A mixed dimensionality approach was proposed in this study, which employed a second dimension to explain the DIF effect. The secondary dimension was assumed to play a role in the DIF class only, and create the DIF. The mixed approach could be used both in the manifest DIF and the latent DIF. Several models were compared through two applications, and the results supported the use of secondary dimension.
Q:
1. The proposed model was said to be used for DIF explanation, rather than DIF detection, what is the difference between these two functions?
2. The secondary dimension was assumed to be the only source of DIF. How to differentiate the DIF effect resulted from the intended dimension and the secondary dimension?
3. I don’t understand how the mixed dimensionality can be related to the notion of measurement invariance.
2. Firstly, DIF effect is viewed as the consequence of the secondary dimension (not intended dimension). But we can model the DIF with one dimensional or two dimensional approach. The different is that: the DIF effect is fixed effect in one dimensional approach whereas it is random effect in the two dimensional approach.
3. Mixed dimensionality means the second dimension plays a role in one group but not in the other group. With the second dimension, the measurement variance (or DIF) could be modelled.