Comparison of approaches in estimating interaction and quadratic effects of latent variables

Multivariate Behavioral Research

Volumn 39, Issue 1, 2004, Pages 37-67

  Lee, Sik Yum ^a   Song, Xin Yuan ^a,b   Poon, Wai Yin ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b SUN YAT SEN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042735142     PISSN: 00273171     EISSN: None     Source Type: Journal    
DOI: 10.1207/s15327906mbr3901_2     Document Type: Article

References (31)

1. Algina, J. & Moulder, B. C. (2001). A note on estimating the Joreskog-Yang model for latent variable interaction using LISREL 8.3. Structural Equation Modeling, 8, 40-52.
2. Arminger, G. &; Muthén, B. O. (1998). A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the Metropolis-Hastings algorithm. Psychometrika, 63, 271-300.
3. Bagozzi, R. P., Baumgartner, H. & Yi, Y. (1992). State versus action orientation and the theory of reasoned action: an application to coupon usage. Journal of Consumer Research, 75, 505-517.
4. Bentler, P. M. (1990). Comparative fit indices in structural models. Psychological Bulletin, 107, 238-246.
5. Bollen, K. A. & Paxton, P. (1998). Two-stage least squares estimation of interaction effects. In Schumacker, R. E. & Marcoulides, G. A. (Eds.), Interaction and nonlinear effects in structural equation models (pp. 125-151). Mahwah, NJ: Lawrence Erlbaum Associates.
6. Broemeling, L. D. (1985). Bayesian analysis of linear models. New York: Marcel Dekker.
7. Browne, M. B. & Cudeck R. (1993). Alternative ways of assessing model fit. In K. Bollen & S. Long (Eds.) Testing structural equation models (pp. 136-162). Newbary Park, CA: Sage.
8. 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.
9. Dempster, A. P., Laird, N. M. & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B, 39, 1-38.
10. Gelman, A., Meng, X. L. & Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6, 733-807.
11. Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
12. Geyer, C. J. (1992). Practical Markov chain Monte Carlo(with discussion). Statistical Science, 7, 473-511.
13. Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their application. Biometrica, 57, 97-109.
14. Jaccard, J. & Wan, C. K. (1995). Measurement error in the analysis of interaction effects between continuous predictors using multiple regression: Multiple indicator and structural equation approaches. Psychological Bulletin, 117, 348-357.
15. Jöreskog, K. G. & Sörbom, D. (1996). LISREL 8: Structural equation modeling with the SIMPLIS command language. Hove & London: Scientific Software International.
16. 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 techniques (pp. 57-88). Hillsdale, NJ: Lawrence Erlbaum.
17. Kenny, D. A. & Judd, C. M. (1984). Estimating the nonlinear and interactive effects of latent variables. Psychological Bulletin, 90, 201-210.
18. Lee, S. Y. & Zhu, H. T. (2000). Statistical analysis of nonlinear structural equation models with continuous and polytomous data. British Journal of Mathematical and Statistical Psychology, 53, 209-232.
19. Lee, S. Y. & Zhu, H. T. (2002). Maximum likelihood estimation of nonlinear structural equation models. Psychometrika, 67, 189-210.
20. Louis, T. A. (1982). Finding the observed information matrix when using EM algorithm. Journal of the Royal Statistical Society, Series B, 44, 226-233.
21. Meng, X. L. & Rubin, D. B. (1993). Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika, 80, 267-278.
22. Meng, X. L. & Wong, H. W. (1996). Simulating ratios of normalizing constants via a simple identity: a theoretical exploration. Statistica Sinica, 6, 831-360.
23. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. & Teller, E. (1953). Equations of state calculations by fast computing machine. Journal of Chemical Physics, 21, 1087-1091.
24. Moulder, B. C. & Algina, J. (2002). Comparison of methods for estimating and testing latent variable interactions. Structural Equation Modeling, 9, 1-9.
25. Ping, R. A. (1996). Latent variable regression: A technique for estimating interaction and quadratic coefficients. Multivariate Behavioral Research, 31, 95-120.
26. Schumacker, R. E. (2002). Latent variable interaction modeling. Structural Equation Modeling, 9, 40-54.
27. Schumacker, R. E. & Marcoulides, G. A. (Eds.) (1998). Interaction and nonlinear effects in structural equation models. Mahwah, NJ: Lawrence Erlbaum Associates.
28. Wall, M. W. & Amemiya, Y. (2001). Generalized appended product indicator procedure for nonlinear structural equation analysis. Journal of Educational and Behavioral Statistics, 26, 1-29.
29. Wei, G. C. G. & Tanner, M. A. (1990). A Monte Carlo implementation of the EM algorithm and the Poor man's data augmentation algorithm. Journal of American Statistical Association, 85, 699-704.
30. Zellner, A. (1971). An introduction to Bayesian inference in econometrics. New York: Wiley.
31. Zhu, H. T. & Lee, S. Y. (1999). Statistical analysis of nonlinear factor analysis models. British Journal of Mathematical and Statistical Psychology, 52, 225-242.