A Test Information Function for Linear Combinations of Traits Without Nuisance Traits in Multidimensional Item Response Theory

In educational evaluation and psychological measurement, we often measure traits that contain several sub-traits. When tests, such as entrance examinations, are used for decision-making, often test users do not evaluate the sub-traits directly, but rather evaluate the linear combination of sub-traits in which weights were pre-specified by the test users. In the present research, we propose a new test information function and item information that enable us to evaluate linear combinations of sub-traits in which the traits are correlated. Nuisance dimensions of linear combinations are integrated out in the proposed information function. This will enable test editing in which linear combinations of sub-traits can be evaluated prior to executing the test. We also propose a method for comparing values of information functions that have different weights and/or different correlations. A numerical simulation study showed the validity of our methods. We also applied our methods to the item pool of Geometry and Statistics of the 1996 NAEP test.