scholarly journals A Note on the Presence of Spurious Pseudo-Guessing Parameters for Three-Parameter Logistic Models in Heterogeneous Populations

2019 ◽  
Vol 80 (3) ◽  
pp. 604-612
Author(s):  
Tenko Raykov ◽  
George A. Marcoulides
Keyword(s):  
Educational Research ◽  
Item Response ◽  
Logistic Model ◽  
Unobserved Heterogeneity ◽  
Logistic Models ◽  
Parameter Estimate ◽  
Response Model ◽  
Measuring Instrument ◽  
Item Response Model ◽  
Two Parameter

This note raises caution that a finding of a marked pseudo-guessing parameter for an item within a three-parameter item response model could be spurious in a population with substantial unobserved heterogeneity. A numerical example is presented wherein each of two classes the two-parameter logistic model is used to generate the data on a multi-item measuring instrument, while the three-parameter logistic model is found to be associated with a considerable pseudo-guessing parameter estimate on an item. The implications of the reported results for empirical educational research are subsequently discussed.

scholarly journals About the Equivalence of the Latent D-Scoring Model and the Two-Parameter Logistic Item Response Model

2021 ◽  
Author(s):  
Alexander Robitzsch
Keyword(s):  
Item Response ◽  
Logistic Model ◽  
Latent Trait ◽  
Response Model ◽  
Item Response Model ◽  
Numerical Illustration ◽  
Scoring Model ◽  
Estimation Techniques ◽  
Pisa Data ◽  
Two Parameter

This article shows that the recently proposed latent D-scoring model of Dimitrov is statistically equivalent to the two-parameter logistic item response model. An analytical derivation and a numerical illustration are employed for demonstrating this finding. Hence, estimation techniques for the two-parameter logistic model can be used for estimating the latent D-scoring model. In an empirical example using PISA data, differences of country ranks are investigated when using different metrics for the latent trait. In the example, the choice of the latent trait metric matters for the ranking of countries. Finally, it is argued that an item response model with bounded latent trait values like the latent D-scoring model might have advantages for reporting results in terms of interpretation.

scholarly journals About the Equivalence of the Latent D-Scoring Model and the Two-Parameter Logistic Item Response Model

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1465
Author(s):  
Alexander Robitzsch
Keyword(s):  
Item Response ◽  
Logistic Model ◽  
Latent Trait ◽  
Response Model ◽  
Item Response Model ◽  
Numerical Illustration ◽  
Scoring Model ◽  
Estimation Techniques ◽  
Pisa Data ◽  
Two Parameter

This article shows that the recently proposed latent D-scoring model of Dimitrov is statistically equivalent to the two-parameter logistic item response model. An analytical derivation and a numerical illustration are employed for demonstrating this finding. Hence, estimation techniques for the two-parameter logistic model can be used for estimating the latent D-scoring model. In an empirical example using PISA data, differences of country ranks are investigated when using different metrics for the latent trait. In the example, the choice of the latent trait metric matters for the ranking of countries. Finally, it is argued that an item response model with bounded latent trait values like the latent D-scoring model might have advantages for reporting results in terms of interpretation.

scholarly journals Detection Rates of the M2 Test for Nonzero Lower Asymptotes Under Normal and Nonnormal Ability Distributions in the Applications of IRT

2018 ◽  
Vol 43 (1) ◽  
pp. 84-88
Author(s):  
Insu Paek ◽  
Jie Xu ◽  
Zhongtian Lin
Keyword(s):  
Item Response ◽  
Response Function ◽  
Logistic Model ◽  
Choice Test ◽  
Multiple Choice Test ◽  
Item Response Model ◽  
Detection Rates ◽  
Item Responses ◽  
Item Response Function ◽  
Two Parameter

When considering the two-parameter or the three-parameter logistic model for item responses from a multiple-choice test, one may want to assess the need for the lower asymptote parameters in the item response function and make sure the use of the three-parameter item response model. This study reports the degree of sensitivity of an overall model test M2 to detecting the presence of nonzero asymptotes in the item response function under normal and nonnormal ability distribution conditions.

scholarly journals A Comparison of Linking Methods for Two Groups for the Two-Parameter Logistic Item Response Model in the Presence and Absence of Random Differential Item Functioning

Foundations ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 116-144
Author(s):  
Alexander Robitzsch
Keyword(s):  
Differential Item Functioning ◽  
Item Response ◽  
Large Scale ◽  
Response Model ◽  
Item Response Model ◽  
Large Scale Assessment ◽  
Item Functioning ◽  
Item Parameters ◽  
Concurrent Calibration ◽  
Two Parameter

This article investigates the comparison of two groups based on the two-parameter logistic item response model. It is assumed that there is random differential item functioning in item difficulties and item discriminations. The group difference is estimated using separate calibration with subsequent linking, as well as concurrent calibration. The following linking methods are compared: mean-mean linking, log-mean-mean linking, invariance alignment, Haberman linking, asymmetric and symmetric Haebara linking, different recalibration linking methods, anchored item parameters, and concurrent calibration. It is analytically shown that log-mean-mean linking and mean-mean linking provide consistent estimates if random DIF effects have zero means. The performance of the linking methods was evaluated through a simulation study. It turned out that (log-)mean-mean and Haberman linking performed best, followed by symmetric Haebara linking and a newly proposed recalibration linking method. Interestingly, linking methods frequently found in applications (i.e., asymmetric Haebara linking, recalibration linking used in a variant in current large-scale assessment studies, anchored item parameters, concurrent calibration) perform worse in the presence of random differential item functioning. In line with the previous literature, differences between linking methods turned out be negligible in the absence of random differential item functioning. The different linking methods were also applied in an empirical example that performed a linking of PISA 2006 to PISA 2009 for Austrian students. This application showed that estimated trends in the means and standard deviations depended on the chosen linking method and the employed item response model.

scholarly journals Fast Bayesian Estimation for the Four-Parameter Logistic Model (4PLM)

SAGE Open ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 215824402110525
Author(s):  
Chanjin Zheng ◽  
Shaoyang Guo ◽  
Justin L Kern
Keyword(s):  
Item Response ◽  
Expectation Maximization ◽  
Logistic Model ◽  
Sampling Method ◽  
Real Data ◽  
R Package ◽  
Response Model ◽  
Item Response Model ◽  
The Em Algorithm ◽  
Bayes Modal

There is a rekindled interest in the four-parameter logistic item response model (4PLM) after three decades of neglect among the psychometrics community. Recent breakthroughs in item calibration include the Gibbs sampler specially made for 4PLM and the Bayes modal estimation (BME) method as implemented in the R package mirt. Unfortunately, the MCMC is often time-consuming, while the BME method suffers from instability due to the prior settings. This paper proposes an alternative BME method, the Bayesian Expectation-Maximization-Maximization-Maximization (BE3M) method, which is developed from by combining an augmented variable formulation of the 4PLM and a mixture model conceptualization of the 3PLM. The simulation shows that the BE3M can produce estimates as accurately as the Gibbs sampling method and as fast as the EM algorithm. A real data example is also provided.

scholarly journals Extensions of the skew-normal ogive item response model

2014 ◽  
Vol 28 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Jorge Luis Bazán ◽  
Márcia D. Branco ◽  
Heleno Bolfarine
Keyword(s):  
Item Response ◽  
Response Model ◽  
Item Response Model ◽  
Skew Normal
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