Determination of selection gradients using multiple regression versus Structural Equation Modeling (SEM)

Selection studies involving multiple intercorrelated independent variables have employed multiple regression analysis as a means to estimate and partition natural and sexual selection's direct and indirect effects. These statistical models assume that independent variables are measured without error. Most would conclude that such is not the case in the field studies for which these methods are employed. We demonstrate that the distortion of estimates resulting from error variance is not trivial. When independent variables are intercorrelated, extreme distortions may occur. We propose to use Structural Equation Models (SEM), to estimate error variance and produce highly accurate coefficients for formulation of selection gradients. This method is particularly appropriate when the selection is viewed as happening at the level of the latent variables.