Independent contrasts and regression through the origin

Independent contrasts and regression through the origin.

Following the pioneering work of Felsenstein and Garland, phylogeneticists have been using regression through the origin to analyze comparative data using independent contrasts. The reason why regression through the origin must be used with such data was revisited. The demonstration led to the formulation of a permutation test for the coefficient of determination and the regression coefficient ...

Regression through the Origin

A lthough ordinary least-squares (OLS) regression is one of the most familiar statistical tools, far less has been written − especially in the pedagogical literature − on regression through the origin (RTO). Indeed, the subject is surprisingly controversial. The present note highlights situations in which RTO is appropriate, discusses the implementation and evaluation of such models and compare...

Independent contrasts and PGLS regression estimators are equivalent.

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 r...

Nonlinear relationships and phylogenetically independent contrasts.

The method of phylogenetically independent contrasts is commonly used for exploring cross-taxon relationships between traits. Here we show that this phylogenetic comparative method (PCM) can fail to detect correlated evolution when the underlying relationship between traits is nonlinear. Simulations indicate that statistical power can be dramatically reduced when independent contrasts analysis ...

Contrasts, Independent Component Analysis, and Blind Deconvolution