Independent contrasts and PGLS regression estimators are equivalent

Blomberg, Simon P., Lefevre, James G., Wells, Jessie A. and Waterhouse, Mary (2012) Independent contrasts and PGLS regression estimators are equivalent. Systematic Biology, 61 3: 382-391. doi:10.1093/sysbio/syr118


Author Blomberg, Simon P.
Lefevre, James G.
Wells, Jessie A.
Waterhouse, Mary
Title Independent contrasts and PGLS regression estimators are equivalent
Journal name Systematic Biology   Check publisher's open access policy
ISSN 1063-5157
1076-836X
Publication date 2012-05-01
Year available 2012
Sub-type Article (original research)
DOI 10.1093/sysbio/syr118
Open Access Status Not yet assessed
Volume 61
Issue 3
Start page 382
End page 391
Total pages 10
Place of publication Oxford, United Kingdom
Publisher Oxford University Press
Language eng
Subject 1105 Ecology, Evolution, Behavior and Systematics
1311 Genetics
Abstract We prove that the slope parameter of the ordinary least squares regression of phylogenetically independent contrasts (PICs) conducted through the origin is identical to the slope parameter of the method of generalized least squares (GLSs) regression under a Brownian motion model of evolution. This equivalence has several implications: 1. Understanding the structure of the linear model for GLS regression provides insight into when and why phylogeny is important in comparative studies. 2. The limitations of the PIC regression analysis are the same as the limitations of the GLS model. In particular, phylogenetic covariance applies only to the response variable in the regression and the explanatory variable should be regarded as fixed. Calculation of PICs for explanatory variables should be treated as a mathematical idiosyncrasy of the PIC regression algorithm. 3. Since the GLS estimator is the best linear unbiased estimator (BLUE), the slope parameter estimated using PICs is also BLUE. 4. If the slope is estimated using different branch lengths for the explanatory and response variables in the PIC algorithm, the estimator is no longer the BLUE, so this is not recommended. Finally, we discuss whether or not and how to accommodate phylogenetic covariance in regression analyses, particularly in relation to the problem of phylogenetic uncertainty. This discussion is from both frequentist and Bayesian perspectives.
Keyword Comparative methods
Generalized least squares
Independent contrasts
Regression
Q-Index Code C1
Q-Index Status Confirmed Code
Grant ID DP0 878542
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2013 Collection
School of Biological Sciences Publications
 
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