A Two-Parameter Logistic Extension Model: An Efficient Variant of the Three-Parameter Logistic Model

Abstract

A three-parameter logistic (3PL) model variant, named the two-parameter logistic extension (2PLE) model, was developed. This new model employs a function that integrates item features according to an examinee’s ability level instead of a fixed guessing parameter used in the 3PL model to quantify guessing behavior. Correct response probabilities from a solution behavior and guessing behavior increase as the level of ability increases. At extreme cases in which the level of ability is close to negative infinity, the 2PLE model degenerates into a 3PL model with a guessing probability at chance level (i.e., 1/ m, where m is the number of options). The properties of the 2PLE model were described and compared with those of other guessing models. Then, a simulation study comparing the performance of the 2PLE model with that of the 3PL model under three scenarios was conducted. Results showed that the 2PLE model generally outperforms the 3PL model. Finally, the application of the new model in comparison with several existing models was demonstrated by using two real data sets.

International Comparative Study of Statistics Learning Trajectories Based on PISA Data on Cognitive Diagnostic Models

“…Owing to a collection of competing models for the data, the AIC estimates the quality of each model relative to those of other models. The BIC is a criterion for model selection among a finite set of models, and the model with the lowest BIC value is preferred ( Zhu et al, 2019 ). In the above, six kinds of different CDMs (DINA, ACDM, GDINA, LLM, LCDM, and RRUM) were evaluated.…”

A General Three-Parameter Logistic Model With Time Effect

“…The most popular IRT model that includes guessing is the 3PL model (Birnbaum, 1968 ), which has been discussed in many papers and books (see e.g., Hambleton et al, 1991 ; van der Linden and Hambleton, 1997 ; Baker and Kim, 2004 ; von Davier, 2009 ; Han, 2012 ). However, several studies have revealed that the 3PL model has technical and theoretical limitations (Swaminathan and Gifford, 1979 ; Zhu et al, 2018 ). In this paper, we focus on another defect of the traditional 3PL model, namely, that it cannot distinguish between different abilities under different time intensities when the examinees have the same response framework.…”

Mixture‐modelling‐based Bayesian MH‐RM algorithm for the multidimensional 4PLM

“…Since Hutchinson (1991) first interpreted the 3PLM with two processes, a p‐process (answering item based on ability) and a g‐process (answering item based on guessing), a large number of studies have used and expanded this understanding of guessing and slipping behaviours. For modelling construction, San Martín et al (2006) proposed a one‐parameter ability‐based guessing (1PL‐AG) model, Culpepper (2015) proposed a four‐parameter normal Ogive (4PNO) model, and Zhu et al (2019) proposed a two‐parameter logistic extension model (2PLE). For parameter estimation, the mixture‐modelling‐based EM approach (Guo et al, 2020; Zheng et al, 2018), the mixed stochastic approximation EM algorithm (Meng & Xu, 2022), and the optimized MCMC algorithm (Béguin & Glas, 2001; Fu et al, 2009) were proposed to obtain more accurate and robust estimates.…”