It is an interesting paper, though not related to IRT. The researchers were interested in modeling the stability of individual response styples in longitudinal data. A two-order model was proposed in which the time-invariant latent traits for response styles was regressed with the personal variables in the second-order, and the time-specific latent traits for response styles was measured by some indicators in the first-order. The model was proposed and estimated within the framework of SEM. The model-data fit was evaluated so as to provide the evidience of the correctness of the model.
Questions and comments:
1. Can the first-order measurement model replaced by an IRT model?
2. The model was quite complex with some residual correlated to each other. For example, epslon 1 and epson 4 are assumed to be correlated. To make model simpler, can we assumed them to be independent and will the independent structure cause the model misspecification and cause the change of the meaning of factors?