Introduction to bifactor polytomous item response theory analysis

A bifactor item response theory model can be used to aid in the interpretation of the dimensionality of a multifaceted questionnaire that assumes continuous latent variables underlying the propensity to respond to items. This model can be used to describe the locations of people on a general continuous latent variable as well as on continuous orthogonal specific traits that characterize responses to groups of items. The bifactor graded response (bifac-GR) model is presented in contrast to a correlated traits (or multidimensional GR model) and unidimensional GR model. Bifac-GR model specification, assumptions, estimation, and interpretation are demonstrated with a reanalysis of data (Campbell, 2008) on the Shared Activities Questionnaire. We also show the importance of marginalizing the slopes for interpretation purposes and we extend the concept to the interpretation of the information function. To go along with the illustrative example analyses, we have made available supplementary files that include command file (syntax) examples and outputs from flexMIRT, IRTPRO, R, Mplus, and STATA. Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.jsp.2016.11.001. Data needed to reproduce analyses in this article are available as supplemental materials (online only) in the Appendix of this article.