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Full-Text Articles in Statistics and Probability
Mle And Eap Methods For Estimating Ability Scores For Data Of Varying Sample Size And Item Length, Sahar Taji
Mle And Eap Methods For Estimating Ability Scores For Data Of Varying Sample Size And Item Length, Sahar Taji
Graduate Theses and Dissertations
In this research, the performance of two popular estimators, Maximum Likelihood Estimator(MLE) and Bayesian Expected a Posteriori (EAP) is studied and compared in estimating the latent ability score in an Item Response Theory (IRT) model. The 2-Parameter Logistic (2PL) IRT model which is characterized by difficulty and discrimination item parameters is used to estimate the latent ability scores. Several datasets are generated for variety of sample size and item length values. The Monte-Carlo simulation is used to analyze the performance of the estimators. Results show that MLE produces reliable results with low root mean square error (RMSE) across all datasets. …
An Investigation Of Chi-Square And Entropy Based Methods Of Item-Fit Using Item Level Contamination In Item Response Theory, William R. Dardick, Brandi A. Weiss
An Investigation Of Chi-Square And Entropy Based Methods Of Item-Fit Using Item Level Contamination In Item Response Theory, William R. Dardick, Brandi A. Weiss
Journal of Modern Applied Statistical Methods
New variants of entropy as measures of item-fit in item response theory are investigated. Monte Carlo simulation(s) examine aberrant conditions of item-level misfit to evaluate relative (compare EMRj, X2, G2, S-X2, and PV-Q1) and absolute (Type I error and empirical power) performance. EMRj has utility in discovering misfit.
Comparison Of Scale Identification Methods In Mixture Irt Models, Youn-Jeng Choi, Allan S. Cohen
Comparison Of Scale Identification Methods In Mixture Irt Models, Youn-Jeng Choi, Allan S. Cohen
Journal of Modern Applied Statistical Methods
The effects of three scale identification constraints in mixture IRT models were studied. A simulation study found no constraint effect on the mixture Rasch and mixture 2PL models, but the item anchoring constraint was the only one that worked well on selecting correct model with the mixture 3PL model.
Assessing Robustness Of The Rasch Mixture Model To Detect Differential Item Functioning - A Monte Carlo Simulation Study, Jinjin Huang
Assessing Robustness Of The Rasch Mixture Model To Detect Differential Item Functioning - A Monte Carlo Simulation Study, Jinjin Huang
Electronic Theses and Dissertations
Measurement invariance is crucial for an effective and valid measure of a construct. Invariance holds when the latent trait varies consistently across subgroups; in other words, the mean differences among subgroups are only due to true latent ability differences. Differential item functioning (DIF) occurs when measurement invariance is violated. There are two kinds of traditional tools for DIF detection: non-parametric methods and parametric methods. Mantel Haenszel (MH), SIBTEST, and standardization are examples of non-parametric DIF detection methods. The majority of parametric DIF detection methods are item response theory (IRT) based. Both non-parametric methods and parametric methods compare differences among subgroups …
A Bayesian Beta-Mixture Model For Nonparametric Irt (Bbm-Irt), Ethan A. Arenson, George Karabatsos
A Bayesian Beta-Mixture Model For Nonparametric Irt (Bbm-Irt), Ethan A. Arenson, George Karabatsos
Journal of Modern Applied Statistical Methods
Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. A simple and more flexible Bayesian nonparametric IRT model for dichotomous items is introduced, which constructs monotone item characteristic (step) curves by a finite mixture of beta distributions, which can support the entire space of monotone curves to any desired degree of accuracy. An adaptive random-walk Metropolis-Hastings algorithm is proposed to estimate the posterior distribution of the model parameters. The Bayesian IRT …
A New Goodness-Of-Fit Test For Item Response Theory, John H. Neel
A New Goodness-Of-Fit Test For Item Response Theory, John H. Neel
Journal of Modern Applied Statistical Methods
Chi-square techniques for testing goodness-of-fit in item response theory are shown to give incorrect results. A new measure, CB, based on cumulants is proposed which avoids the arbitrary nature of interval creation found in chi-square techniques. The distribution of CB is estimated using Monte Carlo techniques and critical values for testing goodness-of-fit are given.