Educational Sciences: Theory & Practice

ISSN: 2630-5984

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

Yusuf Kara
Department of Educational Measurement and Evaluation, Anadolu University, Eskisehir, Turkey
Akihito Kamata
Department of Education Policy & Leadership and Department of Psychology, Southern Methodist University, Dallas, TX, USA

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.