Aster Models and Lande-Arnold Beta

Abstract

Lande and Arnold (1983) proposed an estimate of beta, the directional selection gradient, by ordinary least squares (OLS). Aster models (Geyer, Wagenius and Shaw, 2007; Shaw, Geyer, Wagenius, Hangelbroek, and Etterson, 2008) estimate exactly the same beta, so providing no improvement over the Lande-Arnold method in point estimation of this quantity. Aster models do provide correct confidence intervals, confidence regions, and hypothesis tests for beta; in contrast, such procedures derived from OLS are often invalid because the assumptions for OLS are grossly incorrect.