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« **on:** July 24, 2012, 01:41:18 AM »
These are huge questions. I will do a bit of work on a note that explains the differences, but it will take a while. In the mean time doing some reading on the web and from other available resources might help.

here are a few points.

1. maximum likelihood (MLE) and weighted maximum likelihood (WLE) are point estimates that depend only upon the item response model. The WLE is Warm's improvement on the MLE that is close to an unbiased estimator.

2. EAP is expected a-posterior, or the expectation of the posterior. I believe the term was introduced by Bock. The EAP is a minimum mean squared estimator that is in general biased. The EAP depends upon both the item response model and the population model.

3. PV's are plauible value, they are random draws from the posterior and should be used whenever you wish to undertake analyses with the ability estimates (ie estimate population parameters -- means, variances, covariances, regressions, t-tests and so on)

Ray