The Ordination of Incidence Data

Abstract

Principal components analysis of incidence (presence and absence) data produces a horseshoe effect. A new method, called step-across, is described which removes this effect. From a matrix of joint occurrences, distances are found directly for all positive values. Distances for zero joint occurrences are found from the shortest network distance. The complete distance matrix is then analyzed by Gower''s principal coordinates technique. The method can be used on both rows and columns of an incidence matrix. It is illustrated with artificial data and with data on euphausiids from the Indian Ocean.