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https://hdl.handle.net/2142/82325
Description
Title
Tree Estimation Based on an L(1) Loss Criterion
Author(s)
Smith, Thomas Jay
Issue Date
2000
Doctoral Committee Chair(s)
Hubert, Lawrence J.
Department of Study
Psychology
Discipline
Psychology
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
Abstract
Five applications were carried out in this study. In Application 1, L1 ultrametrics under fixed constraints were fitted to gene frequency data of Cavalli-Sforza et al. (1994) using both the IRIP approach and a linear programming (LP) approach of Spath (1992, Chapter 5). When coded for ultrametric constraints, IRIP showed faster processing speeds and larger object set size capacity than the LP approach. Heuristic fitting of ultrametrics and additive trees were considered in Applications 2 and 3, using occupational data from the U.S. Department of Labor Employment and Training Administration's (1998) O*NET Content Model, and food data from Ross and Murphy (1999). Both the L2 iterative projection (IP) approach of Hubert and Arabie (1995) and the IRIP L1 approach were applied. Both methods identified very similar solutions when the best-fitting and the most frequently-occurring local optima were considered. In Applications 4 and 5, a series of Monte Carlo analyses were carried out to assess metric recovery of ultrametrics and additive trees under (1) typical data error conditions, and (2) extreme data error conditions. Under typical error conditions, the IP approach showed superior metric recovery, while under extreme data error conditions the IRIP approach showed superior metric recovery when a relatively large proportion of extreme data values were present within a smaller object set size. Under extreme data error conditions, metric recovery of additive trees was much higher than metric recovery of ultrametrics (with either method). Possible extensions to other representational structures, and the use of additive trees as resilient structures in the presence of data error are discussed.
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