Testing model nesting and equivalence

Psychological Methods

Volumn 15, Issue 2, 2010, Pages 111-123

  Bentler, Peter M ^a   Satorra, Albert ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b DEPARTMENT OF ECONOMICS AND BUSINESS   (Spain)

Author keywords

Covariance structure models; Equivalent models; Nested models; NET; Structural equation models

Indexed keywords

ARTICLE; COMPUTER GRAPHICS; HUMAN; MATHEMATICAL COMPUTING; PSYCHOLOGICAL MODEL; PSYCHOLOGY; PSYCHOMETRY; REPRODUCIBILITY; STATISTICAL ANALYSIS; STATISTICAL MODEL; STATISTICS; STATISTICS AND NUMERICAL DATA;

COMPUTER GRAPHICS; DATA INTERPRETATION, STATISTICAL; HUMANS; MATHEMATICAL COMPUTING; MODELS, PSYCHOLOGICAL; MODELS, STATISTICAL; PSYCHOLOGY; PSYCHOMETRICS; REPRODUCIBILITY OF RESULTS;

EID: 77955579027     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0019625     Document Type: Article

References (37)

1. Bekker P.A., Merckens A., Wansbeek T.J. Identification, equivalent models, and computer algebra 1994, Academic, London, England.
2. Bentler P.M. Comparative fit indexes in structural models. Psychological Bulletin 1990, 107:238-246.
3. Bentler P.M. EQS 6 structural equations program manual 2006, Multivariate Software, Encino, CA.
4. Bentler P.M., Bonett D.G. Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin 1980, 88:588-606.
5. Bentler P.M., Freeman E.H. Tests for stability in linear structural equation systems. Psychometrika 1983, 48:143-145.
6. Byrne B.M. Structural equation modeling with EQS: Basic concepts, applications, and programming 2006, Erlbaum, Mahwah, NJ. 2nd ed.
7. Cai L. SEM of another flavour: Two new applications of the supplemented EM algorithm. British Journal of Mathematical and Statistical Psychology 2008, 61:309-329.
8. Henley A.B., Shook C.L., Peterson M. The presence of equivalent models in strategic management research using structural equation modeling: Assessing and addressing the problem. Organizational Research Methods 2006, 9:516-535.
9. Hershberger S.L. The specification of equivalent models before the collection of data. Latent variables analysis 1994, 68-108. Sage, Thousand Oaks, CA. A. von Eye, C.C. Clogg (Eds.).
10. Hershberger S.L. The problem of equivalent structural models. Structural equation modeling: A second course 2006, 13-41. Information Age, Greenwich, CT. G.R. Hancock, R.O. Mueller (Eds.).
11. Kline R.B. Principles and practice of structural equation modeling 2005, Guilford, New York, NY.
12. Lee S., Hershberger S. A simple rule for generating equivalent models in covariance structure modeling. Multivariate Behavioral Research 1990, 25:313-334.
13. Luijben T.C. Equivalent models in covariance structure analysis. Psychometrika 1991, 56:653-665.
14. MacCallum R.C., Wegener D.T., Uchino B.N., Fabrigar L.R. The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin 1993, 114:185-199.
15. Mair P., Wu E., Bentler P.M. EQS goes R: Simulations for SEM using the package REQS. Structural Equation Modeling 2010, 17:333-349.
16. Markus K. Statistical equivalence, semantic equivalence, eliminative induction, and the Raykov-Marcoulides proof of infinite equivalence. Structural Equation Modeling 2002, 9:503-522.
17. Meece J.L., Blumenfeld P.C., Hoyle R.H. Students' goal orientations and cognitive engagement in classroom activities. Journal of Educational Psychology 1988, 80:514-523.
18. Mulaik S.A. Linear causal modeling with structural equations 2009, Chapman & Hall/CRC, Boca Raton, FL.
19. Raykov T., Marcoulides G.A. Can there be infinitely many models equivalent to a given covariance structure model?. Structural Equation Modeling 2001, 8:142-149.
20. Raykov T., Marcoulides G.A. A first course in structural equation modeling 2006, Erlbaum, Mahwah, NJ.
21. Raykov T., Marcoulides G.A. Equivalent structural equation models: A challenge and responsibility. Structural Equation Modeling 2007, 14:695-700.
22. Raykov T., Penev S. On structural equation model equivalence. Multivariate Behavioral Research 1999, 34:199-244.
23. Raykov T., Penev S. The problem of equivalent structural equation models: An individual residual perspective. New developments and techniques in structural equation modeling 2001, 297-322. Erlbaum, Mahwah, NJ. G.A. Marcoulides, R.E. Schumacker (Eds.).
24. R: A language and environment for statistical computing 2009, R Development Core Team, Available from http://www.R-project.org.
25. Rigdon E.E. The equal correlation baseline model for comparative fit assessment in structural equation modeling. Structural Equation Modeling 1998, 5:63-77.
26. Rindskopf D. Using phantom and imaginary latent variables to parameterize constraints in linear structural models. Psychometrika 1984, 49:37-47.
27. Satorra A. Alternative test criteria in covariance structure analysis: A unified approach. Psychometrika 1989, 54:131-151.
28. Savalei V., Bentler P.M. A two-stage approach to missing data: Theory and application to auxiliary variables. Structural Equation Modeling 2009, 16:477-497.
29. Sobel M.E., Bohrnstedt G.W. Use of null models in evaluating the fit of covariance structure models. Sociological methodology 1985, 152-178. Jossey Bass, San Francisco, CA. N.B. Tuma (Ed.).
30. Spivak M. Calculus on manifolds 1965, Perseus Books, Reading, MA.
31. Steiger J.H., Shapiro A., Browne M.W. On the multivariate asymptotic distribution of sequential chi-square statistics. Psychometrika 1985, 50:253-264.
32. Stelzl I. Changing a causal hypothesis without changing the fit: Some rules for generating equivalent path models. Multivariate Behavioral Research 1986, 21:309-331.
33. Votaw D.F. Testing compound symmetry in a normal multivariate distribution. Annals of Mathematical Statistics 1948, 19:447-473.
34. Widaman K.F., Thompson J.S. On specifying the null model for incremental fit indices in structural equation modeling. Psychological Methods 2003, 8:16-37.
35. Yuan K.-H., Bentler P.M. Three likelihood-based methods for mean and covariance structure analysis with nonnormal missing data. Sociological Methodology 2000, 30:165-200.
36. Yuan K.-H., Lu L. SEM with missing data and unknown population distributions using two-stage ML: Theory and its application. Structural Equation Modeling 2008, 43:621-652.
37. Yung Y.-F., Bentler P.M. Bootstrapping techniques in analysis of mean and covariance structures. Advanced structural equation modeling techniques 1996, 195-226. LEA, Hillsdale, NJ. G.A. Marcoulides, R.E. Schumacker (Eds.).