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MultiLCIRT: An R package for multidimensional latent class item response models

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  • Bartolucci, Francesco
  • Bacci, Silvia
  • Gnaldi, Michela

Abstract

A class of Item Response Theory (IRT) models for binary and ordinal polytomous items is illustrated and an R package for dealing with these models, named MultiLCIRT, is described. The models at issue extend traditional IRT models allowing for multidimensionality and discreteness of latent traits. They also allow for different parameterizations of the conditional distribution of the response variables given the latent traits, depending on both the type of link function and constraints imposed on the discriminating and difficulty item parameters. These models may be estimated by maximum likelihood via an Expectation–Maximization algorithm, which is implemented in the MultiLCIRT package. Issues related to model selection are also discussed in detail. In order to illustrate this package, two datasets are analyzed: one concerning binary items and referred to the measurement of ability in mathematics and the other one coming from the administration of ordinal polytomous items for the assessment of anxiety and depression. In the first application, aggregation of items in homogeneous groups is illustrated through a model-based hierarchical clustering procedure which is implemented in the proposed package. In the second application, the steps to select a specific model having the best fit in the class of IRT models at issue are described.

Suggested Citation

  • Bartolucci, Francesco & Bacci, Silvia & Gnaldi, Michela, 2014. "MultiLCIRT: An R package for multidimensional latent class item response models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 971-985.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:971-985
    DOI: 10.1016/j.csda.2013.05.018
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    References listed on IDEAS

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    Cited by:

    1. Ping Chen & Chun Wang, 2021. "Using EM Algorithm for Finite Mixtures and Reformed Supplemented EM for MIRT Calibration," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 299-326, March.
    2. Michela Gnaldi & Simone Del Sarto, 2018. "Variable Weighting via Multidimensional IRT Models in Composite Indicators Construction," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 136(3), pages 1139-1156, April.
    3. Francesco Bartolucci & Valentino Dardanoni & Franco Peracchi, 2013. "Ranking Scientific Journals via Latent Class Models for Polytomous Item Response," EIEF Working Papers Series 1313, Einaudi Institute for Economics and Finance (EIEF), revised May 2013.
    4. Michael Brusco & Hans-Friedrich Köhn & Douglas Steinley, 2015. "An Exact Method for Partitioning Dichotomous Items Within the Framework of the Monotone Homogeneity Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 949-967, December.
    5. Silvia Bacci & Michela Gnaldi, 2015. "A classification of university courses based on students’ satisfaction: an application of a two-level mixture item response model," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 927-940, May.
    6. Ewa Genge, 2021. "LC and LC-IRT Models in the Identification of Polish Households with Similar Perception of Financial Position," Sustainability, MDPI, vol. 13(8), pages 1-22, April.
    7. Francesco Bartolucci & Alessio Farcomeni & Luisa Scaccia, 2017. "A Nonparametric Multidimensional Latent Class IRT Model in a Bayesian Framework," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 952-978, December.
    8. Genge, Ewa & Bartolucci, Francesco, 2019. "Are attitudes towards immigration changing in Europe? An analysis based on bidimensional latent class IRT models," MPRA Paper 94672, University Library of Munich, Germany.
    9. Leonard Paas & Tammo Bijmolt & Jeroen Vermunt, 2015. "Long-term developments of respondent financial product portfolios in the EU: a multilevel latent class analysis," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 249-262, August.
    10. Favaro, Donata & Sciulli, Dario & Bartolucci, Francesco, 2020. "Primary-school class composition and the development of social capital," Socio-Economic Planning Sciences, Elsevier, vol. 72(C).
    11. Ewa Genge & Francesco Bartolucci, 2022. "Are attitudes toward immigration changing in Europe? An analysis based on latent class IRT models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 235-271, June.
    12. Luca Brusa & Francesco Bartolucci & Fulvia Pennoni, 2023. "Tempered expectation-maximization algorithm for the estimation of discrete latent variable models," Computational Statistics, Springer, vol. 38(3), pages 1391-1424, September.
    13. Chiara Dal Bianco & Omar Paccagnella & Roberta Varriale, 2016. "A multilevel latent class analysis of the purchasing channels among European consumers," METRON, Springer;Sapienza Università di Roma, vol. 74(3), pages 293-309, December.
    14. Michela Gnaldi, 2017. "A multidimensional IRT approach for dimensionality assessment of standardised students’ tests in mathematics," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(3), pages 1167-1182, May.

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