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

Author/s: Yusuf Kara, Akihito Kamata

DOI: 10.12738/estp.2017.4.0250 

Year: 2017 Vol: 17 Number: 4

Abstract

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.

Keywords
Multilevel IRT, Hierarchical generalized linear model (HGLM), Hierarchical measurement model, Normality violation, Parameter recovery

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