Projects per year
Abstract
Horn’s parallel analysis is a widely used method for assessing the number of principal components and common factors. We discuss the theoretical foundations of parallel analysis for principal components based on a covariance matrix by making use of arguments from random matrix theory. In particular, we show that (i) for the first component, parallel analysis is an inferential method equivalent to the Tracy–Widom test, (ii) its use to test highorder eigenvalues is equivalent to the use of the joint distribution of the eigenvalues, and thus should be discouraged, and (iii) a formal test for higherorder components can be obtained based on a Tracy–Widom approximation. We illustrate the performance of the two testing procedures using simulated data generated under both a principal component model and a common factors model. For the principal component model, the Tracy–Widom test performs consistently in all conditions, while parallel analysis shows unpredictable behavior for higherorder components. For the common factor model, including major and minor factors, both procedures are heuristic approaches, with variable performance. We conclude that the Tracy–Widom procedure is preferred over parallel analysis for statistically testing the number of principal components based on a covariance matrix.
Original language  English 

Pages (fromto)  186209 
Journal  Psychometrika 
Volume  82 
Issue number  1 
DOIs  
Publication status  Published  2017 
Keywords
 common factor analysis
 covariance matrix
 number of common factors
 number of principal components
 principal component analysis
Fingerprint
Dive into the research topics of 'Considering Horn’s Parallel Analysis from a Random Matrix Theory Point of View'. Together they form a unique fingerprint.Projects
 1 Finished

INFECT: Improving Outcome of Necrotizing Fasciitis: Elucidation of Complex Host and Pathogen Signatures that Dictate Severity of Tissue Infection
1/01/13 → 30/06/18
Project: EU research project