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 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 A Bayesian Generalized Explanatory Item Response Model to Account for Learning During the Test

Psychometrika ◽  
2021 ◽  
Author(s):  
José H. Lozano ◽  
Javier Revuelta
Keyword(s):  
Item Response ◽  
Real Data ◽  
Response Model ◽  
Learning Effects ◽  
Item Response Model ◽  
Proposed Model ◽  
Special Cases ◽  
True Model ◽  
Repeated Use ◽  
Specific Learning

AbstractThe present paper introduces a new explanatory item response model to account for the learning that takes place during a psychometric test due to the repeated use of the operations involved in the items. The proposed model is an extension of the operation-specific learning model (Fischer and Formann in Appl Psychol Meas 6:397–416, 1982; Scheiblechner in Z für Exp Angew Psychol 19:476–506, 1972; Spada in Spada and Kempf (eds.) Structural models of thinking and learning, Huber, Bern, Germany, pp 227–262, 1977). The paper discusses special cases of the model, which, together with the general formulation, differ in the type of response in which the model states that learning occurs: (1) correct and incorrect responses equally (non-contingent learning); (2) correct responses only (contingent learning); and (3) correct and incorrect responses to a different extent (differential contingent learning). A Bayesian framework is adopted for model estimation and evaluation. A simulation study is conducted to examine the performance of the estimation and evaluation methods in recovering the true parameters and selecting the true model. Finally, an empirical study is presented to illustrate the applicability of the model to detect learning effects using real data.

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

Are Teachers' Unions Really to Blame? Collective Bargaining Agreements and Their Relationships with District Resource Allocation and Student Performance in California

2011 ◽  
Vol 6 (3) ◽  
pp. 354-398 ◽  
Author(s):  
Katharine O. Strunk
Keyword(s):  
Resource Allocation ◽  
Collective Bargaining ◽  
Student Performance ◽  
Item Response ◽  
Response Model ◽  
Item Response Model ◽  
Teachers Unions ◽  
Achievement Growth ◽  
Unique Measure ◽  
Level Student

Increased spending and decreased student performance have been attributed in part to teachers' unions and to the collective bargaining agreements (CBAs) they negotiate with school boards. However, only recently have researchers begun to examine impacts of specific aspects of CBAs on student and district outcomes. This article uses a unique measure of contract restrictiveness generated through the use of a partial independence item response model to examine the relationships between CBA strength and district spending on multiple areas and district-level student performance in California. I find that districts with more restrictive contracts have higher spending overall, but that this spending appears not to be driven by greater compensation for teachers but by greater expenditures on administrators' compensation and instruction-related spending. Although districts with stronger CBAs spend more overall and on these categories, they spend less on books and supplies and on school board–related expenditures. In addition, I find that contract restrictiveness is associated with lower average student performance, although not with decreased achievement growth.

Psychology of Computer Use: VIII. Utilizing a Nonparametric Item Response Model to Develop Unidimensional Scales: Mokscal

1989 ◽  
Vol 68 (3) ◽  
pp. 987-1000 ◽  
Author(s):  
Elisabeth Tenvergert ◽  
Johannes Kingma ◽  
Terry Taerum
Keyword(s):  
Item Response ◽  
Goodness Of Fit ◽  
Functional Form ◽  
Search Procedure ◽  
Response Model ◽  
Scale Analysis ◽  
Item Response Model ◽  
Goodness Of Fit Test ◽  
Item Coefficient ◽  
Nonparametric Item Response

MOKSCAL is a program for the Mokken (1971) scale analysis based on a nonparametric item response model that makes no assumptions about the functional form of the item trace lines. The only constraint the Mokken model puts on the trace lines is the assumption of double monotony; that is, the item trace lines must be nondecreasing and the lines are not allowed to cross. MOKSCAL provides three procedures of scaling: a search procedure, an evaluation of the whole set of items, and an extension of an existing scale. All procedures provide a coefficient of scalability for all items that meet the criteria of the Mokken model and an item coefficient of scalability of every item. A test of robustness of the found scale can be performed to analyze whether the scale is invariant across different subgroups or samples. This robustness test may serve as a goodness-of-fit test for the established scale. The program is written in FORTRAN 77 and is suitable for both mainframe and microcomputers.

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