History of Item Response Theory (IRT) in Mplus

Following is a brief overview of Item Response Theory (IRT) analysis in Mplus, a list of IRT examples in the Mplus Version 4 User's Guide, and links to technical descriptions of IRT modeling in Mplus.

Starting with Version 1 released in 1998, analysis using the "normal ogive" model of probit regression for binary and ordered polytomous items was possible with limited-information weighted least squares estimation using the WLSMV estimator. The analysis was implemented in the general framework of Muthen (1984; see website References), including covariates, multiple-group analysis, and other model parts. Factor score estimation uses the maximum a posteriori (MAP) approach. For a description of these approaches, see the Technical appendices.

The release of Mplus Version 3 in March 2004 added analysis with a 2-parameter logistic model and maximum-likelihood estimation. As a special case, this gives the 1-parameter Rasch model, where factor loadings (item discriminations) are held equal across items. The items can be binary, ordered polytomous, censored, and counts. Factor score estimation uses the expected a posteriori (EAP) approach. ML estimation is also available with the normal ogive probit model for binary and ordered polytomous items. The analysis is implemented in the general Mplus framework. As such, this also includes finite mixture IRT analysis, multilevel IRT analysis, and multilevel mixture IRT analysis.

Mplus Version 4.1 released in May 2006 added IRT plots to its graphics features. These are item characteristic curves and information curves for individual items, sets of items, and all items. They are available for mixture models, multilevel models, and multilevel mixture models. In addition to presenting parameter estimates and standard errors in the regular factor analysis metric, they are also given in conventional IRT 2PL metric with a single latent variable and binary items.

The 2PL IRT examples in the Mplus Version 4 User's Guide are as follows. Ex 5.5 presents a standard 2PL model. Ex 7.26 presents a mixture approach to a non-parametric alternative of the normality assumption for the latent variable. Ex 7.27 presents a mixture IRT model. Ex 7.29 presents a 2-group 2PL IRT analysis for monozygotic and dizygotic twins. Ex 9.6 presents a 2-level analysis with a random intercept factor and covariates. These examples are also available in Monte Carlo simulation form on the Mplus website and CD.

Mplus Version 7.4 introduced 3PL, 4PL, and generalized Partial Credit Modeling (PCM); see Asparouhov and Muthén (2015). Due to the general modeling framework, this means, for example, that multilevel and mixture PCM with observed and latent predictors are available as well.