Staff Publications

Staff Publications

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    'Staff publications' is the digital repository of Wageningen University & Research

    'Staff publications' contains references to publications authored by Wageningen University staff from 1976 onward.

    Publications authored by the staff of the Research Institutes are available from 1995 onwards.

    Full text documents are added when available. The database is updated daily and currently holds about 240,000 items, of which 72,000 in open access.

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Record number 508903
Title Considering Horn’s Parallel Analysis from a Random Matrix Theory Point of View
Author(s) Saccenti, Edoardo; Timmerman, Marieke E.
Source Psychometrika 82 (2017)1. - ISSN 0033-3123 - p. 186 - 209.
DOI https://doi.org/10.1007/s11336-016-9515-z
Department(s) Systems and Synthetic Biology
VLAG
Publication type Refereed Article in a scientific journal
Publication year 2017
Keyword(s) common factor analysis - covariance matrix - number of common factors - number of principal components - principal component analysis
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 high-order eigenvalues is equivalent to the use of the joint distribution of the eigenvalues, and thus should be discouraged, and (iii) a formal test for higher-order 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 higher-order 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.

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