1) In my experience when I worked in Taiwan, I really met the problem which this paper want to solve, that is, the boss (or you can call him as test developer) want me to do Exploratory Factor Analysis in a data set from CAT which has been implemented for awhile. He want to use this dimensionality method to demonstrate the data corresponding with the structure of test. Since it was a large pool, no one examinee could take whole 800 items even if in the pretest stage. I told to the boss that there were too many missing data at covariance matrix to do this analysis. This test really provided an approach and useful guideline to complete this task.
2) I consider the design of the test mentioned by Condition 3 is a little difficult to be confirmed in practice. It needs that the common booklet comprises all dimensions of whole test under the situation that we don't know the dimension of each item. We use this approach because we want to explore the dimension of each item so how can we confirm the items in common booklet including all possible dimensions? Of course the test developer should have some assumption about dimensions for each item. However, if the assumption existed, whether the confirmatory analysis is simpler to do? By the way, I still appreciated the exploratory approach in this study since the result is good at using in data with so many missing value. let me amazed.