References

General

Mplus analysis

Asparouhov, T. & Muthen, B. (2003a). Full-information maximum-likelihood estimation of general two-level latent variable models. In preparation.

Asparouhov, T. & Muthen, B. (2003b). Maximum-likelihood estimation in general latent variable modeling. In preparation.

Muthen, B. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29, 81-117.

Muthen, B. & Asparouhov, T. (2003a). Advances in latent variable modeling, part I: Integrating multilevel and structural equation modeling using Mplus. In preparation.

Muthen, B. & Asparouhov, T. (2003b). Advances in latent variable modeling, part II: Integrating continuous and categorical latent variable modeling using Mplus. In preparation.

Numerical integration

Aitkin, M. A general maximum likelihood analysis of variance components in

generalized linear models. Biometrics, 1999, 55, 117-128.

Bock, R.D. & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.

General

Muthen, L. & Muthen, B. (1998-2003). Mplus User's Guide. Los Angeles, CA: Muthen & Muthen.

Muthen, L.K. and Muthen, B. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599-620.

Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 34, 1-13.

SEM

Latent variable interactions

Klein, A. & Moosbrugger, H. (2000). Maximum likelihood estimation of latent interaction effects with the LMS method. Psychometrika, 65, 457-474.

Indirect effects

MacKinnon, D.P., Lockwood, C.M., Hoffman, J.M., West, S.G. & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7, 83-104.

Shrout, P.E. & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: New procedures and recommendations. Psychological Methods, 7, 422-445.

Growth Modeling

Carlin, J.B., Wolfe R., Brown, C.H., Gelman, A. (2001). A case study on the choice, interpretation and checking of multilevel models for longitudinal binary outcomes. Biostatistics, 2, 397-416.

Duan, N., Manning, W.G., Morris, C.N. & Newhouse, J.P.( 1983). A comparison of alternative models for the demand for medical care. Journal of Business and Economic Statistics, 1, 115-126.

Farrington, D.P. & West, D.J. (1990). The Cambridge study in delinquent development: A prospective longitudinal study of 411 males. In Criminality: Personality, Behavior, and Life History, edited by Hans-Jurgen Kernere and G. Kaiser. New York: Springer -Verlag.

Hedeker, D. (2000). A fully semi-parametric mixed-effects regression model for categorical outcomes. Presented at the Joint Statistical Meetings, Indianapolis, IN, 2000.

Hedeker, D. & Gibbons, R.D. (1994). A random-effects ordinal regression model for multilevel analysis. Biometrics, 50, 933-944.

Olsen, M. K, & Schafer, J., L. (2001). A two-part random effects model for semicontinuous longitudinal data. Journal of the American Statistical Association, 96, 730-745.

Raudenbush, S.W. & Bryk, A.S. (2002). Hierarchical linear models: Applications and data analysis methods. Second edition. Newbury Park, CA: Sage Publications.

Tobin, J (1958). Estimation of relationships for limited dependent variables. Econometrica, 26, 24-36.

Multilevel Modeling

Choi, K.C. (2002). Latent variable regression in a three-level hierarchical modeling framework: A fully Bayesian approach. Doctoral dissertation, University of California, Los Angeles.

Seltzer, M., Choi, K. & Thum, Y.M. (2002). Examining relationships between where students start and how rapidly they progress: Implications for conducting analyses that help illuminate the distribution of achievement within schools. CSE Technical Report 560. CRESST, University of California, Los Angeles.

Mixture Modeling

Albert, P.A., McShane, L. M., Shih, J.H. & The US NCI Bladder Tumor Marker Network (2001). Latent class modeling approaches for assessing diagnostic error without a gold standard: With applications to p53 immunohistochemical assays in bladder tumors. Biometrics, 57, 610-619.

Bijleveld, C. C. J. H., & van der Kamp, T. (1998). Longitudinal data analysis: Designs, models, and methods. Newbury Park: Sage.

Heinen, D. (1996). Latent class and discrete latent trait models: similarities and differences. Thousand Oakes, CA: Sage Publications.

Land, K.C. (2001). Introduction to the special issue on finite mixture models. Sociological Methods & Research, 29, 275-281.

Lo, Mendell, & Rubin (2001). Testing the number of components in a normal mixture. Biometrika, 88, 767-778.

McLachlan, G. J. & Peel, D. (2000). Finite mixture models. New York: Wiley & Sons.

Mooijaart, A. (1998). Log-linear and Markov modeling of categorical longitudinal data. In Bijleveld, C. C. J. H., & van der Kamp, T. (eds). Longitudinal data analysis: Designs, models, and methods. Newbury Park: Sage.

Muthen, B. (2001b). Two-part growth mixture modeling. Draft.

Muthen, B. (2003a). Statistical and substantive checking in growth mixture modeling. Psychological Methods, 8, 369-377.

Muthen, B. (2003b). Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data. Forthcoming in D. Kaplan (ed.), Handbook of Quantitative Methodology for the Social Sciences, Sage Publications.

Muthen, B. (2003c). Advances in latent variable modeling of heterogeneous phenotypes. Presentation at NIDA, May 2003.

Muthen, B. (2003d). Multilevel growth mixture modeling: Math achievement trajectory classes and high school dropout. Presentation at AERA, March 2003.

Muthen, B., Kreuter, F. & Asparouhov, T. (2003). Applications of growth mixture modeling to non-normal outcomes. In preparation.

Muthen, B. & Masyn, K. (2001). Mixture discrete-time survival analysis. Submitted to Journal of Educational and Behavioral Statistics.

Muthen, B. & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55, 463-469.

Nagin, D.S. (1999). Analyzing developmental trajectories: A semi-parametric, group-based approach. Psychological Methods, 4, 139-157.

Nagin, D.S. & Land, K.C. (1993). Age, criminal careers, and population heterogeneity: Specification and estimation of a nonparametric, mixed Poisson model. Criminology, 31, 327-362.

Qu, Y., Tan, M., & Kutner. M.H. (1996). Random effects models in latent class analysis for evaluating accuracy of diagnostic tests. Biometrics, 52, 797-810.

Roeder, K., Lynch, K.G., & Nagin, D.S. (1999). Modeling uncertainty in latent class membership: A case study in criminology. Journal of the American Statistical Association, 94, 766-776.

Rumberger, R.W. & Larson, K.A. (1998). Student mobility and the increased risk of high school dropout. American Journal of Education, 107, 1-35.

Singer, J.D. & Willett, J.B. (1993). It's about time: using discrete-time survival analysis to study duration and the timing of events. Journal of Educational Statistics, 18, 155-195.

Wang, C. P., Brown, C. H. & Bandeen-Roche, K. (2002). Residual diagnostics for growth mixture models: Examining the impact of a preventive intervention on multiple trajectories of aggressive behavior. Manuscript submitted for publication.

Yamamoto, K. & Gitomer, D. (1993). Application of a HYBRID model to a test of cognitive skill representation. In N. Frederiksen, R. Mislevy, and I Beijar (eds.), Test theory for new generation of tests. Hillsdale, NJ: LEA.