Retaining principal components for discrete variables

SOLANAS, ANTONIO; MANOLOV, RUMEN; LEIVA, DAVID; RICHARD'S, MARÍA MARTA

Anuario de psicología

UB Universitat de Barcelona

Lugar: Enviado en Junio de 2011. Barcelona.; Año: 2011 vol. 41 p. 33 - 50

0066-5126

The present study discusses retention criteria for principal componentsanalysis (PCA) applied to Likert scale items typical in psychological questionnaires.The main aim is to recommend applied researchers to restrain from relyingonly on the eigenvalue-than-one criterion; alternative procedures aresuggested for adjusting for sampling error. An additional objective is to addevidence on the consequences of applying this rule when PCA is used withdiscrete variables. The experimental conditions were studied by means ofMonte Carlo sampling including several sample sizes, different number of variablesand answer alternatives, and four non-normal distributions. The resultssuggest that even when all the items and thus the underlying dimensions areindependent, eigenvalues greater than one are frequent and they can explainup to 80% of the variance in data, meeting the empirical criterion. The consequencesof using Kaiser’s rule are illustrated with a clinical psychology example.The size of the eigenvalues resulted to be a function of the sample sizeand the number of variables, which is also the case for parallel analysis asprevious research shows. To enhance the application of alternative criteria,an R package was developed for deciding the number of principal componentsto retain by means of confidence intervals constructed about the eigenvaluescorresponding to lack of relationship between discrete variables.Keywords: principal components analysis, eigenvalues, parallel analysis,discrete items.