are you sure that the reason it as stated here - maybe not everybody check for local dependence and items, maybe some adjusts for this and other not. Local dependence will falsely inflate reliability .... just a thought

Thank you Tine Nielsen for the reply! That's also a relevant point in reliability estimation. In our simulation, we deliberately simulate the case where the test difficulty does not meet the test takers' achievement level, and these are independent. A kind of situation that a test that would discriminate highly of grade 3 pupils is given to grade 4 or 5 students. Too easy (or difficult) test leads to deflated reliability estimates. In practice, thus, even if the test score would be accurate, it cannot discriminate the test takers. Then, is the test poor as indicated by the low reliability? Or is the test good, but the low reliability is caused by technical reasons as in the traditional estimators (alpha, theta, omega, rho)? In the traditional estimators, the reason is the poor behavior of Rit which gives deflated estimates of correlation. The phenomenon seems the same in IRT estimators. What could be the reason ? Item-wise information function depends of normality? Normality baked to the estimators?

sure. "A kind of situation that a test that would discriminate highly of grade 3 pupils is given to grade 4 or 5 students. Too easy (or difficult) test leads to deflated reliability estimates." this means that variation is very small, as test is to easy (all correct) or to difficult (all wrong) in rough terms, and thus, of course, reliability will decrease...

Tine Nielsen exactly. This is the reason for the deflation in the estimates in the classic estimators: the skewed score is an outcome of too easy or too difficult items, and the item-total correlations based on covariation (R) embedded in the classical reliability estimators are always deflated (approaching 0) with items of extreme difficulty levels regardless of the true correlation. In this kind of artificial setting where a test suitable for G3 pupils is administered to G4-5 pupils is an example of administering a very simple screening test of language, for example, to the students. In both cases, the test may accurately discriminate between the lowest performing test takers and the other test takers (medium or high performing ones), but the traditional estimators cannot detect this. The deflation-corrected estimators can detect this, i.e., if changing the embedded item-total correlation (R), e.g., to polychoric correlation (or some other robust estimator, such as D or G) which is not dependent on the variance in the score or in the items, the reliability estimates are deflation-corrected.

I was kind of hoping that IRT estimators would behave better in this respect because they are not dependent on variance per se. That was my question: what is then the mechanism in those estimators? Or is it so that the item-wise Fisher Information used in some of the estimators is somehow based or affected on variance?