Approaches to determining the number of components to interpret from principal components analysis were compared. Heuristic procedures included: retaining components with eigenvalues (Xs) > 1 (i.e., Kaiser-Guttman criterion); components with bootstrapped Xs > 1 (bootstrapped Kaiser-Guttman); the scree plot; the broken-stick model; and components with Xs totalling to a fixed amount of the total variance. Statistical ap- proaches included: Bartlett's test of sphericity; Bartlett's test of homogeneity of the cor- relation matrix, Lawley's test of the second X; bootstrapped confidence limits on successive Xs (i.e., significant differences between Xs); and bootstrapped confidence limits on eigen- vector coefficients (i.e., coefficients that differ significantly from zero). All methods were compared using simulated data matrices of uniform correlation structure, patterned ma- trices of varying correlation structure and data sets of lake morphometry, water chemistry, and benthic invertebrate abundance. The most consistent results were obtained from the broken-stick model and a combined measure using bootstrapped Xs and associated eigen- vector coefficients. The traditional and bootstrapped Kaiser-Guttman approaches over- estimated the number of nontrivial dimensions as did the fixed-amount-of-variance model. The scree plot consistently estimated one dimension more than the number of simulated dimensions. Bartlett's test of sphericity showed inconsistent results. Both Bartlett's test of homogeneity of the correlation matrix and Lawley's test are limited to testing for only one and two dimensions, respectively.

Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches'

Summary

This paper considers the asymptotic distributions of latent roots and vectors in principal components analysis when the parent population is non-normal. It is shown that sufficient of T. W. Anderson's asymptotic theory in the multivariate normal case carries over for some results to be obtained.

Asymptotic theory for principal component analysis: non-normal case1

Primary objective: To explore the relationships between verbal aggression, physical aggression and inappropriate sexual behaviour following acquired brain injury.Research design: Multivariate statistical modelling of observed verbal aggression, physical aggression and inappropriate sexual behaviour utilizing demographic, pre-morbid, injury-related and neurocognitive predictors.Methods and procedures: Clinical records of 152 participants with acquired brain injury were reviewed, providing an important data set as disordered behaviours had been recorded at the time of occurrence with the Brain Injury Rehabilitation Trust (BIRT) Aggression Rating Scale and complementary measures of inappropriate sexual behaviour. Three behavioural components (verbal aggression, physical aggression and inappropriate sexual behaviour) were identified and subjected to separate logistical regression modelling in a sub-set of 77 participants.Main outcomes and results: Successful modelling was achieved for both verbal and ...

Clinical correlates of verbal aggression, physical aggression and inappropriate sexual behaviour after brain injury

The purpose of this report is to re-examine jaguar (Panthera onca) subspecies using morphometric skull characters and multivariate statistical methods to analyze differences. Eleven skull characters used historically to define jaguar subspecies were measured on 170 specimens in U.S. natural history museums. Relationships among the eight recognized subspecies of jaguar were examined. using Multigroup Discriminant Analysis (MDA) and univarite statistics. Discriminant analyses of these skull characteristics does not indicate distinct groups, supporting the null hypothesis. This analysis was conducted to add to systematic studies such as DNA analysis to assist the Felid Taxon Advisory Group (Felid TAG) and the American Zoo and Aquarium Association (AZA) establish valid taxonomic differences in the jaguar. Zoo Biol 16:107–120, 1997. © 1997 Wiley-Liss, Inc.

Taxonomic Re-Evaluation of the Jaguar

Area-based socioeconomic status and mood disorders: Cross-sectional evidence from a cohort of randomly selected adult women

The asymptotic theory of the distribution of the latent roots and vector of principal components analysis (PCA) of samples has hitherto been tied t multivariate normal (MVN) distributions. However, much real behavior dat are not normal. The results of the present study show, using arguments base on Monte Carlo methods, that if there is enough meaningful structure in th population, then PCA of samples of data with multivariate non-normal (NN distribution may provide answers relative to the "true" population principal components (PC) of comparable reliability to PCA of samples of MVAT data.

C. B. H. Edwards

Papers

Repeatability of principal components in samples: normal and non-normal data sets compared