A General Item Response Theory Model for Unfolding Unidimensional Polytomous Responses

Abstract

The generalized graded unfolding model (GGUM) is developed. This model allows for either binary or graded responses and generalizes previous item response models for unfolding in two useful ways. First, it implements a discrimination parameter that varies across items, which allows items to discriminate among respondents in different ways. Second, the GGUM permits response category threshold parameters to vary across items. A marginal maximum likelihood algorithm is implemented to estimate GGUM item parameters, whereas person parameters are derived from an expected a posteriori technique. The applicability of the GGUM to common attitude testing situations is illustrated with real data on student attitudes toward abortion. Index terms: attitude measurement, generalized graded unfolding model, graded unfolding model, item response theory, Likert scale, marginal maximum likelihood, Thurstone scale, unfolding model.Several researchers have recently argued that binary or graded agree-disagree responses to attitude statements generally result from an ideal point process (Coombs, 1964) in which a person endorses an attitude statement to the extent that it matches the person's opinion (This argument implies that an unfolding (i.e., proximity) model that implements a single-peaked response function would be best for analyzing agree-disagree responses, including both binary and graded responses. In the context of item response theory (IRT), an unfolding model suggests that a person will agree with a statement to the extent that the person and the statement are located near each other on an underlying continuum-a latent continuum that spans the two poles of negative and positive affect.Several unidimensional item response models are available for unfolding agree-disagree responses to attitude statements. Some of these models are appropriate for binary responses, whereas others allow for either binary or graded data. Models for binary data use parametric approaches (Although nonparametric models are practical because they make fewer assumptions about the specific form of the item response function, correctly specified parametric models offer additional measurement advantages. Attitude estimates from parametric models are invariant to the items used to calibrate the estimates. Additionally, estimates of item locations are invariant to the distribution of attitudes in the sample. These two qualities emerge from the fact that if an unfolding model correctly and completely specifies response category probabilities, given only the item and the

Personality Assessment, Forced-Choice

“…Stark and colleagues (2005) use an ideal-point model to substitute the probabilities of accepting and rejecting individual items in general expression (8). Specifically, they advocate the use of a binary version of the Generalized Graded Unfolding Model or GGUM (Roberts, Donoghue, and Laughlin 2000). The GGUM is very flexible and allows items to differ in discrimination, locations and even in maximum probability of endorsement.…”

Teoria da Resposta ao Item

“…Models for binary data can be found in the studies (5,(22)(23)(24)(37)(38) , and models for graded data in others (39)(40) . Of these, the following are worth noting: the Parella Model (22)(23) , GGUM (Generalized Graded Unfolding Model) (40) and the Hyperbolic Cosine Model (HCM) (24) .…”

Constructing a Scale of Attitudes toward School Science Using the General Graded Unfolding Model

“…This argument implies that the unfolding model is more appropriate for the agree-disagree data than the cumulative model (Roberts, 1995;Laughlin, 2000, Roberts andLaughlin, 1996).…”

“…It specifies the relationship between a person's observed responses to a set of items and the unobserved latent trait that is being measured by the item set. It also implements Single-Peaked, nonmonotonic probability functions, and allows for binary or graded agree-disagree responses (Roberts, 2001;Roberts et al, 2000;& Roberts, Lin, & Laughlin, 2001). Furthermore, if a parametric unfolding model is used, and adequately fits the data, then the item parameters will be sample free and the person parameters will be item invariant (Hambleton, Swaminathan, & Rogers,1991;Hoijtink,1990).…”

“…The GGUM allows for differential response category use across items, it also allows variable levels of discrimination among items, and has the properties of sample invariant interpretation of item parameters, item invariant interpretation of person parameters (Roberts, 2001;Roberts, 2003;Roberts et al, 2000;Roberts et al, 2001). …”