Abstract
A number of psychometricians have suggested that parallel analysis (PA) tends to yield more accurate results in determining the number of factors in comparison with other statistical methods. Nevertheless, all too often PA can suggest an incorrect number of factors, particularly in statistically unfavorable conditions (e.g., small sample sizes and low factor loadings). Because of this, researchers have recommended using multiple methods to make judgments about the number of factors to extract. Implicit in this recommendation is that, when the number of factors is chosen based on PA, uncertainty nevertheless exists. We propose a Bayesian parallel analysis (BPA) method to incorporate the uncertainty with decisions about the number of factors. BPA yields a probability distribution for the various possible numbers of factors. We implement and compare BPA with a frequentist approach, revised parallel analysis (RPA), in the contexts of real and simulated data. Results show that BPA provides relevant information regarding the uncertainty in determining the number of factors, particularly under conditions with small sample sizes, low factor loadings, and less distinguishable factors. Even if the indicated number of factors with the highest probability is incorrect, BPA can show a sizable probability of retaining the correct number of factors. Interestingly, when the mode of the distribution of the probabilities associated with different numbers of factors was treated as the number of factors to retain, BPA was somewhat more accurate than RPA in a majority of the conditions.
Original language  English (US) 

Pages (fromto)  466490 
Number of pages  25 
Journal  Educational and Psychological Measurement 
Volume  81 
Issue number  3 
DOIs  
State  Published  Jun 2021 
Keywords
 Bayesian analysis
 dimensionality assessment
 exploratory factor analysis
 parallel analysis
ASJC Scopus subject areas
 Education
 Developmental and Educational Psychology
 Applied Psychology
 Applied Mathematics
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BPA_Code – Supplemental material for Incorporating Uncertainty Into Parallel Analysis for Choosing the Number of Factors via Bayesian Methods
Levy, R. (Creator), Xia, Y. (Creator) & Green, S. B. (Creator), figshare SAGE Publications, 2020
DOI: 10.25384/sage.12707343.v1, https://sage.figshare.com/articles/BPA_Code_Supplemental_material_for_Incorporating_Uncertainty_Into_Parallel_Analysis_for_Choosing_the_Number_of_Factors_via_Bayesian_Methods/12707343/1
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HolzingerSwinefore_GrantWhite_19tests – Supplemental material for Incorporating Uncertainty Into Parallel Analysis for Choosing the Number of Factors via Bayesian Methods
Levy, R. (Creator), Xia, Y. (Creator) & Green, S. B. (Creator), figshare SAGE Publications, 2020
DOI: 10.25384/sage.12707346.v1, https://sage.figshare.com/articles/HolzingerSwinefore_GrantWhite_19tests_Supplemental_material_for_Incorporating_Uncertainty_Into_Parallel_Analysis_for_Choosing_the_Number_of_Factors_via_Bayesian_Methods/12707346/1
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Incorporating Uncertainty Into Parallel Analysis for Choosing the Number of Factors via Bayesian Methods
Levy, R. (Creator), Xia, Y. (Creator) & Green, S. B. (Creator), figshare SAGE Publications, 2020
DOI: 10.25384/sage.c.5072631.v1, https://sage.figshare.com/collections/Incorporating_Uncertainty_Into_Parallel_Analysis_for_Choosing_the_Number_of_Factors_via_Bayesian_Methods/5072631/1
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