Challenges in nonlinear structural equation modeling

Methodology

Volumn 3, Issue 3, 2007, Pages 100-114

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

^a GOETHE UNIVERSITY   (Germany)

Author keywords

Latent product terms; Multicollinearity; Nonlinear regression; Nonlinear structural equation modeling; Reliability

Indexed keywords

EID: 54949152457     PISSN: 16141881     EISSN: 16142241     Source Type: Journal    
DOI: 10.1027/1614-2241.3.3.100     Document Type: Article

References (37)

1. Aguinis, H. (1995). Statistical power with moderated multiple regression in management research. Journal of Management, 21, 1141-1158.
2. Aiken, L.S., & West, S.G. (1991). Multiple regression: Testing and interpreting interactions. Thousand Oaks, CA: Sage.
3. Algina, J., & Moulder, B.C. (2001). A note on estimating the Jöreskog-Yang model for latent variable interaction using LISREL 8.3. Structural Equation Modeling, 8, 40-52.
4. Bohrnstedt, G.W., & Goldberger, A.S. (1969). On the exact covariance of products of random variables. Journal of the American Statistical Association, 64, 1439-1442.
5. Bollen, K.A. (1995). Structural equation models that are nonlinear in latent variables. In P.V. Marsden (Ed.), Sociological methodology 1995 (Vol. 25). Washington, DC: American Sociological Association.
6. Bollen, K.A. (1996). An alternative two-stage least squares (2SLS) estimator for latent variable equations. Psychometrika, 61, 109-121.
7. Busemeyer, J.R., & Jones, L.E. (1983). Analysis of multiplicative combination rules when the casual variables are measured with error. Psychological Bulletin, 93, 549-562.
8. Cohen, J. (1983). The cost of dichotomization. Applied Psychological Measurement, 7, 249-254.
9. Cohen, J., Cohen, P., West, S.G., & Aiken, L.S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences. Mahwah, NJ: Erlbaum.
10. Coulton, C., & Chow, J. (1992). Interaction effects in multiple regression. Journal of Social Service Research, 16(1/2), 179-199.
11. Cronbach, L.J., & Snow, R.E. (1977). Aptitudes and instructional methods: A handbook for research on interactions. New York: Irvington.
12. Evans, M.G. (1991). The problem of analyzing multiplicative composites: Interactions revisited. American Psychologist, 46, 6-15.
13. Ganzach, Y. (1997). Misleading interaction and curvilinear terms. Psychological Methods, 3, 235-247.
14. Humphreys, L.G. (1978). Doing research the hard way: Substituting analysis of variance for a problem in correlational analysis. Journal of Educational Psychology, 70, 873-876.
15. Jöreskog, K.G., & Yang, F. (1996). Nonlinear structural equation models: The Kenny-Judd model with interaction effects. In G. Marcoulides & R. Schumacker (Eds.), Advanced structural equation modeling (pp. 57-87). Mahwah, NJ: Erlbaum.
16. Kelava, A., Moosbrugger, H., Dimitruk, P., & Schermelleh-Engel, K. (submitted). The influence of multicollinearity and missing constraints of nonlinear error covariances on the performance of three estimation approaches for latent interaction and quadratic effects.
17. Kenny, D., & Judd, C.M. (1984). Estimating the nonlinear and interactive effects of latent variables. Psychological Bulletin, 96, 201-210.
18. Klein, A. (2000). Moderatormodelle. Verfahren zur Analyse von Moderatoreffekten in Strukturgleichungsmodellen [Moderator models: Method for the analysis of moderator effects in structural equation models]. Hamburg: Dr. Kovač.
19. Klein, A. (2006). A saturated model and evaluation of model fit for multivariate heteroscedastic models (submitted).
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.O. (2006). Quasi maximum likelihood estimation of structural equation models with multiple interaction and quadratic effects. Multivariate Behavioral Research (in press).
22. Lubinski, D., & Humphreys, L.G. (1990). Assessing spurious "moderator effects": Illustrated substantively with the hypothesized ("synergistic") relation between spatial and mathematical ability. Psychological Bulletin, 107, 385-393.
23. MacCallum, R.C., & Marr, C.M. (1995). Distinguishing between moderator and quadratic effects in multiple regression. Psychological Bulletin, 118, 405-421.
24. MacCallum, R.C., Zhang, S., Preacher, K.J., & Rucker, D.D. (2002). On the practice of dichotomization of quantitative variables. Psychological Methods, 7, 19-40.
25. Marsh, H.W., Wen, Z., & Hau, K.T. (2004). Structural equation models of latent interactions: Evaluation of alternative estimation strategies and indicator construction. Psychological Methods, 9, 275-300.
26. Moosbrugger, H., Schermelleh-Engel, K., & Klein, A. (1997). Methodological problems of estimating latent interaction effects. Methods of Psychological Research Online, 2, 95-111.
27. Muthén, L.K., & Muthén, B.O. (2004). Mplus: The comprehensive modeling program for applied researchers. User's guide (3rd ed.). Los Angeles: Muthén & Muthén.
28. Rigdon, E.E., Schumacker, R.E., & Wothke, W. (1998). A comparative review of interaction and nonlinear modeling. In R.E. Schumacker & G.A. Marcoulides (Eds.), Interaction and nonlinear effects in structural equation modeling (pp. 1-16). Mahwah, NJ: Erlbaum.
29. Satorra, A. (2000). Scaled and adjusted restricted tests in multi-sample analysis of moment structures. In R.D.H. Heijmans, D.S.G. Pollock, & A. Satorra, (Eds.), Innovations in multivariate statistical analysis. A Festschrift for Heinz Neudecker (pp. 233-247). London: Kluwer.
30. 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.
31. Schumacker, R.E., & Marcoulides, G.A. (Eds.). (1998). Interaction and nonlinear effects in structural equation modeling. Mahwah, NJ: Erlbaum.
32. 2 statistics. New York: Springer-Verlag.
33. Wall, M.M., & Amemiya, Y. (2000). Estimation for polynomial structural equation models. Journal of the American Statistical Association, 95, 929-940.
34. Wall, M.M., & Amemiya, Y. (2001). Generalized appended product indicator procedure for nonlinear structural equation analysis. Journal of Education and Behavioral Statistics, 26, 1-29.
35. West, S.G., Aiken, L.S., & Krull, J.L. (1996). Experimental personality designs: Analyzing categorical by continuous variable interactions. Journal of Personality, 64, 1-48.
36. Whisman, M.A., & McClelland, G.H. (2005). Designing, testing, and interpreting interactions and moderator effects in family research. Journal of Family Psychology, 19, 111-120.
37. Yang-Jonsson, F. (1997). Nonlinear structural equation models. Simulation studies of the Kenny-Judd model. Stockholm: Gotab.