Loss of Information in Estimating Item Parameters in Incomplete Designs

The use of the concept of F-information (Eggen, 2000) is generalized to incomplete testing designs. The standardized determinant of the F-information matrix is used for a scalar measure of information in a set of item parameters. In this paper, the relation between the normalization of the Rasch model and this determinant is clarified. It is shown that comparing estimation methods with the defined information efficiency is independent of the chosen normalization.

In examples, information comparisons are conducted. It is found that for both CML and MML some information is lost in all incomplete designs compared to complete designs. A general trend is that with increasing test booklet length the efficiency of an incomplete to a complete design and also the efficiency of CML compared to MML is increasing. The main differences between CML and MML is seen in relation to the length of the test booklet. It will be demonstrated that with very small booklets, there is a substantial loss in information ( about 35%) with CML estimation, while this loss is only about 10% in MML estimation. However,
with increasing test length, the differences between CML and MML quickly disappear.