Revisiting parametrizations for the nominal response model

Abstract

ZÁKLADNÍ ÚDAJE: IMPS 2022 International Meeting of the Psychometric Society. Book of Abstracts (Talks, Posters). Bologna: Psychometric Society, 2022. s. 206-206. [IMPS 2022. International Meeting of the Psychometric Society. 11.07.2022-15.07.2022, Bologna] ABSTRAKT: In this work, we revisit the existing parametrizations of the Nominal Response Model (NRM). We consider two parametrizations of NRM directly linked to the baseline-category logit (BL) nature of the model and using the information on correct answer in multiple-choice items: the BL intercept-slope (BL-IS) parametrization, and BL parametrization using a discrimination and difficulty parameters as is usual in the item response theory models (BL-IRT). An advantage of the BL-IRT parametrization is the graphical interpretation of the model parameters while BL-IS is more often encountered in the GLM framework. We hypothesize that the proposed parametrization accounting for the information on correct answer, and the related setup of starting values, may lead to numerically more precise results and less convergence issues. The relationship between the Bock’s, Thissen et al.’s, and two newly considered parametrizations is explained and illustrated on practical examples