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Rijmen, F. (2010). Formal Relations and an Empirical Comparison among the Bi-Factor, the Testlet, and a Second-Order Multidimensional IRT Models. Journal of Educational Measurement, 47(3), 361-372.


This paper investigates the relationship between three measurement models: the bi-factor model, the testlet model, and second-order multi-dimensional model. All these three models take into accout of ht conditional dependencies between items within a testlet via testlet-specific dimensions. This paper demonstrates the equivalences between these three models. In particular the testlet model was compared with the bi-factor model with empirical data from an international large-scale English test. The bi-facotr model stands out to have a better fit. However, it is unfortunate that bi-factor models are less often to be considered in the educational measurement field.

Comments:
In this paper, a ‘typical’ bi-factor model was tested and compared with other models such as the testlet model and higher-order model. It should be noted that there are more than one form of bi-factor model and the form of a bi-factor model depends on the design of the test, i.e. the positioning and distribution of the ‘common items’ and ‘group (specific )items’. Based on the result of the current article, further studies can be done with more ‘sophisticated’ bi-factor model, such as by manipulating the degree of overlapping of common items and group items. It is an important consideration since the common/ group items are crucial components. Varying this may not replicate the same results as the authors suggested with modeling the international English assessment data.