The hierarchical modeling of response and time is appealing because of introducing the covariance structure between theta and tau. The within-person level, fixed-person level, and a population of fixed persons are considered. Finally, an empirical data were analyzed and estimates of parameters were shown. It seems the person’s theta is correlated positively to response time in medium level, as shown in prior studies.
1. In (21), it has typos that the response model should be (9) instead of (12).
2. In CAT, only the theta and tau is unknown. The MCAT is a good study to do in future. Many item selection methods have been proposed such as KL or MI can be adopted.
3. The Gibbs sampler is appealing due to its high speed to convergence. But derivation of conjugate prior is complicated. General software like WinBUGS or JAGS would be another alternative.
4. The model-data fit is still scanty. The discussion about the results of empirical data is too simple. The correlation (listed in paper) seems not quite large enough to explain anything.
5. The convergences of trace plots are redundant. We’re not interested in them.
6. I don’t quite understand why the correlation between item parameters is important and has effect on the observed scores and time.