Mplus offers IRT analyses using 1PL, 2PL, 3PL, 4PL, and partial credit models. Due to the general modeling framework of Mplus,
the IRT modeling includes unique features that combine multidimensional analysis; twolevel, threelevel, and crossclassified
analysis (Asparouhov & Muthén, 2012, 2013); mixture modeling (Muthén, 2008) and diagnostic classification modeling (Rupp et al., 2010);
as well as multilevel mixture modeling (Asparouhov & Muthén, 2008; Henry & Muthén, 2010).
The models can be estimated by maximumlikelihood, Bayes, and weighted least squares. Graphical displays of item characteristic curves and information curves are also provided.
References:
 Muthén, B. & Asparouhov, T. (2016). MultiDimensional, MultiLevel, and MultiTimepoint Item Response Modeling. In van der Linden, W. J., Handbook of Item Response Theory. Volume One. Models, pp. 527539. Boca Raton: CRC Press. (Download output files, Download Table 6 output).
 Muthén, B. & Asparouhov, T. (2016). Recent methods for the study of measurement invariance with many groups: Alignment and random effects. Mplus scripts.
 Asparouhov, T. & Muthén, B. (2015). General random effect latent variable modeling: Random subjects, items, contexts, and parameters. In Harring, J. R., & Stapleton, L. M., & Beretvas, S. N. (Eds.), Advances in multilevel modeling for educational research: Addressing practical issues found in realworld applications. Charlotte, NC: Information Age Publishing, Inc. Mplus scripts.
 Asparouhov, T., & Muthén, B. (2015). IRT in Mplus. Technical report. www.statmodel.com.
 Muthén, B. & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5: 978. doi: 10.3389/fpsyg.2014.00978.
 Asparouhov, T., & Muthén, B. (2012). Comparison of computational methods for highdimensional item factor analysis. Technical report. www.statmodel.com.
 Henry, K., & Muthén, B. (2010). Multilevel latent class analysis: An application of adolescent smoking typologies with individual and contextual predictors. Structural Equation Modeling, 17, 193215.
 Rupp, A.A., Templin, J., & Henson, R. (2010). Diagnostic measurement: theory, methods, and applications. New York: Guilford.
 Asparouhov, T., & Muthén, B. (2008). Multilevel mixture models. In G. R. Hancock, & K. M. Samuelsen, K. M. (Eds.), Advances in latent variable mixture models (pp. 2751). Charlotte, NC: Information Age Publishing, Inc.
 Muthén, B. (2008). Latent variable hybrids: Overview of old and new models. In Hancock, G. R., & Samuelsen, K. M. (Eds.), Advances in latent variable mixture models, pp. 124. Charlotte, NC: Information Age Publishing, Inc.
A brief technical description of the formulas used in the plots of item characteristics curves and information curves is available. Related technical description can be found
in the Mplus Web Note #4.
The following paper shows the general latent variable modeling framework within which IRT analysis can be performed.
History of IRT developments in Mplus.
For more information, visit our General Description page.
