A Restricted Bi-factor Model of Subdomain Relative Strengths and Weaknesses

Abstract

There are increasing demands to report subscores in educational and psychological assessments. Subscores provide unique information about examinees (Sinharay, Puhan & Haberman, 2011). However, there has been much debate about reporting subscores because subscores require meeting certain standards and psychometric qualities as a prerequisite to reporting them. Because there is an increasing need for improving the methods of estimating subscores, multidimensional item response theory (MIRT) is one of the methods to estimate subscores. One MIRT model is the item bi-factor model, which includes a general dimension on which all items load and specific dimensions corresponding to the subdomains from which the items come (Holzinger & Swineford’s, 1937; Gibbons & Hedeker, 1992). However, there is a challenge to interpreting the specific dimension scores in the item bi-factor model while the general dimension score is readily interpreted. The specific dimension scores are residuals from the general factor and residuals can be difficult to interpret. To solve this issue, a restricted bi-factor model was proposed in this paper. This paper contains a real data study and a simulation study to evaluate this model. The results of two studies, interpretation of the model, and practical application of the model were discussed.