Full-Information Item Bifactor Analysis of Graded Response Data

Abstract

A plausible factorial structure for many types of psychological and educational tests exhibits a general factor and one or more group or method factors. This structure can be represented by a bifactor model. The bifactor structure results from the constraint that each item has a nonzero loading on the primary dimension and, at most, one of the group factors. The authors develop estimation procedures for fitting the graded response model when the data follow the bifactor structure. Using maximum marginal likelihood estimation of item parameters, the bifactor restriction leads to a major simplification of the likelihood equations and (a) permits analysis of models with large numbers of group factors, (b) permits conditional dependence within identified subsets of items, and (c) provides more parsimonious factor solutions than an unrestricted full-information item factor analysis in some cases. Analysis of data obtained from 586 chronically mentally ill patients revealed a clear bifactor structure.

An IRT analysis of motive questionnaires: The Unified Motive Scales

“…As the resulting fear scale is a multifaceted construct, it can be best described by a multidimensional IRT model, namely, the bifactor GRM model (Gibbons et al, 2007;Wirth & Edwards, 2007). This model assumes that item responses are determined by a general factor and by subdomains, which are formed by item parcels.…”

“…This model assumes that item responses are determined by a general factor and by subdomains, which are formed by item parcels. Using the BIFACTOR program (Gibbons et al, 2007), we estimated a unidimensional model as the baseline model and a bifactor model with fear facets as subdomains. The bifactor model showed a significant improvement in fi t compared to the unidimensional model, χ 2 (df = 14) = 1,497.00, p < .001, and an excellent absolute model fit as indicated by a root mean square error (RMSE) of .005 between observed and expected proportions of responses (Gibbons et al, 2007).…”

“…Using the BIFACTOR program (Gibbons et al, 2007), we estimated a unidimensional model as the baseline model and a bifactor model with fear facets as subdomains. The bifactor model showed a significant improvement in fi t compared to the unidimensional model, χ 2 (df = 14) = 1,497.00, p < .001, and an excellent absolute model fit as indicated by a root mean square error (RMSE) of .005 between observed and expected proportions of responses (Gibbons et al, 2007). However, we want to make clear that this bifactor model is a post-hoc evaluation of the obtained data structure and should be rather treated as a starting point to stimulate future research on the fear components of motives.…”

Mental Health Assessment

“…Specifically, if the difference in log-likelihood value between the unidimensional and bifactor model was statistically significant, then it was concluded that the bifactor model more accurately described the scale's multidimensional factor structure. Model-data fit was also judged in terms of correspondence between the observed and expected proportion of item categorical frequencies (17).…”

Future Professionals: A Study of Sustainable Behavior

“…Regarding the IRT models, the so-called hierarchical MIRT models, Gibbons and Hedeker generalized the classical work of Holzinger and Swineford [38] and proposed the full-information bi-factorial (FI bi-factorial) model for dichotomous data [40,41]. This model consists of a general factor and group factors or independent dimensions.…”