Item response function in antagonistic situations

2020 ◽  
Vol 36 (5) ◽  
pp. 917-931
Author(s):  
Vladimir Turetsky ◽  
David M. Steinberg ◽  
Emil Bashkansky
Keyword(s):  
Item Response ◽  
Response Function ◽  
Item Response Function

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.

When Do Item Response Function and Mantel-Haenszel Definitions of Differential Item Functioning Coincide?

1990 ◽  
Vol 15 (3) ◽  
pp. 185-197 ◽  
Author(s):  
Rebecca Zwick
Keyword(s):  
Differential Item Functioning ◽  
Item Response ◽  
Response Function ◽  
Response Functions ◽  
Local Independence ◽  
Matching Criterion ◽  
Demographic Groups ◽  
Item Functioning ◽  
Item Response Function ◽  
The Rasch Model

A test item is typically considered free of differential item functioning (DIF) if its item response function is the same across demographic groups. A popular means of testing for DIF is the Mantel-Haenszel (MH) approach. Holland and Thayer (1988) showed that, under the Rasch model, identity of item response functions across demographic groups implies that the MH null hypothesis will be satisfied when the MH matching variable is test score, including the studied item. This result, however, cannot be generalized to the class of items for which item response functions are monotonic and local independence holds. Suppose that all item response functions are identical across groups, but the ability distributions for the two groups are stochastically ordered. In general, the population MH result will show DIF favoring the higher group on some items and the lower group on others. If the studied item is excluded from the matching criterion under these conditions, the population MH result will always show DIF favoring the higher group.

Nonparametric Item Response Function Estimates with the EM Algorithm

2002 ◽  
Vol 27 (3) ◽  
pp. 291-317 ◽  
Author(s):  
Natasha Rossi ◽  
Xiaohui Wang ◽  
James O. Ramsay
Keyword(s):  
Em Algorithm ◽  
Item Response ◽  
Functional Data ◽  
Latent Variable ◽  
Marginal Likelihood ◽  
Latent Trait ◽  
Functional Variation ◽  
The Em Algorithm ◽  
A New Technique ◽  
Item Response Function

The methods of functional data analysis are used to estimate item response functions (IRFs) nonparametrically. The EM algorithm is used to maximize the penalized marginal likelihood of the data. The penalty controls the smoothness of the estimated IRFs, and is chosen so that, as the penalty is increased, the estimates converge to shapes closely represented by the three-parameter logistic family. The one-dimensional latent trait model is recast as a problem of estimating a space curve or manifold, and, expressed in this way, the model no longer involves any latent constructs, and is invariant with respect to choice of latent variable. Some results from differential geometry are used to develop a data-anchored measure of ability and a new technique for assessing item discriminability. Functional data-analytic techniques are used to explore the functional variation in the estimated IRFs. Applications involving simulated and actual data are included.

A Generalized Formula for the Mantel-Haenszel Differential Item Functioning Parameter

1999 ◽  
Vol 24 (3) ◽  
pp. 293-322 ◽  
Author(s):  
Louis A. Roussos ◽  
Deborah L. Schnipke ◽  
Peter J. Pashley
Keyword(s):  
Differential Item Functioning ◽  
Item Response ◽  
Item Difficulty ◽  
Difficulty Level ◽  
Population Parameter ◽  
Simulation Studies ◽  
Item Functioning ◽  
The Difference ◽  
Item Response Function ◽  
Two Parameter

The present study derives a general formula for the population parameter being estimated by the Mantel-Haenszel (MH) differential item functioning (DIF) statistic. Because the formula is general, it is appropriate for either uniform DIF (defined as a difference in item response theory item difficulty values) or nonuniform DIF; and it can be used regardless of the form of the item response function. In the case of uniform DIF modeled with two-parameter-logistic response functions, the parameter is well known to be linearly related to the difference in item difficulty between the focal and reference groups. Even though this relationship is known to not strictly hold true in the case of three-parameter-logistic (3PL) uniform DIE the degree of the departure from this relationship has not been known and has been generally believed to be small By evaluating the MH DIF parameter, we show that for items of medium or high difficulty, the parameter is much smaller in absolute value than expected based on the difference in item difficulty between the two groups. These results shed new light on results from previous simulation studies that showed the MH DIF statistic has a tendency to shrink toward zero with increasing difficulty level when used with 3PL data.

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