Parameter Recovery for the 1-P HGLLM with Non-Normally Distributed Level-3 Residuals

KARA Y., Kamata A.

EDUCATIONAL SCIENCES-THEORY & PRACTICE, vol.17, no.4, pp.1165-1177, 2017 (SSCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.12738/estp.2017.4.0250
  • Journal Indexes: Social Sciences Citation Index (SSCI), Scopus
  • Page Numbers: pp.1165-1177
  • Keywords: Multilevel IRT, Hierarchical generalized linear model (HGLM), Hierarchical measurement model, Normality violation, Parameter recovery
  • Anadolu University Affiliated: Yes


A multilevel Rash model using a hierarchical generalized linear model is one approach to multilevel item response theory (IRT) modeling and is referred to as a one-parameter hierarchical generalized linear logistic model (1-P HGLLM). Although it has the flexibility to model nested structure of data with covariates, the model assumes the normality of the residuals (i.e., abilities) at all its levels. However, in real-world datasets, the normality assumption of the residuals may not always be sound. This study investigated the parameter recovery characteristics for the 1-P HGLLM when the normality assumption of higher-level residuals is violated. Under a three-level 1-P HGLLM, two separate simulation studies were conducted with skewed and uniformly distributed level-3 residuals. Results from both simulation studies showed that there was not a dramatic effect of the non-normal level-3 residuals on the parameter estimations. Suggestions for further research were also provided in the discussion section.