PARALLEL ANALYSIS - A METHOD FOR DETERMINING SIGNIFICANT PRINCIPAL COMPONENTS

Numerous ecological studies use Principal Components Analysis (PCA) fo r exploratory analysis and data reduction. Determination of the number of components to retain is the most crucial problem confronting the r esearcher when using PCA. An incorrect choice may lead to the underext raction of components, but commonly results in overextraction. Of seve ral methods proposed to determine the significance of principal compon ents, Parallel Analysis (PA) has proven consistently accurate in deter mining the threshold for significant components, variable loadings, an d analytical statistics when decomposing a correlation matrix. In this procedure, eigenvalues from a data set prior to rotation are compared with those from a matrix of random values of the same dimensionality (p variables and n samples). PCA eigenvalues from the data greater tha n PA eigenvalues from the corresponding random data can be retained. A ll components with eigenvalues below this threshold value should be co nsidered spurious. We illustrate Parallel Analysis on an environmental data set. We reviewed all articles utilizing PCA or Factor Analysis ( FA) from 1987 to 1993 from Ecology, Ecological Monographs, Journal of Vegetation Science and Journal of Ecology. Analyses were first separat ed into those PCA which decomposed a correlation matrix and those PCA which decomposed a covariance matrix. Parallel Analysis (PA) was appli ed for each PCA/FA found in the literature. Of 39 analyses (in 22 arti cles), 29 (74.4%) considered no threshold rule, presumably retaining i nterpretable components. According to the PA results, 26 (66.7%) overe xtracted components. This overextraction may have resulted in potentia lly misleading interpretation of spurious components. It is suggested that the routine use of PA in multivariate ordination will increase co nfidence in the results and reduce the subjective interpretation of su pposedly objective methods.