Parallel analysis with unidimensional binary data

Educational and Psychological Measurement

Volumn 65, Issue 5, 2005, Pages 791-810

  Weng, Li Jen ^a   Cheng, Chung Ping ^a,b  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^b KAOHSIUNG MEDICAL UNIVERSITY   (Taiwan)

Author keywords

Dichotomous variables; Factor analysis; Number of factors; Parallel analysis; Unidimensionality

Indexed keywords

EID: 27144446688     PISSN: 00131644     EISSN: None     Source Type: Journal    
DOI: 10.1177/0013164404273941     Document Type: Review

References (44)

1. Allen, S. J., & Hubbard, R. (1986). Regression equations for the latent roots of random data correlation matrices with unities on the diagonal. Multivariate Behavioral Research, 21, 393-398.
2. Bentler, P. M. (1995). EQS structural equations program manual. Encino, CA: Multivariate Software.
3. Bernstein, I. H., & Teng, G. (1989). Factoring items and factoring scales are different: Spurious evidence for multidimensionality due to item categorization. Psychological Bulletin, 105, 467-477.
4. Budescu, D. V., Cohen, Y., & Ben-Simon, A. (1997). A revised modified parallel analysis for the construction of unidimensional item pools. Applied Psychological Measurement, 21, 233-252.
5. Buja, A., & Eyuboglu, N. (1992). Remarks on parallel analysis. Multivariate Behavioral Research, 27, 509-540.
6. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.
7. Collins, L. M., Cliff, N., McCormick, D. J., & Zatkin, J. L. (1986). Factor recovery in binary data sets: A simulation. Multivariate Behavioral Research, 21, 377-391.
8. Comrey, A. L., & Lee, H. B. (1992). A first course in factor analysis (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.
9. Cota, A. A., Longman, R. S., Holden, R. R., Fekken, G. C., & Xinaris, S. (1993). Interpolating 95th percentile eigenvalues from random data: An empirical example. Educational and Psychological Measurement, 53, 585-596.
10. Drasgow, F., & Lissak, R. I. (1983). Modified parallel analysis: A procedure for examining the latent dimensionality of dichotomously scored item responses. Journal of Applied Psychology, 68, 363-373.
11. Enzmann, D. (1997). RanEigen: A program to determine the parallel analysis criterion for the number of principal components. Applied Psychological Measurement, 21, 232.
12. 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, 272-299.
13. Ford, J. K., MacCallum, R. C., & Tait, M. (1986). The application of exploratory factor analysis in applied psychology: A critical review and analysis. Personnel Psychology, 39, 291-314.
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. Hillsdale, NJ: Lawrence Erlbaum.
16. Green, S. B. (1983). Identifiability of spurious factors using linear factor analysis with binary items. Applied Psychological Measurement, 7, 139-147.
17. Harman, H. H. (1976). Modern factor analysis (3rd ed.). Chicago: University of Chicago Press.
18. Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30, 1179-1185.
19. Humphreys, L. G., & Ilgen, D. (1969). Note on a criterion for the number of common factors. Educational and Psychological Measurement, 29, 571-578.
20. Humphreys, L. G., & Montanelli, R. G., Jr. (1975). An investigation of the parallel analysis criterion for determining the number of common factors. Multivariate Behavioral Research, 10, 193-205.
21. Kaufman, J. D., & Dunlap, W. P. (2000). Determining the number of factors to retain: A Windows-based FORTRAN-IMSL program for parallel analysis. Behavior Research Methods, Instruments, and Computers, 32, 389-395.
22. Keeling, K. B. (2000). A regression equation for determining the dimensionality of data. Multivariate Behavioral Research, 35, 457-468.
23. Lautenschlager, G. J. (1989a). A comparison of alternatives to conducting Monte Carlo analyses for determining parallel analysis criteria. Multivariate Behavioral Research, 24, 365-395
24. Lautenschlager, G. J. (1989b). PARANAL.TOK: A program for developing parallel analysis criteria. Applied Psychological Measurement, 13, 176.
25. Lautenschlager, G. J., Lance, C. E., & Flaherty, V. L. (1989). Parallel analysis criteria: Revised equations for estimating the latent roots of random data correlation matrices. Educational and Psychological Measurement, 49, 339-345.
26. Longman, R. S., Cota, A. A., Holden, R. R., & Fekken, G. C. (1989a). PAM: A double-precision FORTRAN routine for the parallel analysis method in principal components analysis. Behavior Research Methods, Instruments, and Computers, 21, 477-480.
27. Longman, R. S., Cota, A. A., Holden, R. R., & Fekken, G. C. (1989b). A regression equation for the parallel analysis criterion in principal components analysis: Mean and 95th percentile eigenvalues. Multivariate Behavioral Research, 24, 59-69.
28. MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Sample size in factor analysis. Psychological Methods, 4, 84-99.
29. Montanelli, R. G., Jr., & Humphreys, L. G. (1976). Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A Monte Carlo study. Psychometrika, 41, 341-348.
30. 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, and Computers, 32, 396-402.
31. Parry, C. D. H., & McArdle, J. J. (1991). An applied comparison of methods for least-squares factor analysis of dichotomous variables. Applied Psychological Measurement, 15, 35-46.
32. Reilly, A., & Eaves, R. C. (2000). Factor analysis of the Minnesota Infant Development Inventory based on a Hispanic migrant population. Educational and Psychological Measurement, 60, 271-285.
33. Roznowski, M., Tucker, L. R., & Humphreys, L. G. (1991). Three approaches to determining the dimensionality of binary items. Applied Psychological Measurement, 15, 109-127.
34. Sarff, P. L. (1997). Using factor replicability to evaluate number of factors rules. Dissertation Abstracts International, Section B: The Sciences & Engineering, 58(4-B), 2175.
35. SAS Institute Inc. (1999). SAS/IML user's guide, Version 8. Cary, NC: Author.
36. Thompson, B., & Daniel, L. G. (1996). Factor analytical evidence for the construct validity of scores: A historical overview and some guidelines. Educational and Psychological Measurement, 56, 197-208.
37. Turner, N. E. (1998). The effect of common variance and structure pattern on random data eigenvalues: Implications for the accuracy of parallel analysis. Educational and Psychological Measurement, 58, 541-568.
38. 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. In R. D. Goffin & E. Helmes (Eds.), Problems and solutions in human assessment: Honoring Douglas N. Jackson at seventy (pp. 41-71). Norwell, MA: Kluwer Academic.
39. Velicer, W. F., & Fava, J. L. (1998). Effects of variable and subject sampling on factor pattern recovery. Psychological Methods, 3, 231-251.
40. Wang, C.-N. (2001). Effect of number of response categories and scale distribution on factor analysis. Unpublished master's thesis, National Taiwan University, Taipei, Taiwan.
41. Wang, C.-N., & Weng, L.-J. (2002). Evaluating the use of exploratory factor analysis in Taiwan: 1993-1999. Chinese Journal of Psychology, 44, 239-251.
42. Weng, L.-J. (1995). An overview of applications of factor analysis. In Y.-H. Chang, Y.-C. Fu, & H.-Y. Chiu (Eds.), Social survey and analysis: The first interdisciplinary symposium on research methods in the social sciences (pp. 245-265). Taipei, Taiwan: Institute of Ethnology, Academia Sinica.
43. Wothke, W. (1993). Nonpositive definite matrices in structural modeling. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 256-293). Newbury Park, CA: Sage.
44. Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432-442.