Generalized latent variable models with non-linear effects

British Journal of Mathematical and Statistical Psychology

Volumn 61, Issue 2, 2008, Pages 415-438

  Rizopoulos, Dimitris ^a   Moustaki, Irini ^b,c  

^a ERASMUS MEDICAL CENTER   (Netherlands)

^b ATHENS UNIVERSITY OF ECONOMICS AND BUSINESS   (Greece)

^c LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; HUMAN; METHODOLOGY; NONLINEAR SYSTEM; PSYCHOLOGICAL MODEL; PSYCHOLOGY; STATISTICS;

HUMANS; MODELS, PSYCHOLOGICAL; NONLINEAR DYNAMICS; PSYCHOLOGY;

EID: 56649095767     PISSN: 00071102     EISSN: None     Source Type: Journal    
DOI: 10.1348/000711007X213963     Document Type: Article

References (58)

1. Arminger, G., & Muthén, B. (1998). A Bayesian approach to nonlinear latent variables models using the Gibbs sampler and the Metropolis-Hastings algorithm. Psychometrika, 63, 271-300.
2. Bartholomew, D. J. (1981). Posterior analysis of the factor model. British Journal of Mathematical and Statistical Psychology, 34, 93-99.
3. Bartholomew, D. J. (1985). Foundations of factor analysis: Some practical implications. British Journal of Mathematical and Statistical Psychology, 38, 1-10.
4. Bartholomew, D. J. (1998). Scaling unobservable constructs in social science. Applied Statistics, 47, 1-13.
5. Bartholomew, D. J., & Knott, M. (1999). Latent variable models and factor analysis (2nd ed.). London: Arnold.
6. Bartholomew, D. J., & McDonald, R. P. (1986). The foundations of factor analysis: A further comment. British Journal of Mathematical and Statistical Psychology, 39, 228-229.
7. Bartholomew, D. J., Steele, E, Moustaki, I., & Galbraith, J. (2008). Analysis of multivariate social science data. Boca Raton, FL: Chapman & Hall/CRC.
8. Bartlett, M. S. (1953). Factor analysis in psychology as a statistician sees it. Uppsala Symposium Psychological Factor Analysis (pp. 23-34). Nordisk Psykologi's Monograph Series No.3. Copenhagen: Ejnav Mundsgaards Stockholm: Almqvlst & Wiksell.
9. Bock, R. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29-51.
10. Bock, R., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
11. Bollen, K. (1995). Structural equation models that are nonlinear in latent variables: A least-squares estimator. Sociological Methodology, 25, 223-251.
12. Bollen, K. (1996). An alternative two stage least squares (2SLS) estimator for latent variable equation. Psychometrika, 61, 109-121.
13. Bollen, K., & Paxton, P. (1998). Two-stage least squares estimation of interaction effects. In R. Schumacker & G. Marcoulides (Eds.), Interaction and nonlinear effects in structural equation models (pp. 125-151). Mahwah, NJ: Erlbaum.
14. Booth, J., & Hobert, J. (1999). Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. Journal of the Royal Statistical Society, Series B, 61, 265-285.
15. Busemeyer, J., & Jones, L. (1983). Analysis of multiplicative combination rules when the causal variables are measured with error. Psychological Bulletin, 93, 549-562.
16. Cox, D., & Hinkley, D. (1974). Theoretical statistics. London: Chapman & Hall.
17. Dempster, A., Laird, N., & Rubin, D. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39, 1-38.
18. Etezadi-Amoli, J., & McDonald, R. P. (1983). A second generation nonlinear factor analysis. Psychometrika, 48, 315-342.
19. Gibson, W. (1960). Nonlinear factors in two dimensions. Psychometrika, 25, 381-392.
20. Huber, P., Ronchetti, E., & Victoria-Feser, M. (2004). Estimation of generalized latent trait models. Journal of the Royal Statistical Society, Series B, 66, 893-908.
21. Jöreskog, K. (1990). New developments in LISREL: Analysis of ordinal variables using polychoric correlations and weighted least squares. Quality and Quantity, 24, 387-404.
22. Joreskog, K. (1994). On the estimation of polychoric correlations and their asymptotic covariance matrix. Psychometrika, 59, 381-389.
23. Joreskog, K., & 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. 57-88). Mahwah, NJ: Erlbaum.
24. Kenny, D., & Judd, C. (1984). Estimating the nonlinear and interactive effects of latent variables. Psychological Bulletin, 96, 201-210.
25. Klein, A., & Moosbrugger, H. (2000). Maximum likelihood estimation of latent interaction effects with the LMS method. Psychometrika, 65, 457-474.
26. Lange, K. (2004). Optimization. New York: Springer-Verlag.
27. Lawley, D., & Maxwell, A. (1971). Factor analysis as a statistical method (2nd ed.). London: Butterworth.
28. Lee, S.-Y., Poon, W.-Y., & Bentler, P. (1992). Structural equation models with continuous and polytomous variables. Psychometrika, 57, 89-105.
29. Lee, S.-Y., & Song, X.-Y. (2004a). Bayesian model comparison of nonlinear structural equation models with missing continuous and ordinal categorical data. British Journal of Mathematical and Statistical Psychology, 57, 131-150.
30. Lee, S.-Y., & Song, X.-Y. (2004b). Maximum likelihood analysis of a generalized latent variable model with hierarchically mixed data. Biometrics, 60, 624-636.
31. Lee, S.-Y., Song, X.-Y., & Poon, W. -Y. (2004). Comparison of approaches in estimating interaction and quadratic effects of latent variables. Multivariate Behavioral Research, 39, 37-67.
32. Lee, S.-Y., & Zhu, H.-T. (2002). Maximum likelihood estimation of nonlinear structural equation models. Psychometrika, 67, 189-210.
33. Lesaffre, E., & Spiessens, B. (2001). On the effect of the number of quadrature points in a logistic random-effects model: An application. Applied Statistics, 50, 325-335.
34. McCullagh, P., & Nelder, J. (1989). Generalized linear models (2nd ed.). London: Chapman & Hall.
35. McDonald, R. P. (1962). A general approach to non-linear factor analysis. Psychometrika, 27, 397-415.
36. McDonald, R. P. (1967a). Factor interaction in nonlinear factor analysis. British Journal of Mathematical and Statistical Psychology, 20, 205-215.
37. McDonald, R. P. (1967b). Non-linear factor analysis. Psychometric Monograph, 15. Grensbaro, NC: Psychonetic society.
38. McDonald, R. P. (1967c). Numerical methods for polynomial models in nonlinear factor analysis. Psychometrika, 32(1), 77-111.
39. Moulder, B., & Algina, J. (2002). Comparison of methods for estimating and testing latent variable interactions. Structural Equation Modeling, 9, 1-19.
40. Moustaki, I. (2003). A general class of latent variable models for ordinal manifest variables with covariate effects on the manifest and latent variables. British Journal of Mathematical and Statistical Psychology, 56, 337-357.
41. Moustaki, I., & Knott, M. (2000). Generalized latent trait models. Psychometrika, 65, 391-411.
42. Moustaki, I., & Steele, F. (2005). Latent variable models for mixed categorical and survival responses, with an application to fertility preferences and family planning in Bangladesh. Statistical Modelling, 5, 327-342.
43. Muthén, B. (1984). A general structural model with dichotomous, ordered categorical and continuous latent variable indicators. Psychometrika, 49, 115-132.
44. Ping, R. (2005). Latent variable interactions and quadratics in survey data: A source book for theoretical model testing (2nd ed.) On-line monograph, http://home.att.net/rpingjr/intquad2/toc2.htm, Last accessed March 2007.
45. Pinheiro, J., & Bates, D. (1995). Approximations to the log-likelihood function in the nonlinear mixed-effects model. Journal of Computational and Graphical Statistics, 4, 12-35.
46. Rizopoulos, D. (2006). ltm: An R package for latent variable modelling and item response theory analyses. Journal of Statistical Software, 17(5), 1-25.
47. Rubin, D. (1987). Multiple imputation for nonresponse in surveys. New York: Wiley.
48. Schilling, R., & Bock, S. G. (2005). High-dimensional maximum marginal likelihood item factor analysis by adaptive numerical integration. Psychometrika, 70, 533-555.
49. Schumacker, R., & Marcoulides, G. (1998). Interaction and nonlinear effects in structural equation models. Mahwah, NJ: Erlbaum.
50. Shi, J., & Lee, S.-Y. (1998). Bayesian sampling-based approach for factor analysis model with continuous and polytomous data. British Journal of Mathematical and Statistical Psychology, 51, 233-252.
51. Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent variable modeling: Multilevel, longitudinal and structural equation models. Boca Raton, FL: Chapman & Hall/CRC.
52. Song, X.-Y., & Lee, S.-Y. (2004). Bayesian analysis of two-level nonlinear structural equation models with continuous and polytomous data. British Journal of Mathematical and Statistical Psychology, 57, 29-52.
53. Song, X.-Y., & Lee, S.-Y. (2006). Bayesian analysis of latent variable models with non-ignorable missing outcomes from exponential family. Statistics in Medicine, 26, 681-693.
54. Wall, M., & Amemiya, Y. (2000). Estimation of polynomial structural equation analysis. Journal of the American Statistical Association, 95, 929-940.
55. Wall, M., & Amemiya, Y. (2001). Generalized appended product indicator procedure for nonlinear structural equation analysis. Journal of Educational and Behavioral Statistics, 26, 1-29.
56. White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrics, 50, 1-25.
57. Yang, F. (1997). Non-linear structural equation models: Simulation studies of the Kenny-Judd model. Unpublished doctoral dissertation, Uppsala University.
58. Zhu, H.-T., & Lee, S.-Y. (1999). Statistical analysis of nonlinear factor analysis models. British Journal of Mathematical and Statistical Psychology, 52, 225-242.