Semi-nonparametric methods for detecting latent non-normality: A fusion of latent trait and ordered latent class modeling

Multivariate Behavioral Research

Volumn 41, Issue 4, 2006, Pages 427-443

  Eric Schmitt, J ^a   Mehta, Paras D ^b   Aggen, Steven H ^a   Kubarych, Thomas S ^a   Neale, Michael C ^a,c  

^a VIRGINIA COMMONWEALTH UNIVERSITY SCHOOL OF MEDICINE   (United States)

^b UNIVERSITY OF HOUSTON   (United States)

^c VIRGINIA COMMONWEALTH UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846989307     PISSN: 00273171     EISSN: None     Source Type: Journal    
DOI: 10.1207/s15327906mbr4104_1     Document Type: Article

References (36)

1. Abramowitz, M., & Stegan, I. E. (1972). Handbook of mathematical fonctions with formulas, graphs, and mathematical tables ( 10th ed.). Washington, DC: U.S. Government Printing Office.
2. American Psychiatric Association. (1994). Diagnostic and statistical manual of mental disorders ( 4th ed.). Washington, DC: Author.
3. Bock, R., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
4. Bock, R., & Aitkin, M. (1982). Errata: "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm." Psychometrika, 47, 369.
5. Clogg, C. C. (1988). Latent class models for measuring. In R. Langeheine & J. Rost (Eds.), Latent trait and latent class models (pp. 173-205). New York: Plenum.
6. Croon, M. A. (1990). Latent class analysis with ordered latent classes. British Journal of Mathematical and Statistical Psychology, 43, 171-192.
7. de Leeuw, J., & Verhelst, N. (1986). Maximum-likelihood-estimation in generalized Rasch models. Journal of Educational Statistics, 11, 183-196.
8. Falconer, D. S. (1965). The inheritance of liability to certain Diseases, estimated from the incidence among relatives. Annals of Human Genetics, 51-76.
9. Follman, D. (1988). Consistent estimation in the Rasch model based on nonparametric margins. Psychometrika, 53, 553-562.
10. Heinen, T. (1993). Discrete latent class models. Tilburg, The Netherlands: Tilburg University Press.
11. Ihaka, R., & Gentleman, R. (1996). R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics, 5, 299-314.
12. Kendler, K. S., Neale, M. C., Kessler, R. C., Heath, A. C., & Eaves, L. J. (1992). A population-based twin study of major depression in women: The impact of varying definitions of illness. Archives of General Psychiatry, 49, 257-266.
13. Kessler, R. C., McGonagle, K. A., Zhao, S., Nelson, C. B., Hughes, M., Eshleman, S., et al. (1994). Lifetime and 12-month prevalence of DSM-III-R psychiatric disorders in the United States: Results from the National Comorbidity Survey. Archives of General Psychiatry, 51, 8-19.
14. Langeheine, R. (1988). New developments in latent class theory. In R. Langeheine & J. Rost (Eds.), Latent trait and latent class models (pp. 77-108). New York: Plenum.
15. Langeheine, R., & Rost, J. (1988). Introduction and overview. In R. Langeheine & J. Rost (Eds.), Latent trait and latent class models (pp. 1-7). New York: Plenum.
16. Lazarsfeld, P. F. (1950a). The interpretation and computation of some latent structures. In S. A. Stouffer (Ed.), Measurement and prediction (pp. 413-472). Princeton, NJ: Princeton University Press.
17. Lazarsfeld, P. F. (1950b). The logical and mathematical foundation of latent structure analysis. In S. A. Stouffer (Ed.), Measurement and prediction (pp. 362-412). Princeton, NJ: Princeton University Press.
18. Lazarsfeld, P. F., & Henry, N. W. (1968). Latent structure analysis. Boston: Houghton Mifflin.
19. Lord, F. M. (1980). Applications of item response theory to practical te sting problems. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
20. Magder, L. S., & Zeger, S. L. (1996). A smooth nonparametric estimate of a mixing distribution using mixtures of Gaussians. Journal of the American Statistical Association, 91, 1141-1151.
21. Muthén, L. K., & Muthén, B. O. (2001). Mplus user's guide. Los Angeles: Muthén & Muthén.
22. Neale, M. C., Boker, S. M., Xie, G., & Maes, H. H. (2002). Mx: Statistical modeling ( 5th ed.) [Computer software]. Richmond: Department of Psychiatry, Medical College of Virginia, Virginia Commonwealth University.
23. Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine, 50, 157-175.
24. R Development Core Team. (2005). R: A language and environment for statistical computing. The R Foundation for Statistical Computing, Vienna, Austria.
25. Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2004a). Generalized multilevel structural equation modeling. Psychometrika, 69, 167-190.
26. Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2004b). GLLAMM manual. (Working Paper 160). UC Berkeley Division of Biostatistics Working Paper Series, Berkeley, CA. Available from http://www.bepress.com/ucbbiostat/ paper160
27. SAS Institute. (2000). SAS/STAT User's Guide (Version 8) [Computer software]. Cary, NC: Author.
28. Takane, Y., & de Leeuw, J. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393-408.
29. Tutz, G. (1990). Sequential item response models with an ordered response. British Journal of Mathematical and Statistical Psychology, 43, 39-55.
30. van den Berg, S. M., Glas, C. A. W., & Boomsma, D. I. (2005). Variance decomposition using an IRT measurement model. Manuscript submitted for publication.
31. van den Oord, E. J. (2005). Estimating Johnson curve population distributions in MULTILOG. Applied Psychological Measurement, 29, 45-64.
32. van Onna, M. J. H. (2004). Ordered latent class models in nonparametric item response theory. Groningen, The Netherlands: Groningen University Library.
33. Vermunt, J. K. (2001). The use of restricted latent class models for defining and testing nonparametric and parametric item response theory models. Applied Psychological Measurement, 25, 283-294.
34. Vermunt, J. K. (2004). An EM algorithm for the estimation of parametric and nonparametric hierarchical nonlinear models. Statistica Neerlandica, 58, 220-233.
35. Vermunt, J. K., & Hagenaars, J. A. (2004). Ordinal longitudinal data analysis. In R. C. Hauspie, N. Cameron, & L. Molinari (Eds.), Methods in human growth research (pp. 374-393). Cambridge, UK: Cambridge University Press.
36. Zimowski, M. F., Muraki, E., Mislevy, R. J., & Bock, R. D. (1996). BILOG-MG: Multiple-group IRT analysis and test maintenance for binary items [Computer software]. Chicago: Scientific Software International.