Recursive partition and amalgamation with the exponential family: Theory and applications

A. Ciampi, Z. Lou, Qian Lin, Abdissa Negassa

Research output: Contribution to journalArticle

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Abstract

The theory of tree‐growing (RECPAM approach) is developed for outcome variables which are distributed as the canonical exponential family. The general RECPAM approach (consisting of three steps: recursive partition, pruning and amalgamation), is reviewed. This is seen as constructing a partition with maximal information content about a parameter to be predicted, followed by simplification by the elimination of ‘negligible’ information. The measure of information is defined for an exponential family outcome as a deviance difference, and appropriate modifications of pruning and amalgamation rules are discussed. It is further shown how the proposed approach makes it possible to develop tree‐growing for situations usually treated by generalized linear models (GLIM). In particular, Poisson and logistic regression can be tree‐structured. Moreover, censored survival data can be treated, as in GLIM, by observing a formal equivalence of the likelihood under random censoring and an appropriate Poisson model. Three examples are given of application to Poisson, binary and censored survival data.

Original languageEnglish (US)
Pages (from-to)121-137
Number of pages17
JournalApplied Stochastic Models and Data Analysis
Volume7
Issue number2
DOIs
Publication statusPublished - 1991
Externally publishedYes

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Keywords

  • Censored survival data
  • Generalized linear model (GLIM)
  • Logistic regression
  • Poisson regression
  • Tree growing

ASJC Scopus subject areas

  • Modeling and Simulation
  • Management of Technology and Innovation

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