The paper describes the application of bifactor model in vertical scaling with construct shift.
The overall article is made of three parts. First off, it explains why we should adopt the bifactor model and what is vertical scaling. Secondly, the simulations of parameter estimation were conducted and manipulated in different sorts of conditions. Thirdly, the proposed model was applied to real data, which was compared with the uni-dimensional IRT model. Lastly, a few conclusions and discussions were given.
The main feature of bifactor model is that it assumes there is a common factor governing the targeted latent trait. In contrast, the second factor is regard as the other interfering sources that could be lower the validity of the test. In this paper, it assumes the second factor can be interpreted as the grade-specific dimension for each grade. To enhance the accuracy of parameter estimation, the bifactor model was used due to its simpleness and readiness rather than multidimensional IRT models. The results of simulations indicate that the parameters were well recovered under conditions, especially when the sample size is larger. For real data analysis, the results suggest the small amount of variances of second factor exist.
Some questions:
1. Though it assumes the second factor can be seen as grade-specific effect, it sounds like they are sort of random errors but with different size of variances. Why not just using the multilevel IRT model? It may be an alternative.
2. In real data analysis, it is a bit odd the author compared the bifactor model with testlet models. Competing models such as MIRT or multilevel models can be included for comparison, because they are more appropriate for the structure of data.