1. the magnitude of exposure of every item should be considered, not just the same. Some items were exposed to the public frequently, others were not.
2. the T =0 only if theta=theta_c. But in computer computation, this may be probelmatic due to rounding error.
3. In p. 491, he used to BILOG fit the unexposed items and DGM fit the all items.
The theta_c in DGM can be regarded as an explanation ability or can explain the random error (no matter what it is). I think the theta in BILOG and DGM would be the same without doubt. The correlation estimate says nothing. The authour's way of explanation seems misleading.
4. In p.492, the bootstrap results looks not meaningful and redundant. The bootstrap method cannot be used to confirm or prove the "internal consistency" of model (the author claimed in the last sentence).