Testing for Differential Item Functioning Under the -Scoring Method.

This study offers an approach to testing for differential item functioning (DIF) in a recently developed measurement framework, referred to as -scoring method (DSM). Under the proposed approach, called method of testing for DIF, the item response functions of two groups (reference and focal) are compared by transforming their probabilities of correct item response, estimated under the DSM, into Z-scale normal deviates. Using the liner relationship between such Z-deviates, the testing for DIF is reduced to testing two basic statistical hypotheses about equal variances and equal means of the Z-deviates for the reference and focal groups.

Latent -Scoring Modeling: Estimation of Item and Person Parameters.

This study presents a latent (item response theory-like) framework of a recently developed classical approach to test scoring, equating, and item analysis, referred to as -scoring method. Specifically, (a) person and item parameters are estimated under an item response function model on the -scale (from 0 to 1) using marginal maximum-likelihood estimation and (b) analytic expressions are provided for item information function, test information function, and standard error of estimation for -scores obtained under the proposed latent treatment of the -scoring method. The results from a simulation study reveal very good recovery of item and person parameters via the marginal maximum-likelihood estimation method.