Revisiting the 4-Parameter Item Response Model: Bayesian Estimation and Application

Culpepper, Steven Andrew

doi:10.1007/s11336-015-9477-6

Cited by 53 publications

(122 citation statements)

References 28 publications

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“…The most complex model I will consider in this paper is the 4-parameter logistic (4PL) model and all other simpler models result from this model by fixing some item parameters to certain values. In recent years, the 4PL model has received much attention in IRT research due to its flexibility in modeling complex binary response processes (e.g., Culpepper, 2016Culpepper, , 2017Loken & Rulison, 2010;Waller & Feuerstahler, 2017). Under this model, we express P (y ji = 1) via the equation…”

Section: Bayesian Irt Models For Binary Datamentioning

confidence: 99%

Analysing Standard Progressive Matrices (SPM-LS) with Bayesian Item Response Models

Bürkner¹

2019

Preprint

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Raven’s Standard Progressive Matrices (SPM) test and related matrix-based tests are widely applied measures of cognitive ability. Using Bayesian Item Response Theory (IRT) models, I reanalyse data of an SPM short form proposed by Myszkowski & Storme (2018) and, at the same time, illustrate the application of these models. Results indicate that a 3-parameter logistic (3PL) model is sufficient to describe participants dichotomous responses (correct vs. incorrect) while persons' ability parameters are quite robust across IRT models of varying complexity. These conclusions are in line with the original results of Myszkowski & Storme (2018). Using Bayesian as opposed to frequentist IRT models offered advantages in the estimation of more complex (i.e., 3-4PL) IRT models and provided more sensible and robust uncertainty estimates.

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Section: Bayesian Irt Models For Binary Datamentioning

confidence: 99%

Analysing Standard Progressive Matrices (SPM-LS) with Bayesian Item Response Models

Bürkner¹

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…The most complex model I consider in this paper is the four-parameter logistic (4PL) model and all other simpler models result from this model by fixing some item parameters to certain values. In recent years, the 4PL model has received much attention in IRT research due to its flexibility in modeling complex binary response processes (e.g., Culpepper 2016Culpepper , 2017Loken and Rulison 2010;Waller and Feuerstahler 2017). Under this model, we express P(y ji = 1) via the equation…”

Section: Bayesian Irt Models For Binary Datamentioning

confidence: 99%

Analysing Standard Progressive Matrices (SPM-LS) with Bayesian Item Response Models

Bürkner

2020

J. Intell.

View full text Add to dashboard Cite

Raven’s Standard Progressive Matrices (SPM) test and related matrix-based tests are widely applied measures of cognitive ability. Using Bayesian Item Response Theory (IRT) models, I reanalyzed data of an SPM short form proposed by Myszkowski and Storme (2018) and, at the same time, illustrate the application of these models. Results indicate that a three-parameter logistic (3PL) model is sufficient to describe participants dichotomous responses (correct vs. incorrect) while persons’ ability parameters are quite robust across IRT models of varying complexity. These conclusions are in line with the original results of Myszkowski and Storme (2018). Using Bayesian as opposed to frequentist IRT models offered advantages in the estimation of more complex (i.e., 3–4PL) IRT models and provided more sensible and robust uncertainty estimates.

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“…The second idea is the definition of a prior distribution for the item parameters. Several prior distributions were proposed in the literature (e.g., Culpepper, 2016;Fox, 2010). Technical introductions to this method in the context of IRT were provided by Baker and Kim (2004) and Mislevy (1986).…”

Section: Bayesian Maximum-a-posteriori Item Parameter Estimationmentioning

confidence: 99%

“…The pseudo-guessing parameters were sampled from a beta distribution B(5, 45). These distributions were inspired by prior distributions typically found in the literature (Culpepper, 2016;Fox, 2010). • Presence and type of a DIF effect: In addition to a baseline condition where no DIF effects were present, several conditions with DIF were included.…”

Section: An Evaluation With a Simulation Studymentioning

confidence: 99%

Score-Based Measurement Invariance Checks for Bayesian Maximum-a-Posteriori Estimates in Item Response Theory

Debelak¹,

Pawel²,

Strobl³

et al. 2020

Preprint

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A family of score-based tests has been proposed in the past years for assessing the invariance of model parameters in several models of item response theory. These tests were originally developed in a maximum likelihood framework. This study extends the framework of these tests to Bayesian maximum-a-posteriori estimates. Such extensions are especially useful for applying the tests to models like the three- and four-parametric logistic test models, where prior distributions often facilitate successful model estimation. The resulting tests were evaluated by a simulation study, which investigated their sensitivity against differential item functioning with respect to a continuous person covariate. The new method was found to be of higher or comparable sensitivity than score-based tests based on maximum likelihood estimates if the prior distributions of the item parameter estimates were non-informative or close to the true parameter distribution.

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Revisiting the 4-Parameter Item Response Model: Bayesian Estimation and Application

Cited by 53 publications

References 28 publications

Analysing Standard Progressive Matrices (SPM-LS) with Bayesian Item Response Models

Analysing Standard Progressive Matrices (SPM-LS) with Bayesian Item Response Models

Analysing Standard Progressive Matrices (SPM-LS) with Bayesian Item Response Models

Score-Based Measurement Invariance Checks for Bayesian Maximum-a-Posteriori Estimates in Item Response Theory

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