The Use of an Identifiability-Based Strategy for the Interpretation of Parameters in the 1PL-G and Rasch Models

Abstract

Using the well-known strategy in which parameters are linked to the sampling distribution via an identification analysis, we offer an interpretation of the item parameters in the one-parameter logistic with guessing model (1PL-G) and the nested Rasch model. The interpretations are based on measures of informativeness that are defined in terms of odds of correctly answering the items. It is shown that the interpretation of what is called the difficulty parameter in the random-effects 1PL-G model differs from that of the item parameter in a random-effects Rasch model. It is also shown that the traditional interpretation of the guessing parameter in the 1PL-G model changes, depending on whether fixed-effects or random-effects versions of both models are considered.

Developing authentic assessment instrument based on multiple representations to measure students' critical thinking skills

“…- ----------------------------------------------------------------------------- ---------------------------------------------------------------------------- ---------------------------------------------------------------------------- ----------------------------------------------------------------------------- Figure 3 shows the item analysis based on the fit order item. Based on the table, the item fit criteria for the model if the OUTFIT MNSQ is between 0.5 to 1.5, the ZSTD value is between -2.0 to +2.0, and the Pt Mean Corr value is 0.4 to 0.8 (Fariña et al, 2019). Based on this description, it can be concluded that 14 instrument items (7 indicators) of authentic assessment of critical thinking skills fit the Rasch model.…”

“…The reliability analysis of the test instruments was carried out with the help of the Winsteps 3.37 program. The Winsteps program can provide instrument reliability information, namely person spacing index and item spacing index, and Cronbach's Alpha value, namely the interaction between person and item (Fariña et al, 2019). Yanto (2019) state that the higher the item reliability, the more precise the overall item is analyzed according to the model used.…”

“…The level of student's ability in answering the instruments can be seen with the help of the Winsteps program with Rasch modeling. Fariña et al (2019) state that the ability level of these students is indicated by the logit value on the person measure.…”

Bayesian Modal Estimation for the One-Parameter Logistic Ability-Based Guessing (1PL-AG) Model

“…The IRT models with guessing effects (e.g., 3PLM) suffer from the identification issue which causes estimation difficulty (Lord, 1980), and the 1PL-AG model is no exception (San Martín et al, 2015). However, several studies have been done to address this issue (Fariña et al, 2019; San Martín et al, 2006, 2013, 2015). Especially, San Martín et al (2006) have shown that the identification issue of the 1PL-AG model can be avoided if we assume the latent variable θ follows a normal distribution with a fixed mean of zero.…”

“…To solve this problem, the one-parameter logistic guessing (1PL-G) IRT model and its ability-based guessing version (1PL-AG) are proposed (San Martín et al, 2006, 2013). Increasingly, applications of the 1PL-AG model have appeared in the literature as supporting evidence of its usefulness (Fariña et al, 2019; San Martín et al, 2013; Wang & Huang, 2011).…”