Subject-Centered Scalability: The Sine Qua Non of Summated Ratings

Psychological Methods

Volumn 14, Issue 3, 2009, Pages 258-274

  Drewes, Donald W ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

reliability; scalability; scale construction; summated rating scales; unit rank

Indexed keywords

ARTICLE; FACTORIAL ANALYSIS; HUMAN; NORMAL DISTRIBUTION; PSYCHOLOGIC TEST; PSYCHOLOGY; PSYCHOMETRY; REPRODUCIBILITY; STATISTICAL MODEL; STATISTICS;

FACTOR ANALYSIS, STATISTICAL; HUMANS; MODELS, STATISTICAL; NORMAL DISTRIBUTION; PSYCHOLOGICAL TESTS; PSYCHOLOGY; PSYCHOMETRICS; REPRODUCIBILITY OF RESULTS;

EID: 70249140276     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0016621     Document Type: Article

References (91)

1. Anderson J.C., and Gerbing D.W. Structural equation modeling in practice: A review and recommended two-step approach. Psychological Bulletin 103 (1988) 411-423
2. Anderson T.W. An introduction to multivariate statistical analysis. 2nd ed. (1984), Wiley, New York
3. Andrich D. An elaboration of Guttman scaling with Rasch models for measurement. Sociological Methodology 15 (1985) 33-80
4. Babakus E., Ferguson C.E., and Jöreskog K.G. The sensitivity of confirmatory maximum likelihood factor analysis to violations of measurement scale and distributional assumptions. Journal of Marketing Research 24 (1987) 222-228
5. Bentler P.M. EQS: Structural equations program manual (Version 3.0) (1989), BMDP Statistical Software, Los Angeles
6. Bentler P.M., and Bonett D.G. Significance tests and goodness-of-fit in the analysis of covariance structure. Psychological Bulletin 88 (1980) 588-606
7. Bentler P.M., and Chou C. Practical issues in structural modeling. Sociological Methods & Research 16 (1987) 78-117
8. Bishir J.W., and Drewes D.W. Mathematics in the behavioral and social sciences (1970), Harcourt, Brace & World, New York
9. Bollen K.A. Structural equations with latent variables (1989), Wiley, New York
10. Bollen K.A., and Ting K. Confirmatory tetrad analysis. In: Marsden P.V. (Ed). Sociological methodology 23 (1993), Blackwell, Cambridge, MA 147-175
11. Bollen K.A., and Ting K. Bootstrapping a test statistic for vanishing tetrads. Sociological Methods & Research 27 (1998) 77-102
12. Borsboom D., Mellenbergh G.J., and van Heerden J. The theoretical status of latent variables. Psychological Review 110 (2003) 203-219
13. Brown T.A., and Barlow D.H. Dimensional versus categorical classification of mental disorders in the fifth edition of the Diagnostic and Statistical Manual of Mental Disorders and beyond: Comment on the special section. Journal of Abnormal Psychology 114 (2005) 551-556
14. Browne E.T. Introduction to theory of determinants and matrices (1958), University of North Carolina Press, Chapel Hill
15. Browne M.W., and Cudeck R. Alternate ways of assessing model fit. In: Bollen K.A., and Long J.S. (Eds). Testing structural equation models (1993), Sage, Newbury Park, CA 136-162
16. Browne M.W., and Mels G. Path analysis: RAMONA. SYSTAT 9.0 for Windows: Statistics (1999), SPSS, Chicago 607-665
17. Cliff N. Abstract measurement theory and the revolution that never happened. Psychological Science 3 (1992) 186-190
18. Cohen J., Cohen P., West S.G., and Aiken L.S. Applied multiple regression/correlation analysis for the behavioral sciences. 3rd ed. (2003), Erlbaum, Mahwah, NJ
19. Colman A.M. A dictionary of psychology. 2nd ed. (2006), Oxford University Press, New York
20. Coombs C.H., Dawes R.M., and Tversky A. Mathematical psychology: An elementary introduction (1970), Prentice-Hall, Englewood Cliffs, NJ
21. Cortina J.M. What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology 78 (1993) 98-104
22. Crano W.D., and Brewer M.B. Principles of research in social psychology (1973), McGraw-Hill, New York
23. Cronbach L.J. Coefficient alpha and the internal structure of tests. Psychometrika 16 (1951) 297-334
24. Cudeck R., and Browne M.W. Cross-validation of covariance structures. Multivariate Behavioral Research 18 (1983) 147-167
25. Curran P.J., West S.G., and Finch J.F. The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods 1 (1996) 16-29
26. Dawes R. Psychological measurement. Psychological Review 101 (1994) 278-281
27. Dawis R.V. Scale construction. Journal of Counseling Psychology 34 (1987) 481-489
28. DeCarlo L.T. On the meaning and use of kurtosis. Psychological Methods 2 (1997) 292-307
29. DeCoster J. Scale construction notes (2005). http://www.stat-help.com/scale.pdf Retrieved January 26, 2009, from http://www.stat-help.com/scale.pdf
30. DeVellis R.F. Scale development: Theory and application (1991), Sage, Newbury Park, NJ
31. Drewes D.W. Beyond the Spearman-Brown: A structural approach to maximal reliability. Psychological Methods 5 (2000) 214-227
32. Embretson S.E., and Reise S.P. Item response theory for psychologists (2000), Erlbaum, Mahwah, NJ
33. Garnett J.C.M. On certain independent factors in mental measurement. Proceedings of the Royal Society of London, Series A 96 (1919) 91-111
34. Garson G.D. Factor analysis (2009). http://faculty.chass.ncsu.edu/garson/PA765/factor.htm Retrieved April 13, 2009, from http://faculty.chass.ncsu.edu/garson/PA765/factor.htm
35. Gerbing D.W., and Anderson J.C. An updated paradigm for scale development incorporating unidimensionality and its assessment. Journal of Marketing Research 25 (1988) 186-192
36. Glymour C., Scheines R., Sprites P., and Kelley K. Discovering causal structure: Artificial intelligence, philosophy of science, and statistical modeling (1987), Academic Press, Orlando, FL
37. Green S.B., Lissitz R.W., and Mulaik S.A. Limitations of coefficient alpha as an index of test undimensionality. Educational and Psychological Measurements 37 (1977) 827-838
38. Guilford J.P. Psychometric methods. 2nd ed. (1954), McGraw-Hill, New York
39. Gulliksen H. Theory of mental tests (1950), Wiley, New York
40. Guttman L. The irrelevance of factor analysis for the study of group differences. Multivariate Behavioral Research 27 (1992) 175-204
41. Hattie J. Methodology review: Assessing unidimensionality of tests and items. Applied Psychological Measurement 9 (1985) 139-164
42. Hipp J.R., Bauer D.J., and Bollen K.A. Conducting tetrad tests of model fit and contrasts of tetrad-nested models: A new SAS macro. Structural Equation Modeling 12 (2005) 76-93
43. Holzinger K. Statistical resume of the Spearman two-factor theory (1930), University of Chicago Press, Chicago
44. Horst P. Psychological measurement and prediction (1966), Wadsworth, Belmont, CA
45. Jöreskog K.G. A general approach to confirmatory maximum likelihood factor analysis. Psychometrika 34 (1969) 183-202
46. Jöreskog K.G. Statistical analysis of sets of congeneric tests. Psychometrika 36 (1971) 109-133
47. Jöreskog K.G., and Sörbom D. LISREL 8: User's reference guide (1996), Scientific International, Chicago
48. Kelley T. Crossroads in the mind of man (1928), Stanford University Press, Stanford, CA
49. Kenny D.A. Correlation and causality (1979), Wiley, New York
50. Khattree R., and Naik D.N. Applied multivariate statistics with SAS software. 2nd ed. (1999), SAS Institute, Cary, NC
51. Krantz D.H., Luce R.D., Suppes P., and Tversky A. Foundations of measurement 1 (1971), Academic Press, New York
52. Lei M., and Lomax R.G. The effect of varying degrees of nonnormality in structural equation modeling. Structural Equation Modeling 12 (2005) 1-27
53. Lindley D.V. Introduction to probability from a Bayesian point of view (1965), Cambridge University Press, Cambridge, England
54. Littell R.C., Milliken G.A., Stroup W.W., and Wolfinger R.D. SAS system for mixed models (1996), SAS Institute, Cary, NC
55. Little T.D., Lindenberger U., and Nesselroade J.R. On selecting indicators for multivariate measurement and modeling with latent variables: When "good" indicators are bad and "bad" indicators are good. Psychological Methods 4 (1999) 192-211
56. Lord F.M., and Novick M.R. Statistical theories of mental test scores (1968), Addison-Wesley, Reading, MA
57. Luce R.D., Krantz D.H., Suppes P., and Tversky A. Foundations of measurement: Vol. III. Representation, axiomatization, and invariance (1990), Academic Press, San Diego, CA
58. Luce R.D., and Tukey J.W. Simultaneous conjoint measurement: A new type of fundamental measurement. Journal of Mathematical Psychology 1 (1964) 1-27
59. MacCallum R.C., Widaman K.F., Zhang S., and Hong S. Sample size in factor analysis. Psychological Methods 4 (1999) 84-99
60. MacCallum R.C., Zhang S., Preacher K.J., and Rucker D.D. On the practice of dichotomization of quantitative variables. Psychological Methods 7 (2002) 19-40
61. Marcoulides G.A., and Saunders C. PLS: A silver bullet?. MIS Quarterly 30 2 (2006) iii-ix
62. Marsh H.W., Hau K., Balla J.R., and Grayson D. Is more ever too much? The number of indicators per factor in confirmatory factor analysis. Multivariate Behavioral Research 33 (1998) 181-220
63. Marsh H.W., Hau K., and Wen Z. In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler's (1999) findings. Structural Equation Modeling 11 (2004) 320-341
64. McAlister-Kizzier D.L. Survey methods in education research (1998). http://unl.edu/kizzier/900D/powerpoint/attitude/sld013.htm Retrieved January 26, 2009, from University of Nebraska-Lincoln Web site: http://unl.edu/kizzier/900D/powerpoint/attitude/sld013.htm
65. McDonald R.P. The dimensionality of tests and items. British Journal of Mathematical and Statistical Psychology 34 (1981) 100-117
66. Michell J. Normal science, pathological science and psychometrics. Theory & Psychology 10 (2000) 639-667
67. Montgomery D.C., Peck E.A., and Vining G.G. Introduction to linear regression analysis. 4th ed. (2006), Wiley, Hoboken, NJ
68. Murphy K.R., and Davidshofer C.O. Psychological testing: Principles and applications. 6th ed. (2005), Pearson Prentice Hall, Upper Saddle River, NJ
69. Muthén L.K., and Muthén B.O. Mplus users guide. 5th ed. (1998-2008), Authors, Los Angeles
70. Norman G.R., and Streiner D.L. Biostatistics: The bare essentials (1994), Mosby, St. Louis, MO
71. Nunnally J.C. Introduction to psychological measurement (1970), McGraw-Hill, New York
72. Osburn H.G. Coefficient alpha and related internal consistency reliability coefficients. Psychological Methods 5 (2000) 343-355
73. Pearl J. Causality: Models, reasoning, and inference (2000), Cambridge University Press, Cambridge, England
74. Raubenheimer J.E. An item selection procedure to maximize scale reliability and validity. South African Journal of Industrial Psychology 30 (2004) 59-64
75. SAS Institute. SAS/STAT user's guide (Version 6, 4th ed., Vols. 1-2) (1990), Author, Cary, NC
76. Schmitt N. Uses and abuses of coefficient alpha. Psychological Assessment 8 (1996) 350-353
77. Segars A.H. Assessing the unidimensionality of measurement: A paradigm and illustration within the context of information systems research. Omega: The International Journal of Management Science 25 (1997) 107-121
78. Spearman C. General intelligence objectively determined and measured. American Journal of Psychology 15 (1904) 201-292
79. Spearman C. The abilities of man (1927), Macmillan, New York
80. Spector P.E. Summated rating scale construction: An introduction (1992), Sage, Newbury Park, CA
81. Sprites P., Glymour C., and Scheines R. Causation, prediction, and search (1993), Springer-Verlag, New York
82. Sprites P., Scheines R., Meek C., Richardson T., Glymour C., Hoijtink H., et al. TETRAD 3: Tools for causal modeling. User's manual (2009). http://www.phil.cmu.edu/projects/tetrad/tetrad3.html Retrieved January 26, 2009, from Carnegie Mellon Web site: http://www.phil.cmu.edu/projects/tetrad/tetrad3.html
83. Srinivasan V., and Basu A.K. The metric quality of ordered categorical data. Marketing Science 8 (1989) 205-230
84. Steiger J.H. Structural equation modeling. STATISTICA for Windows (Vol. III): Statistics II. 2nd ed. (1995), StatSoft, Tulsa, OK 3539-3688
85. Suppes P., Krantz D.H., Luce R.D., and Tversky A. Foundations of measurement: Vol. II. Geometrical, threshold, and probability representations (1989), Academic Press, San Diego, CA
86. Suppes P., and Zinnes J.L. Basic measurement theory. In: Luce R.D., Bush R.R., and Galanter E. (Eds). Handbook of mathematical psychology 1 (1963), Wiley, New York 1-76
87. Sutcliffe J.P. A probability model for errors of classification. I: General considerations. Psychometrika 30 (1965) 73-96
88. ten Holt J.C., van Duijn M.A., and Boomsma A. Scale construction and evaluation in practice: Factor analysis versus item response theory (2008). http://www.fordham.edu/academics/programs_at_fordham_/psychology/sychometrics/pdf/FCAP_PPT/tenHolt.pdf Retrieved January 26, 2009, from http://www.fordham.edu/academics/programs_at_fordham_/psychology/sychometrics/pdf/FCAP_PPT/tenHolt.pdf
89. Thomas H. IQ, interval scales, and normal distributions. Psychological Bulletin 91 (1982) 198-202
90. Torgerson W.S. Theory and methods of scaling (1958), Wiley, New York
91. Yu C. Evaluating cutoff criteria of model fit indices for latent variable models with binary and continuous outcomes (2002). http://www.statmodel.com/download/Yudissertation.pdf Retrieved January 26, 2009, from http://www.statmodel.com/download/Yudissertation.pdf