Metrika članka

  • citati u SCindeksu: [1]
  • citati u CrossRef-u:0
  • citati u Google Scholaru:[=>]
  • posete u poslednjih 30 dana:3
  • preuzimanja u poslednjih 30 dana:3
članak: 7 od 7  
Back povratak na rezultate
2013, vol. 46, br. 3, str. 331-347
jezik rada: engleski
vrsta rada: originalan članak
objavljeno: 04/10/2013
doi: 10.2298/PSI130801008Z
Impact of different conditions on accuracy of five rules for principal components retention
(naslov ne postoji na srpskom)
Univerzitet u Beogradu, Filozofski fakultet, Odeljenje za psihologiju



(ne postoji na srpskom)
Polemics about criteria for nontrivial principal components are still present in the literature. Finding of a lot of papers, is that the most frequently used Guttman Kaiser's criterion has very poor performance. In the last three years some new criteria were proposed. In this Monte Carlo experiment we aimed to investigate the impact that sample size, number of analyzed variables, number of supposed factors and proportion of error variance have on the accuracy of analyzed criteria for principal components retention. We compared the following criteria: Bartlett's χ2 test, Horn's Parallel Analysis, Guttman-Kaiser's eigenvalue over one, Velicer's MAP and CHull originally proposed by Ceulemans & Kiers. Factors were systematically combined resulting in 690 different combinations. A total of 138,000 simulations were performed. Novelty in this research is systematic variation of the error variance. Performed simulations showed that, in favorable research conditions, all analyzed criteria work properly. Bartlett's and Horns criterion expressed the robustness in most of analyzed situations. Velicer's MAP had the best accuracy in situations with small number of subjects and high number of variables. Results confirm earlier findings of Guttman-Kaiser's criterion having the worse performance.

Ključne reči

principal component analysis; criterion for extraction; factor retention


Bartlett, M.S. (1950) Tests of significance in factor analysis. British Journal of Statistical Psychology, 3(2): 77-85
Bentler, P.M. (1990) Comparative fit indexes in structural models. Psychological Bulletin, 107(2): 238-246
Buja, A., Eyuboglu, N. (1992) Remarks on Parallel Analysis. Multivariate Behavioral Research, 27(4): 509-540
Cangelosi, R., Goriely, A. (2007) Component retention in principal component analysis with application to cDNA microarray data. Biology direct, 2: 2
Cattell, R.B. (1966) The Scree Test for the Number of Factors. Multivariate Behavioral Research, 1(2): 245-276
Ceulemans, Eva., Kiers, H.A.L. (2006) Selecting among three-mode principal component models of different types and complexities: A numerical convex hull based method. British Journal of Mathematical and Statistical Psychology, 59(1): 133-150
Conway, J.M., Huffcutt, A.I. (2003) A Review and Evaluation of Exploratory Factor Analysis Practices in Organizational Research. Organizational Research Methods, 6(2): 147-168
Costello, A.B., Osborne, J.W. (2005) Best practices in exploratory factor analysis: Four recommendations for getting the Most from your analysis. Practical Assesment, Research & Evaluation, 10: 7
Fabrigar, L.R., Wegener, D.T., MacCallum, R.C., Strahan, E.J. (1999) Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3): 272-299
Ferré, L. (1995) Selection of components in principal component analysis: A comparison of methods. Computational Statistics & Data Analysis, 19(6): 669-682
Ford, K.J., Maccallum, R.C., Tait, M. (1986) The application of exploratory factor analysis in applied psychology: A critical review and analysis. Personnel Psychology, 39(2): 291-314
Franklin, S.B., Gibson, D.J., Robertson, P.A., Pohlmann, J.T., Fralish, J.S. (1995) Parallel Analysis: a method for determining significant principal components. Journal of Vegetation Science, 6(1): 99-106
Gorsuch, R.L. (1973) Using Bartlett's Significance Test to Determine the Number of Factors to Extract. Educational and Psychological Measurement, 33(2): 361-364
Guttman, L. (1953) Image theory for the structure of quantitative variates. Psychometrika, 18(4): 277-296
Guttman, L. (1954) Some necessary conditions for common-factor analysis. Psychometrika, 19(2): 149-161
Hayton, J.C., Allen, D.G., Scarpello, V. (2004) Factor Retention Decisions in Exploratory Factor Analysis: a Tutorial on Parallel Analysis. Organizational Research Methods, 7(2): 191-205
Henson, R.K. (2006) Use of Exploratory Factor Analysis in Published Research: Common Errors and Some Comment on Improved Practice. Educational and Psychological Measurement, 66(3): 393-416
Hong, S. (1999) Generating correlation matrices with model error for simulation studies in factor analysis: A combination of the Tucker-Koopman-Linn model and Wijsman’s algorithm. Behavior Research Methods, Instruments, & Computers, 31(4): 727-730
Horn, J.L. (1965) A rationale and test for the number of factors in factor analysis. Psychometrika, 30(2): 179-185
Horn, J.L., Engstrom, R. (1979) Cattell's Scree Test In Relation To Bartlett's Chi-Square Test And Other Observations On The Number Of Factors Problem. Multivariate Behavioral Research, 14(3): 283-300
Hubbard, R., Allen, S.J. (1987) An empirical comparison of alternative methods for principal component extraction. Journal of Business Research, 15(2): 173-190
Jackson, D.A. (1993) Stopping Rules in Principal Components Analysis: A Comparison of Heuristical and Statistical Approaches. Ecology, 74(8): 2204
Josse, J., Husson, F. (2012) Selecting the number of components in principal component analysis using cross-validation approximations. Computational Statistics & Data Analysis, 56(6): 1869-1879
Ledesma, R.D., Valero-Mora, P. (2007) Determining the Number of Factors to Retain in EFA: an easy-to- use computer program for carrying out Parallel Analysis. Practical Assessment. Research & Evaluation, 12(2)
Lorenzo-Seva, U., Timmerman, M.E., Kiers, H.A.L. (2011) The Hull Method for Selecting the Number of Common Factors. Multivariate Behavioral Research, 46(2): 340-364
Mulaik, S.A. (1972) The foundations of factor analysis. New York, itd: McGraw-Hill
O’connor, B.P. (2000) SPSS and SAS programs for determining the number of components using parallel analysis and Velicer’s MAP test. Behavior Research Methods, Instruments, & Computers, 32(3): 396-402
Peres-Neto, P.R., Jackson, D.A., Somers, K.M. (2005) How many principal components? stopping rules for determining the number of non-trivial axes revisited. Computational Statistics & Data Analysis, 49(4): 974-997
R Core Team (2013) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vol. 1,
Raîche, G., Walls, T.A., Magis, D., Riopel, M., Blais, J. (2013) Non-Graphical Solutions for Cattell’s Scree Test. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 9(1): 23-29
Rawelle, W. (2013) Psych: Procedures for personality and psychological research. Evanston, Illinois, USA: Northwestern University, Version 1. 3. 2.,
Tucker, L.R., Koopman, R.F., Linn, R.L. (1969) Evaluation of factor analytic research procedures by means of simulated correlation matrices. Psychometrika, 34(4): 421-459
Velicer, W.F., Eaton, C.A., Fava, J.L. (2000) Construct explication through factor or component analysis: A review and evaluation of alternative procedures for determining the number of factors or components
Velicer, W.F. (1976) Determining the number of components from the matrix of partial correlations. Psychometrika, 41(3): 321-327
Velicer, W.F., Jackson, D.N. (1990) Component Analysis versus Common Factor Analysis: Some issues in Selecting an Appropriate Procedure. Multivariate Behavioral Research, 25(1): 1-28
Wilderjans, T.F., Ceulemans, E., Meers, K. (2013) CHull: A generic convex-hull-based model selection method. Behavior Research Methods, 45(1): 1-15
Zwick, W.R., Velicer, W.F. (1982) Factors Influencing Four Rules For Determining The Number Of Components To Retain. Multivariate Behavioral Research, 17(2): 253-269
Zwick, W.R., Velicer, W.F. (1986) Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99(3): 432-442