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Dimensionality of the Latent Structure and Item Selection Via Latent Class Multidimensional IRT Models

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  • F. Bartolucci
  • G. Montanari
  • S. Pandolfi

Abstract

With reference to a questionnaire aimed at assessing the performance of Italian nursing homes on the basis of the health conditions of their patients, we investigate two relevant issues: dimensionality of the latent structure and discriminating power of the items composing the questionnaire. The approach is based on a multidimensional item response theory model, which assumes a two-parameter logistic parameterization for the response probabilities. This model represents the health status of a patient by latent variables having a discrete distribution and, therefore, it may be seen as a constrained version of the latent class model. On the basis of the adopted model, we implement a hierarchical clustering algorithm aimed at assessing the actual number of dimensions measured by the questionnaire. These dimensions correspond to disjoint groups of items. Once the number of dimensions is selected, we also study the discriminating power of every item, so that it is possible to select the subset of these items which is able to provide an amount of information close to that of the full set. We illustrate the proposed approach on the basis of the data collected on 1,051 elderly people hosted in a sample of Italian nursing homes. Copyright The Psychometric Society 2012

Suggested Citation

  • F. Bartolucci & G. Montanari & S. Pandolfi, 2012. "Dimensionality of the Latent Structure and Item Selection Via Latent Class Multidimensional IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 782-802, October.
    • Handle: RePEc:spr:psycho:v:77:y:2012:i:4:p:782-802
    DOI: 10.1007/s11336-012-9278-0
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    References listed on IDEAS

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    1. Hans‐Peter Kohler & Francesco C. Billari & José Antonio Ortega, 2002. "The Emergence of Lowest‐Low Fertility in Europe During the 1990s," Population and Development Review, The Population Council, Inc., vol. 28(4), pages 641-680, December.
    2. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    3. Francesco Bartolucci, 2007. "A class of multidimensional IRT models for testing unidimensionality and clustering items," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 141-157, June.
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    1. Francesco Dotto & Alessio Farcomeni & Maria Grazia Pittau & Roberto Zelli, 2019. "A dynamic inhomogeneous latent state model for measuring material deprivation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(2), pages 495-516, February.
    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. Michela Gnaldi & Simone Del Sarto, 2018. "Time Use Habits of Italian Generation Y: Dimensions of Leisure Preferences," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 138(3), pages 1187-1203, August.
    4. Simone Del Sarto & Michela Gnaldi, 2022. "Spare time use: profiles of Italian Millennials (beyond the media hype)," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1403-1428, December.
    5. 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.
    6. 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.

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