On the Loss of Information in Conditional Maximum Likelihood Estimation of Item Parameters

This paper addresses the loss of information in CML estimation by using the information concept of F-information (Liang, 1983). This concept makes it possible to specify the conditions for no loss of information and to define a quantification of information loss. For the dichotomous Rasch model, the derivations will be given in detail to show the use of the F-information concept for making efficiency comparisons for different estimation methods. It is shown that by using CML for item parameter estimation, some information is almost always lost. But compared to JML Goint maximum likelihood) as well as to MML (marginal maximum likelihood) the loss is very small. The reported efficiency of CML to JML and to MML in several comparisons is always larger than 93 % , and in tests with a length of 20 items or more, larger than 99 %.