Modeling of Item Response Functions Under the D-Scoring Method

Abstract

This study presents new models for item response functions (IRFs) in the framework of the D-scoring method (DSM) that is gaining attention in the field of educational and psychological measurement and largescale assessments. In a previous work on DSM, the IRFs of binary items were estimated using a logistic regression model (LRM). However, the LRM underestimates the item true scores at the top end of the D-scale (ranging from 0 to 1), especially for relatively difficult items. This entails underestimation of true D-scores, inaccuracy in the estimates of their standard errors, and other psychometric issues. The inverse-regression adjustments used to fix this problem are too complicated for regular applications of the DSM and not in line with its simplicity. This issue is resolved with the IRF models proposed in this study, referred to as rational function models (RFMs) with one parameter (RFM1), two parameters (RFM2), and three parameters (RFM3). The proposed RFMs are discussed and illustrated with simulated and real data.

Person-Fit Assessment under the D-scoring Method

“…This study examines and compares four PFSs, denoted Ud, Zd, Ht, and U3, on efficiency to detect misfitting response patterns resulting from guessing and cheating in the framework of the D-scoring method (DSM; Dimitrov, 2018Dimitrov, , 2019. Two of these PFSs, Ud, and Zd, represent modifications of the popular statistics U3 (van der Flier, 1980(van der Flier, , 1982 and Z3 (e.g., Drasgow et al, 1985), respectively.…”

“…Under the DSM (Dimitrov, 2018(Dimitrov, , 2019, the D-score of an examinee on a test of binary items is based on his/her response vector of (1/0) item scores and the expected difficulties of the items, δ i ("delta"; hence the name "delta-scoring" method, DSM). It should be noted that the expected item difficulty is δ i = 1 -π i , where π i is the expected 'easiness' of the item (that is, the expected proportion of correct item responses for a targeted population of examinees).…”

“…A key feature of the DSM is the two-parameter rational function model (RFM2) which is used to obtain IRFs on the D-scale (Dimitrov, 2019). The analytic form of RFM2 is…”

“…It should be noted that the shape parameter s governs the shape of the IRF in fitting the empirical item characteristic curve (ICC) on the D-scale, but it is not the slope of the IRF at the item location, b; that is, s does not represent directly the item discrimination parameter. Instead, the discrimination parameter, a, is obtained "post-hoc" as a function of the parameters b and s as follows (see Dimitrov, 2019).…”

“…the present study is to examine and compare some PFSs on their efficiency to detect person misfit under IRF modeling on the D-scale (Dimitrov, 2019).…”