1. Formula (9) to (12) used the MAP estimate only and assumed the same MAP in two repeated measurement, while they used resampled thetas (implying not always using MAP) to calculate reliability in IRT model. I suspect the two approaches used unequal information, which led to overestimated DCM reliability. Because the approach they used for DCM seems have ignored uncertainty of estimates.
2. Why not just using latent continuous attribute in DCM for equal comparison to IRT model? (however, the DCM and IRT should be almost the same when using two-category attribute) The resampling approach to calculate reliability can be implemented via MCMC which would obtain more precise measurement.
3. Formula (15) and (16) looks strange cos there is a integral within the logit.