Item Response Theory (IRT)

Mplus offers IRT analyses using 1PL, 2PL, 3PL, 4PL, partial credit, and generalized partial credit models. Due to the general modeling framework of Mplus, the IRT modeling includes unique features that combine multidimensional analysis; two-level, three-level, and cross-classified 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 maximum-likelihood, Bayes, and weighted least squares. The relative strengths of the estimators is discussed in the document Estimator choices with categorical outcomes. Bootstrap standard errors and confidence intervals are also available. Graphical displays of item characteristic curves and information curves are also provided.

References:

• Asparouhov, T., & Muthén, B. (2020). IRT in Mplus. Version 4. Technical report. www.statmodel.com.
  
  
• Montoya, A.K. & Jeon, M. (2019). MIMIC models for uniform and nonuniform DIF as moderated mediation models. Applied Psychological Measurement. DOI: 10.1177/0146621619835496
  
  
• Muthén, B. & Asparouhov, T. (2018). Recent methods for the study of measurement invariance with many groups: Alignment and random effects. Sociological Methods & Research, 47:4 637-664. DOI: 10.1177/0049124117701488 Mplus scripts.
  
  
• Muthén, B. & Muthén, L. (2016). Mplus: A General Latent Variable Modeling Program. In van der Linden, W. J., Handbook of Item Response Theory. Boca Raton: CRC Press.
  
  
• Muthén, B. & Asparouhov, T. (2016). Multi-Dimensional, Multi-Level, and Multi-Timepoint Item Response Modeling. In van der Linden, W. J., Handbook of Item Response Theory. Volume One. Models, pp. 527-539. Boca Raton: CRC Press. (Download output files, Download Table 6 output).
  
  
• Asparouhov, T. & Muthén, B. (2016). 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 real-world applications (pp. 163-192). Charlotte, NC: Information Age Publishing, Inc. Mplus scripts.
  
  
• 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 high-dimensional 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, 193-215.
  
  
• 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. 27-51). 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. 1-24. Charlotte, NC: Information Age Publishing, Inc.
  
  
• Muthén, B. & Asparouhov, T. (2006). Item response mixture modeling: Application to tobacco dependence criteria. Addictive Behaviors 31, 1050 – 1066.
  
  

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.