Regression Models for an Angular Response

Abstract

SUMMARY This paper considers the problem of regressing an angular response variate on a set of linear explanatory variables. A general class of models is proposed in which the mean direction and dispersion of a von Mises variate are related to the explanatory variables by general link functions. Appropriate regression diagnostics, estimation and testing procedures are developed for fitting the models. The meaning of between an angular and a linear variable is clarified, and leads to a general notion of multiple correlation associated with the regression model. The methods are applied to a set of data arising from a study of movements of intertidal gastropods.