Online Program

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

Michael Berbaum, University of Illinois at Chicago 
Hakan Demirtas, University of Illinois at Chicago 
*Donald Hedeker, University of Illinois at Chicago 
Robin Mermelstein, University of Illinois at Chicago 

Keywords: heterogeneity, ordinal, IRT, scale

Questionnaires are commonly used in studies of health to measure severity of illness, for example. 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 or their "ability") and characteristics of the items (e.g., item difficulty and discrimination). These item parameters characterize the mean model and indicate the level of item endorsement (difficulty) and the degree to which the item separates subjects of varying ability levels (discrimination). In this presentation, in addition to the subject's random ability, we also model the within-subjects variance and allow for a random subject scale effect ("variability"). In terms of item parameters, this extended IRT model includes item difficulty and discrimination scale parameters, which indicate the degree to which items are scaled differently across the ordinal categories (scale difficulty) and separate subjects of varying levels of variability (scale discrimination). We illustrate application of this location scale IRT model using data from the Alcohol Motives Scale assessed in an adolescent study. We show that these additional item and subject parameters provide improved fit of the data and yield interesting results on the utility of the items and response characteristics of the subjects. The proposed location scale IRT model has useful applications in health research where questionnaires are often rated on an ordinal scale, and there is interest in characterizing both items and subjects in terms of their mean and variance properties.