Roles of Fisher Type Information in Latent Trait Models

In the present paper, recent development in latent trait models, or item response theory, will be reviewed, and roles of the Fisher type information will be discussed by introducing various information functions and the ways they are used in latent trait models. Weakly parallel tests and their usefulness will be discussed. It will be shown that the test information function can be used to link modern mental test theory with classical mental test theory, through so-called the reliability coefficient of a test and the standard error of measurement. It will be demonstrated that the square root of the test information function is useful in the transformation of the ability scale to provide us with a new scale with a constant amount of test information, or a equally discriminating ability scale, and the transformation will make mathematics simpler in certain nonparametric methods of estimating the operating characteristics, among others. Nonparametric estimation of the operating characteristics of discrete item responses will be introduced which includes Bivariate P.D.F. Approach and Conditional P.D.F. Approach, and, in particular, Simple Sum and Differential Weight Procedures of the Conditional P.D.F. Approach will be discussed. A certain constancy in the amount of information provided by a single dichotomous item will be observed.