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Multilevel IRT Modeling in Practice with the Package mlirt

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  • Fox, Jean-Paul

Abstract

Variance component models are generally accepted for the analysis of hierarchical structured data. A shortcoming is that outcome variables are still treated as measured without an error. Unreliable variables produce biases in the estimates of the other model parameters. The variability of the relationships across groups and the group-effects on individuals' outcomes differ substantially when taking the measurement error in the dependent variable of the model into account. The multilevel model can be extended to handle measurement error using an item response theory (IRT) model, leading to a multilevel IRT model. This extended multilevel model is in particular suitable for the analysis of educational response data where students are nested in schools and schools are nested within cities/countries.

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  • Fox, Jean-Paul, 2007. "Multilevel IRT Modeling in Practice with the Package mlirt," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i05).
    • Handle: RePEc:jss:jstsof:v:020:i05
    DOI: http://hdl.handle.net/10.18637/jss.v020.i05
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    3. Jean‐Paul Fox, 2004. "Modelling response error in school effectiveness research," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(2), pages 138-160, May.
    4. Jean-Paul Fox & Cees Glas, 2001. "Bayesian estimation of a multilevel IRT model using gibbs sampling," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 271-288, June.
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    Cited by:

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    3. Brzezińska Justyna, 2016. "Latent Variable Modelling and Item Response Theory Analyses in Marketing Research," Folia Oeconomica Stetinensia, Sciendo, vol. 16(2), pages 163-174, December.
    4. repec:jss:jstsof:39:i12 is not listed on IDEAS
    5. Lara Fontanella & Mara Maretti & Annalina Sarra, 2014. "Gender fluidity across the world: a Multilevel Item Response Theory approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(5), pages 2553-2568, September.
    6. Minjeong Jeon & Sophia Rabe-Hesketh, 2012. "Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models With Factor Structures," Journal of Educational and Behavioral Statistics, , vol. 37(4), pages 518-542, August.
    7. de Leeuw, Jan & Mair, Patrick, 2007. "An Introduction to the Special Volume on "Psychometrics in R"," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i01).
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