Two-Tier Latent Class IRT Models in R

In analyzing data deriving from the administration of a questionnaire to a group of individu als, Item Response Theory (IRT) models provide a flexible framework to account for several aspects involved in the response process, such as the existence of multiple latent traits. In this paper, we focus on a class of semi-parametric multidimensional IRT models, in which these traits are represented through one or more discrete latent variables; these models allow us to cluster individuals into homo geneous latent classes and, at the same time, to properly study item characteristics. In particular, we follow a within-item multidimensional formulation similar to that adopted in the two-tier models, with each item measuring one or two latent traits. The proposed class of models may be estimated through the package MLCIRTwithin, whose functioning is illustrated in this paper with examples based on data about quality-of-life measurement and about the propensity to commit a crime.

Silvia Bacci , Francesco Bartolucci

CRAN packages used

MLCIRTwithin, MultiLCIRT, CDM, mirt, flirt, covLCA, lavaan, OpenMx, LMest

CRAN Task Views implied by cited packages

Psychometrics, Econometrics, OfficialStatistics


Text and figures are licensed under Creative Commons Attribution CC BY 4.0. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ...".


For attribution, please cite this work as

Bacci & Bartolucci, "The R Journal: Two-Tier Latent Class IRT Models in R", The R Journal, 2016

BibTeX citation

  author = {Bacci, Silvia and Bartolucci, Francesco},
  title = {The R Journal: Two-Tier Latent Class IRT Models in R},
  journal = {The R Journal},
  year = {2016},
  note = {},
  doi = {10.32614/RJ-2016-038},
  volume = {8},
  issue = {2},
  issn = {2073-4859},
  pages = {139-166}