Multicollinearity and missing constraints: A comparison of three approaches for the analysis of latent nonlinear effects

Methodology

Volumn 4, Issue 2, 2008, Pages 51-66

  Kelava, Augustin ^a   Moosbrugger, Helfried ^a   Dimitruk, Polina ^a   Schermelleh Engel, Karin ^a  

^a GOETHE UNIVERSITY   (Germany)

Author keywords

Constraints; Interaction; Measurement error; Multicollinearity; Nonlinear structural equation models; Quadratic; Reliability

Indexed keywords

EID: 69949093695     PISSN: 16141881     EISSN: 16142241     Source Type: Journal    
DOI: 10.1027/1614-2241.4.2.51     Document Type: Article

References (38)

1. Ajzen, I. (1987). Attitudes, traits, and actions: Dispositional prediction of behavior in personality and social psychology. In L. Berkowitz (Ed.), Advances in experimental social psychology, Vol. 20 (Vol. 20, p. 1-63). New York: Academic Press.
2. Algina, J., & Moulder, B.C. (2001). A note on estimating the Jöreskog-Yang model for latent variable interaction using LIS-REL 8.3. Structural Equation Modeling, 8, 40-52.
3. Anderson, J.C., & Gerbing, D.W. (1988). Structural equation modeling in practice: A review and recommended two-step approach. Psychological Bulletin, 103, 411-423.
4. Arminger, G., & Muthén, B. (1998). A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the Metropolis-Hastings algorithm. Psychometrika, 63, 271-300.
5. Bohrnstedt, G.W., & Goldberger, A.S. (1969). On the exact covariance of products of random variables. American Statistical Association Journal, 64, 1439-1442.
6. Bollen, K.A. (1995). Structural equation models that are nonlinear in latent variables: A least squares estimator. Sociological Methodology, 1995, 223-251.
7. Busemeyer, J.R., & Jones, L.E. (1983). Analysis of multiplicative combination rules when the causal variables are measured with error. Psychological Bulletin, 93, 549-562.
8. Cronbach, L.J., & Snow, R.E. (1977). Aptitudes and instructional methods: A handbook for research on interactions. New York: Irvington.
9. Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Ser. B, 39, 1-38.
10. Dimitruk, P., Schermelleh-Engel, K., Kelava, A., & Moosbrugger, H. (in press). Challenges in nonlinear structural equation modeling. Methodology.
11. Fox, J. (2005). Structural equation modeling with the sem package in R. Retrieved on August 1, 2007, from http://cran.rproject.org/doc/ packages/sem.pdf
12. Ganzach, Y. (1997). Misleading interaction and curvilinear terms. Psychological Methods, 3, 235-247.
13. Grewal, R., Cote, J., & Baumgartner, H. (2004). Multicollinearity and measurement error in structural equation models: Implications for theory testing. Marketing Science, 23, 519-529.
14. Jaccard, J., & Wan, C. (1995). Measurement error in the analysis of interaction effects between continuous predictors using multiple regression: Multiple indicator indicator and structural equation approaches. Psychological Bulletin, 117, 348-357.
15. Jöreskog, K.G., & Sörbom, D. (1996). LISREL 8: User's Reference Guide. Lincolnwood, IL: Scientific Software International.
16. Jöreskog, K.G., & Sörbom, D. (1999). PRELIS 2: User's Reference Guide. Lincolnwood, IL: Scientific Software International.
17. Jöreskog, K.G., & Yang, F. (1996). Nonlinear structural equation models: The Kenny-Judd model with interaction effects. In G.A. Marcoulides & R.E. Schumacker (Eds.), Advanced structural equation modeling: Issues and techniques (pp. 57-87). Mahwah, NJ: Erlbaum.
18. Karasek, R. (1979). Job demands, job decision latitude, and mental strain: Implication for job redesign. Administrative Quarterly, 24, 285-307.
19. Kenny, D., & Judd, C.M. (1984). Estimating the nonlinear and interactive effects of latent variables. Psychological Bulletin, 96, 201-210.
20. Klein, A., & Moosbrugger, H. (2000). Maximum likelihood estimation of latent interaction effects with the LMS method. Psychometrika, 65, 457-474.
21. Klein, A., & Muthén, B. (in press). Quasi maximum likelihood estimation of structural equation models with multiple interaction and quadratic effects. Multivariate Behavioral Research.
22. Lee, S., Song, X., & Poon, W. (2004). Comparison of approaches in estimating interaction and quadratic effects of latent variables. Multivariate Behavioral Research, 39, 37-67.
23. Little, T., Bovaird, J., & Widaman, K. (2006). On the merits of orthogonalizing powered and interaction terms: Implications for modeling interactions among latent variables. Structural Equation Modeling, 13, 497-519.
24. Lusch, R.F., & Brown, J.R. (1996). Interdependency, contracting, and relational behavior in marketing channels. Journal of Marketing, 60, 19-38.
25. MacCallum, R.C., & Mar, C.M. (1995). Distinguishing between moderator and quadratic effects in multiple regression. Psychological Bulletin, 118, 405-421.
26. Marsh, H., Wen, Z., & Hau, K. (2004). Structural equation models of latent interactions: Evaluation of alternative estimation strategies and indicator construction. Psychological Methods, 9, 275-300.
27. Moosbrugger, H., Schermelleh-Engel, K., & Klein, A. (1997). Methodological problems of estimating latent interaction effects. Methods of Psychological Research Online, 2, 95-111.
28. Moulder, B.C., & Algina, J. (2002). Comparison of methods for estimating and testing latent variable interactions. Structural Equation Modeling, 9, 1-19.
29. Muthén, L.K., & Muthén, B.O. (2004). Mplus user's guide version 3.1. Los Angeles: Muthén & Muthén.
30. Paxton, P., Curran, P.J., Bollen, K.A., Kirby, J., & Chen, F. (2001). Monte Carlo experiments: Design and implementation. Structural Equation Modeling, 8, 287-312.
31. Ping, R.A. (1995). A parsimonious estimating technique for interaction and quadratic latent variables. Journal of Marketing Research, 32, 336-347.
32. Ping, R.A. (1996). Latent variable interaction and quadratic effect estimation: A two-step technique using structural equation analysis. Psychological Bulletin, 119, 166-175.
33. R Development Core Team. (2006). R: A language and environment for statistical computing. Vienna, Austria. Retrieved on June 1, 2005, from http://www.R-project.org, ISBN 3-900051-07-0
34. Schermelleh-Engel, K., Klein, A., & Moosbrugger, H. (1998). Estimating nonlinear effects using a latent moderated structural equations approach. In R.E. Schumacker & G.A. Marcoulides (Eds.), Interaction and nonlinear effects in structural equation modeling (pp. 203-238). Mahwah, NJ: Erlbaum.
35. Schumacker, R., & Marcoulides, G. (1998). Interaction and nonlinear effects in structural equation modeling. Mahwah, NJ: Erlbaum.
36. Snyder, M., & Tanke, E.D. (1976). Behavior and attitude: Some people are more consistent than others. Journal of Personality, 44, 501-517.
37. Wall, M.M., & Amemiya, Y. (2000). Estimation for polynomial structural equation models. Journal of the Statistical American Association, 95, 929-940.
38. Wall, M.M., & Amemiya, Y. (2001). Generalized appended product indicator procedure for nonlinear structural equation analysis. Journal of Educational and Behavioral Statistics, 26, 1-29.