A Location Scale Item Response Theory (IRT) Model for Analysis of Ordinal Questionnaire Data

• Activity Number: 335
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Donald Hedeker*+ and Robin Mermelstein and Hakan Demirtas
• Companies: University of Illinois-Chicago and University of Illinois at Chicago and University of Illinois at Chicago
• Keywords: IRT ; multilevel ; ordinal ; complex variation

Abstract

Questionnaires are commonly used in many studies, and the items that comprise the questionnaire are often scored on an ordinal scale, for example on a Likert scale. For such questionnaires, item response theory (IRT) models provide a useful approach for obtaining summary scores for subjects (i.e., the model's random subject effect) and characteristics of the items (e.g., item difficulty and discrimination). In this presentation, we describe an extended IRT model that allows the items to additionally exhibit different within-subject variance, and also extend the ordinal IRT model by adding a subject-level random effect to the within-subject variance specification. This permits subjects to be characterized in terms of their mean level, or location, and also their variability, or (square of the) scale. Additionally, we allow the random effects to be correlated. We illustrate application of this location scale IRT model using data from the Nicotine Dependence Syndrome Scale (NDSS) assessed in an adolescent smoking study.