Review of methods for determining the number of factors and components to retain (in EFA and PCA)

Abstract

Although very popular, factor analysis (and principal components analysis) is often incorrectly applied statistical procedure. One of the typical sources of error concerns the decision of how many dimensions to retain. Although the procedures for deciding on this number have significantly advanced, most authors still adhere to outdated and inaccurate methods, which compromises the validity of scientific research and slows the scientific development. The aims of this article are to determine the frequency of the use of specific methods for determining the number of dimensions to retain in locally published articles, and to present an overview of these methods and illustrates their (in)accuracy, with suggestions for the more appropriate procedures. Evaluation, conducted on the domestic articles (available online) published from 1995 to mid 2012, which used the factor analysis and principal components analysis (139 articles from 25 journals), suggests that a lot of the authors (29.50%) do not specify the method for determining the number of dimensions to retain, and that most use obviously imprecise procedures, such as Kaiser- Guttman’s Eigenvalue > 1 rule, Cattell’s Scree Test, or a combination, with the most robust procedure known to date, Parallel Analysis, used alone or in combination with other procedures in only 5.03% of cases. Following these findings and based on the results of existing largescale simulation studies the extensive overviews of Parallel Analysis, Eigenvalue >1 rule, Scree Test, MAP, and Hull procedures were given and several 'non-technical' examples were used to demonstrate the ineffectiveness of the most popular procedures, while suggesting the robust alternatives. Finally, the recommendations were given on how to apply and combine the procedures for determining the number of factors and components to retain, with the emphasis on the Parallel Analysis of Likert items.