Covariance Structure Models for Maximal Reliability of Unit-Weighted Composites

Handbook of Latent Variable and Related Models

Volumn , Issue , 2007, Pages 1-19

  Bentler, Peter M ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 55449083601     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-044452044-9/50004-5     Document Type: Chapter

References (67)

1. Barchard K.A., Hakstian A.R. The effects of sampling model on inference with coefficient alpha. Educational & Psychological Measurement 1997, 57:893-905.
2. Becker G. Coefficient alpha: Some terminological ambiguities and related misconceptions. Psychological Reports 2000, 86:365-372.
3. Bentler P.M. Alpha-maximized factor analysis (Alphamax): Its relation to alpha and canonical factor analysis. Psychometrika 1968, 33:335-345.
4. Bentler P.M. A lower-bound method for the dimension-free measurement of internal consistency. Social Science Research 1972, 1:343-357.
5. Bentler P.M. Should coefficient alpha be replaced by model-based reliability coefficients? Invited address. Psychometric Society IMPS-2003, Cagliari, Italy 2003.
6. Bentler P.M. Maximal reliability for unit-weighted composites. UCLA Statistics Preprint No. 405 2004, Department of Statistics, UCLA.
7. Bentler, P.M. (In press). EQS 6 Structural Equations Program Manual. Multivariate Software. Encino, CA.
8. http://www.mvsoft.com.
9. Bentler P.M., Weeks D.G. Linear structural equations with latent variables. Psychometrika 1980, 45:289-308.
10. Bentler P.M., Woodward J.A. Inequalities among lower bounds to reliability: With applications to test construction and factor analysis. Psychometrika 1980, 45:249-267.
11. Bentler P.M., Woodward J.A. The greatest lower bound to reliability. Principals of Modern Psychological Measurement: A Festschrift for Frederic M. Lord 1983, 237-253. Erlbaum, Hillsdale, NJ. H. Wainer, S. Messick (Eds.).
12. Bollen K.A. Issues in the comparative measurement of political democracy. American Sociological Review 1980, 45:370-390.
13. Bonett D.G. Sample size requirement for testing and estimating coefficient alpha. Journal of Educational and Behavioral Statistics 2003, 27:335-340.
14. Choulakian V. The optimality of the centroid method. Psychometrika 2003, 68:473-475.
15. Cronbach L.J. Coefficient alpha and the internal structure of tests. Psychometrika 1951, 16:297-334.
16. della Riccia G., Shapiro A. Minimum rank and minimum trace of covariance matrices. Psychometrika 1982, 47:443-448.
17. Drewes D.W. Beyond the Spearman-Brown: A structural approach to maximal reliability. Psychological Methods 2000, 5:214-227.
18. Enders C.K. Using the expectation maximization algorithm to estimate coefficient alpha for scales with item-level missing data. Psychological Methods 2003, 8:322-337.
19. Enders C.K., Bandalos D.L. The effects of heterogeneous item distributions on reliability. Applied Measurement in Education 1999, 12:133-150.
20. Feldt L.S., Charter R.A. Estimating the reliability of a test split into two parts of equal or unequal length. Psychological Methods 2003, 8:102-109.
21. Green B.F. A note on the calculation of weights for maximum battery reliability. Psychometrika 1950, 15:57-61.
22. Green S.B. A coefficient alpha for test-retest data. Psychological Methods 2003, 8:88-101.
23. Green S.B., Hershberger S.L. Correlated errors in true score models and their effect on coefficient alpha. Structural Equation Modeling 2000, 7:251-270.
24. Hakstian A.R., Barchard K.A. Toward more robust inferential procedures for coefficient alpha under sampling of both subjects and conditions. Multivariate Behavioral Research 2000, 35:427-456.
25. Hancock G.R., Mueller R.O. Rethinking construct reliability. Structural Equation Modeling: Present and Future 2001, 195-216. Scientific Software International, Lincolnwood, IL. R. Cudeck, S. du Toit, D. Sörbom (Eds.).
26. Harman H. Modern Factor Analysis 1976, University of Chicago Press, Chicago. third ed.
27. Heise D.R., Bohrnstedt G.W. Validity, invalidity, and reliability. Sociological Methodology 1970 1970, 104-129. Jossey-Bass, San Francisco. E.F. Borgatta (Ed.).
28. Hogan P.H., Benjamin A., Brezinsky K.L. Reliability methods: A note on the frequency of use of various types. Educational and Psychological Measurement 2000, 60:523-531.
29. Jackson P.H., Agunwamba C.C. Lower bounds for the reliability of total scores on a test composed of nonhomogeneous items: I. Algebraic lower bounds. Psychometrika 1997, 42:567.
30. Jamshidian M., Bentler P.M. A quasi-Newton method for minimum trace factor analysis. Journal of Statistical Computation and Simulation 1998, 62:73-89.
31. Jamshidian M., Bentler P.M. ML estimation of mean and covariance structures with missing data using complete data routines. Journal of Educational and Behavioral Statistics 1999, 24:21-41.
32. Jöreskog K.G. Some contributions to maximum likelihood factor analysis. Psychometrika 1967, 32:443-482.
33. Jöreskog K.G. Statistical analysis of sets of congeneric tests. Psychometrika 1971, 36:109-133.
34. Kano Y., Azuma Y. Use of SEM programs to precisely measure scale reliability. New Developments in Psychometrics 2003, 141-148. Springer-Verlag, Tokyo. H. Yanai, A. Okada, Y. Shigemasu, J.J. Kano, K. Meulman (Eds.).
35. Komaroff E. Effect of simultaneous violations of essential tau-equivalence and uncorrelated error on coefficient alpha. Applied Psychological Measurement 1997, 21:337-348.
36. Ledermann W. On the rank of the reduced correlation matrix in multiple-factor analysis. Psychometrika 1937, 2:85-93.
37. Li H. A unifying expression for the maximal reliability of a linear composite. Psychometrika 1997, 62:245-249.
38. Li H., Rosenthal R., Rubin D.B. Reliability of measurement in psychology: From Spearman-Brown to maximal reliability. Psychological Methods 1996, 1:98-107.
39. Li L., Bentler P.M. The greatest lower bound to reliability: Corrected and resampling estimators 2004, Unpublished manuscript.
40. Liang J.-J., Bentler P.M. An EM algorthm for fitting two-level structural equation models. Psychometrika 2004, 69:101-122.
41. McDonald R.P. Factor Analysis and Related Methods 1985, Erlbaum, Hillsdale, NJ.
42. McDonald R.P. Test Theory: A Unified Treatment 1999, Erlbaum, Mahwah, NJ.
43. Miller M.B. Coefficient alpha: A basic introduction from the perspectives of classical test theory and structural equation modeling. Structural Equation Modeling 1995, 2:255-273.
44. Novick M.R., Lewis C. Coefficient alpha and the reliability of composite measurements. Psychometrika 1967, 32:1-13.
45. Osburn H.G. Coefficient alpha and related internal consistency reliability coefficients. Psychological Methods 2000, 5:343-355.
46. Rao C.R. Estimation and tests of significance in factor analysis. Psychometrika 1955, 20:93-111.
47. Raykov T. Scale reliability, Cronbach's coefficient alpha, and violations of essential tau-equivalence with fixed congeneric components. Multivariate Behavioral Research 1997, 32:329-353.
48. Raykov T. Coefficient alpha and composite reliability with interrelated nonhomogeneous items. Applied Psychological Measurement 1998, 22:375-385.
49. Raykov T. Bias of coefficient α for fixed congeneric measures with correlated errors. Applied Psychological Measurement 2001, 25:69-76.
50. Raykov T. Point and interval estimation of reliability for multiple-component measuring instruments via linear constraint covariance structure modeling. Structural Equation Modeling 2004, 11:342-356.
51. Raykov T. Estimation of maximal reliability: A note on a covariance structure modelling approach. British Journal of Mathematical and Statistical Psychology 2004, 57:21-27.
52. Raykov T., Shrout P.E. Reliability of scales with general structure: Point and interval estimation using a structural equation modeling approach. Structural Equation Modeling 2002, 9:195-212.
53. Schmidt F.L., Le H., Heus R. Beyond alpha: An empirical examination of the effects of different sources of measurement error on reliability estimates for measures of individual-differences constructs. Psychological Methods 2003, 8:206-224.
54. Schmitt N. Uses and abuses of coefficient alpha. Psychological Assessment 1996, 8:350-353.
55. Shapiro A. Rank reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis. Psychometrika 1982, 47:187-199.
56. Shapiro A. Weighted minimum trace factor analysis. Psychometrika 1982, 47:243-264.
57. Shapiro A., ten Berge J.M.F. The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability. Psychometrika 2000, 65:413-425.
58. Shapiro A., ten Berge J.M.F. Statistical inference of minimum rank factor analysis. Psychometrika 2002, 67:79-94.
59. Shevlin M., Miles J.N.V., Davies M.N.O., Walker S. Coefficient alpha: A useful indicator of reliability?. Personality Individual Differences 2000, 28:229-237.
60. Spearman C. "General intelligence", objectively determined and measured. American Journal of Psychology 1904, 15:201-293.
61. Spearman C. Demonstration of formulae for true measurement of correlation. American Journal of Psychology 1907, 18:161-169.
62. ten Berge J.M.F. Linking reliability and factor analysis: Recent developments in some classical psychometric problems. Advances in Personality Psychology 2000, vol. 1:138-156. Psychology Press/Taylor & Francis, Philadelphia. S.E. Hampson (Ed.).
63. ten Berge J.M.F., Kiers H.A.L. A numerical approach to the exact and the approximate minimum rank of a covariance matrix. Psychometrika 1991, 56:309-315.
64. ten Berge J.M.F., Sočan G. The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality. Psychometrika 2004, 69:613-625.
65. ten Berge J.M.F., Snijders T.A.B., Zegers F.E. Computational aspects of the greatest lower bound to reliability and constrained minimum trace factor analysis. Psychometrika 1981, 46:201-213.
66. Vautier S., Jmel S. Transient error or specificity? An alternative to the staggered equivalent split-half procedure. Psychological Methods 2003, 8:225-238.
67. H: Their relations with each other and two alternate conceptualizations of reliability. Psychometrika 2005, 70:1-11.