WELCOME to our site devoted to item response theory (IRT) models for unfolding responses to rating scale items.

Item response theory models have become increasingly popular measurement tools in the past thirty-five years. These models use responses to items on a test or survey questionnaire to simultaneously locate both the items and the respondents on the same latent continuum (or latent space in the case of multidimensional IRT). This enables one to measure individuals on the latent trait defined by the set of items (e.g., ability, attitude, craving, satisfaction, quality of life, etc.) while simultaneously scaling each item on the very same dimension (e.g., easy versus hard items in the case of an ability test, unfavorable versus favorable statements in the case of an attitude questionnaire).

Most of the IRT models described in the psychometric literature have been cumulative in nature. They imply that higher levels of the latent trait (i.e., higher levels of ability, higher levels of satisfaction) should, in all probability, lead to higher item scores, which, in turn, should lead to higher total test scores. However, this is often not the case when binary disagree-agree or graded disagree-agree (i.e., Strongly Disagree, Disagree, Slightly Disagree, Slightly Agree, Agree, Strongly Agree) responses are studied. These responses are often more consistent with a different model – a model referred to as an unfolding model.

An unfolding model suggests that higher item scores should, in all probability, be observed to the extent that the individual and the item are located close to each other on the latent continuum. Unfolding models are, thus, proximity models that predict item scores, and consequently total scores, on the basis of the distances between a given individual and each item in question. These models have been useful in studies of individual attitudes and preferences. For example, proponents of the unfolding approach to attitude measurement believe that an individual agrees with an attitude statement to the extent that the sentiment conveyed by the statement matches the individual’s own opinion on the issue. In terms of the IRT model, the degree of matching between an individual and an item is represented by the proximity of the individual to the item on the hypothetical latent attitude continuum which extends from an unfavorable pole to a favorable pole. If responses reflective of progressively stronger levels of agreement were coded with successive integers (i.e., 1, 2, 3, 4, 5, 6), then an unfolding model would predict larger item scores when the item and individual in question are near each other on the attitude continuum. Proponents of unfolding models suggest that the models are often appropriate whenever binary or graded disagree-agree responses are obtained in a rating scale format as in the case of a Thurstone scale or a Likert scale.

Unfolding models have been proposed in many different contexts in the psychometric literature. This site is devoted to exploring unfolding models within the context of item response theory. IRT unfolding models hold the possibility of sample free measurement, item banking, computer adaptive testing, and individual-based estimates of measurement precision. Our goal is to provide you with information and computing resources that will enable you to use IRT models for unfolding in your own research or practice. We hope to accomplish this goal by providing you with important scientific references on IRT unfolding models and applications, free modeling software, and illustrative data sets.

If you would like to contribute to or comment about this site, then please contact the founder (James S. Roberts). We want to hear from you! Good luck in your measurement endeavors.