERIC
• Date: 1992-01
• Year: 1992
• Book Topics/Themes: ERIC Archive, Error of Measurement, Models, Regression (Statistics), Sample Size, Selection, Simulation

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