Estimation of Two-Parameter Logistic Item Response Curves

1984 ◽  
Vol 9 (4) ◽  
pp. 263 ◽  
Author(s):  
Robert K. Tsutakawa
Keyword(s):  
Item Response ◽  
Response Curves ◽  
Two Parameter

Estimation of Two-Parameter Logistic Item Response Curves

1984 ◽  
Vol 9 (4) ◽  
pp. 263-276 ◽  
Author(s):  
Robert K. Tsutakawa
Keyword(s):  
Maximum Likelihood ◽  
Item Response ◽  
Information Matrix ◽  
Simulated Data ◽  
Maximum Likelihood Estimates ◽  
Response Curves ◽  
Numerical Work ◽  
Item Parameters ◽  
The Em Algorithm ◽  
Two Parameter

Under the assumption that ability parameters are sampled from a normal distribution, the EM algorithm is used to derive maximum likelihood estimates for item parameters of the two-parameter logistic item response curves. The observed information matrix is then used to approximate the covariance matrix of these estimates. Responses to a questionnaire on general arthritis knowledge are used to illustrate the procedure and simulated data are used to compare the estimated and actual item parameters. The resulting estimates are found to be very close to those obtained from LOGIST. A computational note is included to facilitate the extensive numerical work required to implement the procedure.

scholarly journals A Short Note on Estimating the Testlet Model With Different Estimators in Mplus

2017 ◽  
Vol 78 (3) ◽  
pp. 517-529 ◽  
Author(s):  
Yong Luo
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Latent Variable ◽  
Short Note ◽  
Bifactor Model ◽  
Estimation Methods ◽  
Full Information ◽  
Modeling Software ◽  
Two Parameter ◽  
Item Response Theory Models

Mplus is a powerful latent variable modeling software program that has become an increasingly popular choice for fitting complex item response theory models. In this short note, we demonstrate that the two-parameter logistic testlet model can be estimated as a constrained bifactor model in Mplus with three estimators encompassing limited- and full-information estimation methods.

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.

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.

Nonparametric Item Response Curve Estimation With Correction for Measurement Error

2011 ◽  
Vol 36 (6) ◽  
pp. 755-778 ◽  
Author(s):  
Hongwen Guo ◽  
Sandip Sinharay
Keyword(s):  
Measurement Error ◽  
Item Response ◽  
Response Curve ◽  
Item Analysis ◽  
Kernel Estimation ◽  
Regression Estimation ◽  
Response Curves ◽  
Curve Estimation ◽  
Kernel Regression Estimation ◽  
Operational Data

Nonparametric or kernel regression estimation of item response curves (IRCs) is often used in item analysis in testing programs. These estimates are biased when the observed scores are used as the regressor because the observed scores are contaminated by measurement error. Accuracy of this estimation is a concern theoretically and operationally. This study investigates the deconvolution kernel estimation of IRCs, which corrects for the measurement error in the regressor variable. A comparison of the traditional kernel estimation and the deconvolution estimation of IRCs is carried out using both simulated and operational data. It is found that, in item analysis, the traditional kernel estimation is comparable to the deconvolution kernel estimation in capturing important features of the IRC.

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.

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