Using data augmentation to obtain standard errors and conduct hypothesis tests in latent class and latent transition analysis

Psychological Methods

Volumn 10, Issue 1, 2005, Pages 84-100

  Lanza, Stephanie T ^a   Collins, Linda M ^a   Schafer, Joseph L ^a   Flaherty, Brian P ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Data augmentation; Latent class analysis; Latent transition analysis; Latent variable model; Multiple imputation

Indexed keywords

ARTICLE; HUMAN; METHODOLOGY; PSYCHOLOGICAL MODEL; PSYCHOLOGY;

HUMANS; MODELS, PSYCHOLOGICAL; PSYCHOLOGY;

EID: 17444404172     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/1082-989X.10.1.84     Document Type: Article

References (48)

1. Agresti, A. (1990). Categorical data analysis. New York: Wiley.
2. Anderson, T. W. (1954). Probability models for analyzing time changes in attitudes. In P. F. Lazarsfeld (Ed.), Mathematical thinking in the social sciences (pp. 17-66). New York: Free Press.
3. Bergan, J. R. (1983). Latent-class models in educational research. Review of Research in Education, 10, 305-360.
4. Biemer, P. P., Woltmann, H., Raglin, D., & Hill, J. (2001). Enumeration accuracy in a population census: An evaluation using latent class analysis. Journal of Official Statistics, 17, 129-148.
5. Challis, R. E., & Kitney, R. I. (1991). Biomedical signal processing (in four parts). Part 1: Time-domain methods. Medical and Biological Engineering and Computing, 28, 509-524.
6. Chung, H. (2003). Latent-class modeling with covariates (Tech. Rep. No. 03-56). University Park, PA: Pennsylvania State University, The Methodology Center.
7. Chung, H., Loken, E., & Schafer, J. L. (2004). Difficulties in drawing inferences with finite-mixture models: A simple example with a simple solution. The American Statistician, 58, 1-7.
8. Collins, L. M., & Cliff, N. (1990). Using the longitudinal Guttman simplex as a basis for measuring growth. Psychological Bulletin, 108, 128-134.
9. Collins, L. M., & Flaherty, B. P. (2002). Latent class models for longitudinal data. In J. A. Hagenaars & A. L. McCutcheon (Eds.), Applied latent class analysis (pp. 287-303). Cambridge, England: Cambridge University Press.
10. Collins, L. M., Graham, J. W., Long, J., & Hansen, W. B. (1994). Crossvalidation of latent class models of early substance use onset. Multivariate Behavioral Research, 29, 165-183.
11. Collins, L. M., Graham, J. W., Rousculp, S. S., & Hansen, W. B. (1997). Heavy caffeine and the beginning of the substance use onset process: An illustration of latent transition analysis. In K. Bryant, M. Windle, & S. West (Eds.), The science of prevention: Methodological advances from alcohol and substance abuse research (pp. 79-99). Washington, DC: American Psychological Association.
12. Collins, L. M., Hyatt, S. L., & Graham, J. W. (2000). LTA as a way of testing models of stage-sequential change in longitudinal data. In T. D. Little, K. U. Schnabel, & J. Baumert (Eds.), Modeling longitudinal and multiple-group data: Practical issues, applied approaches, and specific examples (pp. 147-161). Hillsdale, NJ: Erlbaum.
13. Collins, L. M., Lanza, S. T., & Schafer, J. L. (2002). WinLTA user's guide for data augmentation [Computer software manual]. University Park, PA: Pennsylvania State University, The Methodology Center.
14. Collins, L. M., Schafer, J. L., & Kam, C.-M. (2001). A comparison of inclusive and restrictive strategies in modern missing-data procedures. Psychological Methods, 6, 330-351.
15. Collins, L. M., & Wugalter, S. E. (1992). Latent class models for stage-sequential dynamic latent variables. Multivariate Behavioral Research, 27, 131-157.
16. 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 (B), 39, 1-38.
17. Elliott, D. S., Huizinga, D., & Ageton, S. S. (1985). Explaining delinquency and drug use. Beverly Hills, CA: Sage.
18. Erikson, E. H. (1950). Childhood and society. New York: Norton.
19. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian data analysis (2nd ed.). London: Chapman & Hall.
20. Gilks, W. R., Richardson, S., & Spiegelhalter, D. (1996). Practical Markov chain Monte Carlo. New York: Chapman & Hall.
21. Goodman, L. A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215-231.
22. Graham, J. W., Collins, L. M, Wugalter, S. E., Chung, N. K., & Hansen, W. B. (1991). Modeling transitions in latent stage-sequential processes: A substance use prevention example. Journal of Consulting and Clinical Psychology, 59, 48-57.
23. Hoijtink, H., & Molenaar, I. W. (1997). A multidimensional item response model: Constrained latent class analysis using the Gibbs sampler and posterior predictive checks. Psychometrika, 62, 171-189.
24. Hyatt, S. L., & Collins, L. M. (2000). Using latent transition analysis to examine the relationship between parental permissiveness and the onset of substance use. In J. Rose, L. Chassin, C. Presson, & S. Sherman (Eds.), Multivariate applications in substance use research (pp. 259-288). Hillsdale, NJ: Erlbaum.
25. Kendler, K. S., Karkowski, L. M., & Walsh, D. (1998). The structure of psychosis: Latent class analysis of probands from the Roscommon Family Study. Archives of General Psychiatry, 55, 492-499.
26. Langeheine, R. (1994). Latent variable Markov models. In A. von Eye & C. C. Clogg (Eds.), Latent variable analysis: Applications for developmental research (pp. 373-375). Beverly Hills, CA: Sage.
27. Lanza, S. T., & Collins, L. M. (2002). Pubertal timing and the onset of substance use in females during early adolescence. Prevention Science, 3, 69-82.
28. Lanza, S. T., Flaherty, B. P., & Collins, L. M. (2003). Latent class and latent transition analysis, In J. A. Schinka & W. F. Velicer (Eds.), Handbook of psychology: Vol. 2. Research methods in psychology (pp. 663-685). Hoboken, NJ: Wiley.
29. Lazarsfeld, P. F., & Henry, N. W. (1968). Latent structure analysis. Boston: Houghton Mifflin.
30. McCutcheon, A. L. (1987). Latent class analysis. Newbury Park, CA: Sage.
31. Muthén, L. K., & Muthén, B. O. (2004). Mplus user's guide (3rd ed.) [Computer software and manual]. Los Angeles, CA: Muthén & Muthén.
32. Piaget, J. (1973). The child and reality. New York: Grossman.
33. Posner, S. F., Collins, L. M., Longshore, D., & Anglin, D. (1996). The acquisition and maintenance of safer sexual behaviors among injection drug users. Substance Use and Misuse, 31, 1995-2015.
34. Read, T., & Cressie, N. (1988). Goodness-of-fit statistics for discrete multivariate data. New York: Springer-Verlag.
35. Rubin, D. B. (1984). Bayesianly justifiable and relevant frequency calculations for the applied statistician. Annals of Statistics, 12, 1151-1172.
36. Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys. New York: Wiley.
37. Rubin, D. B., & Schenker, N. (1987). Logit-based interval estimation for binomial data using the Jeffreys prior. In C. C. Clogg (Ed.), Sociological methodology (pp. 131-144). Washington, DC: American Sociological Association.
38. Rubin, D. B., & Stern, H. S. (1994). Testing in latent class models using a posterior predictive check distribution. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis (pp. 420-438). Thousand Oaks, CA: Sage.
39. Schafer, J. L. (1997). Analysis of incomplete multivariate data. London: Chapman & Hall.
40. Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7, 147-177.
41. Schwartz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-464.
42. Singer, J. D., & Willett, J. B. (2002). Applied longitudinal data analysis: Modeling change and event occurrence. New York: Oxford University Press.
43. Tanner, M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation (with discussion). Journal of the American Statistical Association, 82, 528-550.
44. Udry, J. R. (2003). The national longitudinal study of adolescent health (Add Health), Waves I & II, 1994-1996; Wave III, 2001-2002 [Data file]. Chapel Hill, NC: University of North Carolina at Chapel Hill, Carolina Population Center.
45. van de Pol, F., & Langeheine, R. (1990). Mixed Markov latent class models. In C. C. Clogg (Ed.), Sociological methodology (pp. 213-247). Oxford, England: Blackwell.
46. van der Heijden, P. G. M., Dessens, J., & Böckenholt, U. (1996). Estimating the concomitant-variable latent-class model with the EM algorithm. Journal of Educational and Behavioral Statistics, 21, 215-229.
47. Velicer, W. F., Martin, R. A., & Collins, L. M. (1996). Latent transition analysis for longitudinal data. Addiction, 91 (Suppl. S), S197-S209.
48. Vermunt, J., Langeheine, R., & Böckenholt, U. (1999). Discrete-time discrete-state latent Markov models with time-constant and time-varying covariates. Journal of Educational and Behavioral Statistics, 24, 179-207.