The influence of reliability on four rules for determining the number of components to retain

Journal of Modern Applied Statistical Methods

Volumn 5, Issue 2, 2006, Pages 332-343

  Kanyongo, Gibbs Y ^a  

^a DUQUESNE UNIVERSITY   (United States)

Author keywords

Factor analysis; Kaiser rule; Modified Horn's parallel analysis; Monte Carlo; Parallel analysis; Principal components analysis; Scree plot

Indexed keywords

EID: 48349111275     PISSN: 15389472     EISSN: 15389472     Source Type: Journal    
DOI: 10.22237/jmasm/1162353960     Document Type: Article

References (39)

1. Brooks, G. P. (2002). MNDG. http://oak.cats.ohiou.edu.edu/~brooksg/mndg. htm.
2. Brooks, G. P., Barcikowski, R. S., & Robey, R. R. (1999). Monte Carlo simulation for perusal and practice. A paper presented at the meeting of the American Educational Research Association, Montreal, Quebec, Canada. (ERIC Document Reproduction Service No. ED449178).
3. Buja, A., & Eyuboglu, N. (1992) Remarks on parallel aalysis. Multivariate Behavioral Research, 27, 509-540.
4. Cattell, R. B. (1958). Extracting the correct number of factors in factor analysis. Educational and Psychological Measurement, 18, 791-838.
5. Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1, 245-276.
6. Cattell, R. B., & Jaspers, J. (1967). A general plasmode for factor analytic exercises and research. Multivariate Behavioral Research Monographs, 3, 1-212.
7. Cattell, R. B., & Volgemann, S. A. (1977). A comprehensive trial of the scree and Kaiser-Guttman criteria for determining the number of factors. Multivariate Behavioral Research, 12, 289-325.
8. Cliff, N. (1970). The relation between sample and population characteristics vectors. Psychometrika, 35, 163-178.
9. Cliff, N. (1988). The eigenvalues-greater-than-one rule and the reliability of components. Psychological Bulletin, 103, 276-279.
10. Comrey, A.L. (1973). A first course in factor analysis. New York: Plenum Press.
11. Cota, A. A., Longman, R. S., Holden, R. R., & Fekken, G. C. (1993). Comparing different methods for implementing parallel analysis: A practical index of accuracy. Educational and Psychological Measurement, 53, 865-877.
12. Fava, J. L., & Velicer, W. F. (1992). The effects of overextraction on factor and component analysis. Multivariate Behavioral Research, 27, 387-415.
13. Fava, J. L., & Velicer, W. F. (1996). The effects of underextraction in factor and component analysis. Educational and Psychological Measurement, 56, 907-29.
14. Glorfeld, L. W. (1995). An improvement on Horn's parallel analysis methodology for selecting the correct number of factors to retain. Educational and Psychological Measurement, 55, 377-393.
15. Gorsuch, R. L. (1983). Factor analysis (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.
16. Guadagnoli, E., & Velicer, W. F. (1988). Relation of sample size to the stability of component patterns. Psychological Bulletin, 103, 265-275.
17. Guttman, L. (1954). Some necessary conditions for common factor analysis. Psychometrika, 19, 149-162.
18. Hakstian, A. R., Rogers, W. T., & Cattell, R. B. (1982). The behavior of number-of-factors rules with simulated data. Multivariate Behavioral Research, 17, 193-219.
19. Harshman, R. A., & Reddon, J. R. (1983). Determining the number of factors by comparing real with random data: A serious flaw and some possible corrections. Applied Psychological Measurement, 9, 14-15.
20. Henson, R.K. (2001). Understanding internal consistency reliability estimates: A conceptual primer on coefficient alpha. Measurement and Evaluation in Counseling and Development, 34, 177-189.
21. 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, 727-730.
22. Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30, 179-185.
23. Hutcheson, G., & Sofroniou, N. (1999). The multivariate social scientist. Thousand Oaks, CA: Sage Publications.
24. Hutchinson, S. R., & Bandalos, D. L. (1997). A guide to Monte Carlo simulation research for applied researchers. Journal of Vocational Education Research, 22, 233-245.
25. Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20, 141-151.
26. Kuder, G. F., & Richardson, M. W. (1937). The theory of estimation of test reliability. Psychometrika, 2, 151-160.
27. Linn, R. L. (1968). A Monte Carlo approach to the number of factors problem. Psychometrika, 33, 37-71.
28. McMillan, J. H., & Schumacher, S. (2001). Research in Education: A conceptual introduction. (5th ed.). San Francisco, CA: Addison Wesley Longman.
29. Merenda, F. P. (1997). A Guide to the proper use of factor analysis in the conduct and reporting of research: Pitfalls to avoid. Measurement and Evaluation in Counselling and Development, 30, 156-164.
30. Moiser, C. I. (1939). Influence of chance error on simple structure: An empirical investigation of the effect of chance error and estimated communalities on simple structure in factorial analysis. Psychometrika, 4, 33-44.
31. Mooney, C. Z. (1997). Monte Carlo simulation (Sage University Paper series on Quantitative Applications in the Social Sciences, series no. 07-116). Thousand Oaks, CA: Sage.
32. 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, 396-402.
33. Stevens, J. (2002). Applied multivariate statistics for the social sciences. Mahwah. NJ: Lawrence Erlbaum Associates.
34. Tabachnick , B. G., & Fidell, L. S. (2001). Using multivariate statistics (4th ed.). Needham Heights., MA: Pearson.
35. Tucker, L. R., Koopman, R. F., & Linn, R. L. (1969). Evaluation of factor analytic research procedures by means of simulated correlation matrices. Psychometrika, 34, 421-459.
36. Tuckman, B. W. (1999). Conducting educational research (5th ed.). Orlando, FL: Harcourt Brace College.
37. Velicer, F. W., 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. In R. D. Goffin, & E. Helmes (Eds.), Problems and Solutions in Human Assessment (pp. 42-71). Boston: Kluwer Academic Publishers.
38. Zwick, R. W., & Velicer, W. F. (1982). Factors influencing four rules of determining the number of components to retain. Multivariate Behavioral Research, 17, 253-269.
39. Zwick, R. W., & Velicer, F. V. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432-442.