Skip to main content
Log in

A Latent Transition Model With Logistic Regression

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

Latent transition models increasingly include covariates that predict prevalence of latent classes at a given time or transition rates among classes over time. In many situations, the covariate of interest may be latent. This paper describes an approach for handling both manifest and latent covariates in a latent transition model. A Bayesian approach via Markov chain Monte Carlo (MCMC) is employed in order to achieve more robust estimates. A case example illustrating the model is provided using data on academic beliefs and achievement in a low-income sample of adolescents in the United States.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bandeen-Roche, K., Miglioretti, D.L., Zeger, S.L., & Rathouz, P.J. (1997). Latent variable regression for multiple discrete outcomes. Journal of the American Statistical Association, 92, 1375–1386.

    Article  Google Scholar 

  • Best, N., Cowles, M., & Vines, S. (1995). Coda: Convergence diagnostics and output analysis software for Gibbs sampler output, version 0.3 (Technical Report). MRC Biostatistics Unit.

  • Chung, H., Flaherty, B.P., & Schafer, J.L. (2006). Latent class logistic regression: Application to marijuana use and attitudes among high school seniors. Journal of the Royal Statistical Society, Series A, 169, 723–743.

    Google Scholar 

  • 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, 152–158.

    Article  Google Scholar 

  • Chung, H., Park, Y., & Lanza, S.T. (2005). Latent transition analysis with covariates: Pubertal timing and substance use behaviors in adolescent females. Statistics in Medicine, 24, 2895–2910.

    Article  PubMed  Google Scholar 

  • Clogg, C.C., & Goodman, L.A. (1984). Latent structure analysis of a set of multidimensional contingency tables. Journal of the American Statistical Association, 79, 762–771.

    Article  Google Scholar 

  • Collins, L.M., Fidler, P.L., Wugalter, S.E., & Long, J.L. (1993). Goodness-of-fit testing for latent class models. Multivariate Behavioral Research, 28, 375–389.

    Article  Google Scholar 

  • Collins, L.M., & Wugalter, S.E. (1992). Latent class models for stage-sequential dynamic latent variables. Multivariate Behavioral Research, 27, 131–157.

    Article  Google Scholar 

  • Eccles, J.S., Early, D., Frasier, K., Belansky, E., & McCarthy, K. (1997). The relation of connection, regulation, and support for autonomy to adolescent’s functioning. Journal of Adolescent Research, 12, 263–286.

    Article  Google Scholar 

  • Garrett, E.S., Eaton, W.W., & Zeger, S.L. (2002). Methods for evaluating the performance of diagnostic tests in the absence of a gold standard: A latent class model approach. Statistics in Medicine, 21, 1289–1307.

    Article  PubMed  Google Scholar 

  • Garrett, E.S., & Zeger, S.L. (2000). Latent class model diagnosis. Biometrics, 56, 1055–1067.

    Article  PubMed  Google Scholar 

  • Gelfand, A.E., & Smith, A.F.M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398–409.

    Article  Google Scholar 

  • Gelman, A., Carlin, J.B., Stern, H.S., & Rubin, D.B. (2004). Bayesian data analysis (2nd ed.). London: Chapman & Hall.

    Google Scholar 

  • Gelman, A., Meng, X.L., & Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies (with discussion). Statistica Sinica, 6, 733–807.

    Google Scholar 

  • Gelman, A., & Rubin, D.B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457–511.

    Article  Google Scholar 

  • Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In J.M. Bernardo, J.O. Berger, A.P. Dawid, & A.F.M. Smith (Eds.), Bayesian statistics (Vol. 4, pp. 169–193). Oxford: Oxford University Press.

  • Goodman, L.A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215–231.

    Article  Google Scholar 

  • Hoijtink, H. (1998). Constrained latent class analysis using the Gibbs sampler and posterior predictive p-values: Applications to educational testing. Statistica Sinica, 8, 691–711.

    Google Scholar 

  • Kennedy, W.J., & Gentle, J.E. (1980). Statistical computing. New York: Marcel Dekker.

    Google Scholar 

  • Langeheine, R., Pannekoek, J., & van de Pol, F. (1996). Bootstrapping goodness-of-fit measures in categorical data analysis. Sociological Methods and Research, 24, 492–516.

    Article  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • Lanza, S.T., Collins, L.M., Schafer, J.L., & Flaherty, B.P. (2005). Using data augmentation to obtain standard errors and conduct hypothesis tests in latent class and latent transition analysis. Psychological Methods, 10, 84–100.

    Article  PubMed  Google Scholar 

  • 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 (pp. 663–685). Hoboken, NJ: Wiley.

  • Lazarsfeld, P.F., & Henry, N.W. (1968). Latent structure analysis. Boston: Houghton Mifflin.

    Google Scholar 

  • Lo, Y., Medell, N.R., & Rubin, D.B. (2001). Testing the number of components in a normal mixture. Biometrika, 88, 767–778.

    Article  Google Scholar 

  • Lopez, D.F., Little, T.D., Oettingen, G., & Baltes, P.B. (1998). Self-regulation and school performance: Is there optimal level of action-control? Journal of Experimental Child Psychology, 70, 54–74.

    Article  PubMed  Google Scholar 

  • Martin, R.A., Velicer, W.F., & Fava, J.L. (1996). Latent transition analysis to the stages of change for smoking cessation. Addictive Behaviors, 21, 67–80.

    Article  PubMed  Google Scholar 

  • McHugh, R.B. (1956). Efficient estimation and local identification in latent class analysis. Psychometrika, 21, 331–347.

    Article  Google Scholar 

  • Metropolis, M., 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.

    Article  Google Scholar 

  • Muthén, B.O., & Muthén, L.K. (2000). Intergrating person-centered and variable centered analyses: Growth mixture modeling with latent trajectory classes. Alcoholism: Clinical and Experimental Research, 24, 882–891.

    Article  Google Scholar 

  • Muthén, L.K., & Muthén, B.O. (2004). Mplus user’s guide (3rd ed.). Los Angeles: Muthén & Muthén.

    Google Scholar 

  • Pfeffermann, D., Skinner, C., & Humphreys, K. (1998). The estimation of gross flows in the presence of measurement error using auxiliary variables. Journal of the Royal Statistical Society, Series A, 161, 13–32.

    Google Scholar 

  • Richardson, S., & Green, P.J. (1997). On Bayesian analysis of mixtures with an unknown number of components. Journal of the Royal Statistical Society, Series B, 59, 731–792.

    Article  Google Scholar 

  • Robert, C.P. (1996). Mixtures of distributions: Inference and estimation. In W.R. Gilks, S. Richardson, & D.J. Spiegelhalter (Eds.), Markov chain Monte Carlo in practice (pp. 441–464). London: Chapman & Hall.

  • Robert, C.P., & Casella, G. (2004). Monte Carlo statistical methods (2nd ed.). New York: Springer-Verlag.

    Google Scholar 

  • Roberts, G.O. (1992). Convergence diagnostics of the gibbs Sampler. In J.M. Bernardo, J.O. Berger, A.P. Dawid, & A.F.M. Smith (Eds.), Bayesian statistics (Vol. 4, pp. 775–782). Oxford: Oxford University Press.

  • Roeser, R.W., & Eccles, J.S. (1998). Adolescent’s perceptions of middle school: Relation to longitudinal changes in academic and psychological adjustment. Journal of Research on Adolescence, 8(1), 123–158.

    Article  Google Scholar 

  • Rubin, D.B. (1976). Inference and missing data. Biometrika, 63, 581–592.

    Article  Google Scholar 

  • 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: Applications for developmental research (pp. 420–438). Thousand Oaks, CA: Sage.

  • Schafer, J.L. (1997). Analysis of incomplete multivariate data. London: Chapman & Hall.

    Google Scholar 

  • Tanner, W.A., & Wong, W.H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82, 528–550.

    Article  Google Scholar 

  • Tierney, L. (1994). Markov chains for exploring posterior distributions (with discussion). Annals of Statistics, 22, 1701–1762.

    Article  Google Scholar 

  • Van de Pol, F., & Langeheine, R. (1990). Mixed Markov latent class models. In C.C. Clogg (Ed.), Sociological methodology 1990 (pp. 213–247). Oxford: Blackwell.

  • Van de Pol, F., & Langeheine, R. (1994). Discrete-time mixed Markov models. In A. Dale, & R.B. Davies (Eds.), Analyzing social and political change: A casebook of methods (pp. 170–197). London: Sage.

  • Vermunt, J.K., 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.

    Google Scholar 

  • Vermunt, J.K., & Magidson, J. (2005). Latent GOLD 4.0 user’s guide. Belmont, MA: Statistical Innovations.

    Google Scholar 

  • Walls, T.A., & Little, T.D. (2005). Relations among personal agency, motivation, and school adjustment in early adolescence. Journal of Educational Psychology, 97(1), 23–31.

    Google Scholar 

  • Wong, C.A., Eccles, J.S., & Sameroff, A. (2003). The influence of ethnic discrimination and ethnic identification on African American adolescents’ school and socioemotional adjustment. Journal of Personality, 71(6), 1197–1232.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hwan Chung.

Additional information

This research was partially supported by the National Institute on Drug Abuse Grant 1-R03-DA021639. This research was partially supported by the National Institute on Drug Abuse Grant 1-P50-DA10075, The Methodology Center, The Pennsylvania State University. This research was partially supported by the National Institute of Mental Health funds as part of the Studying Diverse Lives research support program at the Henry A. Murray Research Archive, Institute for Quantitative Science, Harvard University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chung, H., Walls, T.A. & Park, Y. A Latent Transition Model With Logistic Regression. Psychometrika 72, 413–435 (2007). https://doi.org/10.1007/s11336-005-1382-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11336-005-1382-y

Key words

Navigation