Estimating Score Probabilities
Marie Wiberg, Jorge González, Alina A. von Davier · 2024
The estimation of score probabilities that can be used in the generalized kernel equating (GKE) framework is described beyond the use of design functions. The discussed data collection designs are equivalent groups (EG) design, single group (SG) design, counterbalanced (CB) design, non-equivalent groups with anchor test (NEAT) design, and non-equivalent groups with covariates (NEC) design. A review of design functions (DF) is given, and new methods are introduced for the estimation of score probabilities when item response (IRT) models have been used in the presmoothing step in the generalized kernel equating (GKE) framework. Methods for estimate probabilities from IRT models include the Lord-Wingersky algorithm, the Poisson-Binomial distribution, and other approximate and exact methods. The chapter ends with a brief description of conditional probabilities and how they are used in local kernel equating.