title: Linking Item Response Model Parameters.
abstract: With a few exceptions, the problem of linking item response model parameters from different item calibrations has been conceptualized as an instance of the problem of test equating scores on different test forms. This paper argues, however, that the use of item response models does not require any test score equating. Instead, it involves the necessity of parameter linking due to a fundamental problem inherent in the formal nature of these models-their general lack of identifiability. More specifically, item response model parameters need to be linked to adjust for the different effects of the identifiability restrictions used in separate item calibrations. Our main theorems characterize the formal nature of these linking functions for monotone, continuous response models, derive their specific shapes for different parameterizations of the 3PL model, and show how to identify them from the parameter values of the common items or persons in different linking designs.
authors.affiliation: CTB/McGraw-Hill Education, 20 Ryan Ranch Road, Monterey, CA, 93940 , USA. wjvdlinden@gmail.com.
authors.forename: Wim J
authors.initials: WJ
authors.lastname: van der Linden
authors.affiliation: CTB/McGraw-Hill Education, 20 Ryan Ranch Road, Monterey, CA, 93940 , USA.
authors.forename: Michelle D
authors.initials: MD
authors.lastname: Barrett
mesh_terms: D002138:Calibration; D004521:Educational Measurement; D006801:Humans; D015233:Models, Statistical; D008962:Models, Theoretical
keywords: 3PL response model; item calibration; linking design; linking function; parameter identifiability