Exploring the Full-Information Bifactor Model in Vertical Scaling with construct shift
Ying Li & Robert Lissitz
The bifactor model has several advantages. In vertical scaling, two basic assumptions are assumed: (1) unidimensionality at each grade-level test, (2) test construct invariance across grades. In this study, shifts in constructs over grades in vertical scaling was investigate using the bifactor model. The item parameters recovery were examined under various conditions. The item and person parameters estimation were compared between the bifactor model and unidimensional model. It was found that bifactor model were well recovered overall though the grade-specific dimensional were not desirable. The item discrimination and person parameters of unidmensional models were not accurate when the ‘true’ model is bifactor model.
Question and Comments:
1. It is odd to me that the results of empirical data that the degree of construct shift was small (the estimated variance are 0.21, 0.14 and 0.18 for G3, 4 and 5, respectively). In a common sense, the constructs in these grades should be shifted greatly.
2. With Question 1. It was found in the simulation that the grade-specific variance parameters were not well recovered. Thus, for the small construct shift in the empirical study, is it the result of the ‘true’ small construct shift, or inaccurate estimation of the grade-specific variance?
3. I’m interesting to know if the discrimination parameter for the grade-specific dimension in bifactor model was not fixed to the true parameter value, will it affect the estimation of grade-specific variance?
4. The common item design for vertical linking is applicable for ability-based subjects, for example, mathematical test. However, for non ability-based subjects, for example, science, biology, etc, it is hard to design common items for the adjacent grades.