This study demonstrated how bi-factor model can be applied in vertical scaling through simulation study and real data analysis. Items in bi-factor model are required to have a nonzero loading on a general factor and only one nonzero loading on the group-specific factor. Additionally, group factors are orthogonal to one another and to the general factor. Only common-item design for vertical scaling was used in simulation. Among the three manipulated factors, sample size and variance of grade-specific dimension were found to significantly affect the parameter estimation.
Q:
1. Refer to the simulation design, a set of common items is used for adjacent grades. However, as the participants come from different grades, are common items really “common” across these groups? It is reasonable to assume that these common items have different meanings and difficulty levels for different groups.
2. It is strange in figure 2, that all sets of common items measure more than one grade-specific dimension.
3. For the simulation study, it is expected that true model should provide better parameter recovery. Then what is the meaning comparing performance of bi-factor model and UIRT model?
4. How to assess whether the two requirements for bi-factor are met for real data? They are strict requirements and what is the consequence if not satisfied?