March 2023 Revisiting the Samejima–Bolfarine–Bazán IRT models: New features and extensions
Jorge Luis Bazán, Sandra Elizabeth Flores Ari, Caio L. N. Azevedo, Dipak K. Dey
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Braz. J. Probab. Stat. 37(1): 1-25 (March 2023). DOI: 10.1214/22-BJPS558


In 2010, the Samejima–Bolfarine–Bazán (SBB) Item Response Theory (IRT) models were introduced by (Journal of Educational and Behavioral Statistics 35 (2010) 693–713) under a Bayesian approach. These models extend the regular Bayesian One and Two Parameter Logistic IRT models by incorporating a parameter accounting for asymmetry of the Item Characteristic Curve (ICC) which is named the complexity of the item. It includes the Logistic Positive Exponent (LPE) IRT model formulated initially by (Psychometrika 65 (2000) 319–335) and the Reflection of the LPE (RLPE). In the present work, new properties of the SBB models are developed including a random effect for testlet structures with a Bayesian inference through a Markov chain Monte Carlo (MCMC) algorithm which includes the parameter estimation and model comparison. The asymmetric behavior of the Item Characteristic Curve (ICC) is detected using a marginal item information function. Two simulation studies are developed to analyze the sensitiveness of the penalized parameter in the asymmetric behavior of the ICC and to evaluate the parameter recovery of the proposed model. A real data set, with a testlet structure and empirical evidence of asymmetric behavior of the ICCs, is used to apply the models.


The first author was partially supported by FAPESP (2021/11720-0). This study was partially financed by the Coordination for the Improvement of Higher Education Personnel—Brazil (CAPES)—Finance Code 001 for the second author. We thank the anonymous reviewers and Editor for their careful reading of the different versions our manuscript and their many insightful comments and suggestions providing directions for additional work which has resulted in this paper.


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Jorge Luis Bazán. Sandra Elizabeth Flores Ari. Caio L. N. Azevedo. Dipak K. Dey. "Revisiting the Samejima–Bolfarine–Bazán IRT models: New features and extensions." Braz. J. Probab. Stat. 37 (1) 1 - 25, March 2023.


Received: 1 September 2022; Accepted: 1 November 2022; Published: March 2023
First available in Project Euclid: 27 April 2023

MathSciNet: MR4580882
Digital Object Identifier: 10.1214/22-BJPS558

Keywords: Asymmetrical link , Bayesian estimation , Complexity , item response model , logistic positive exponent , SBB models , testlet-effect

Rights: Copyright © 2023 Brazilian Statistical Association


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Vol.37 • No. 1 • March 2023
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