Explorations In Recursive Designs

To construct a test from an item bank in a psychometrically sound way, we need data on these items. These data are obtained by administering them to a sample of students, and to register their responses. A response
to an item is also called an observation. Because the number of items in an item bank usually is large, each student is administered only a small part of all items in the bank. For these observations to be useful they have to be carefully planned. Therefore, many tests are administered as part of a so-called structurally incomplete design. In such a design the complete set of items is divided into partially overlapping subsets of items called a booklet. The number of items a booklet contains, is such that the intended student
can finish it in time. With observations obtained from such a design the item parameters are usually estimated with the method of Conditional Maximum Likelihood ( CML).

In this report it is investigated for a structured set of design patterns how certain properties of the design affect the quality of the item parameter estimates, as measured for instance by their estimation error.
Maximum Likelihood estimation in general accommodates missing data in a natural way. However, the pattern of the observations does affect the quality of the parameter estimates.