On Lagrange Multiplier Tests in Multidimensional Item Response Theory: Information Matrices and Model Misspecification

Falk, Carl F.; Monroe, Scott

doi:10.1177/0013164417714506

Cited by 12 publications

(15 citation statements)

References 42 publications

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“…The score test of Glas (1999), for example, tests whether the item difficulty in one item depends on the response to another item. One can also test for local violations of conditional independence with the help of a bifactor logistic model that assumes an additional latent trait for a pair of items (Liu and Thissen, 2012) or by testing for omitted cross loadings (Falk and Monroe, 2018). This is similar to testing for correlated residuals in structural equation models, an approach, that has also been suggested for item response models (Edwards et al, 2018).…”

Section: Tests Of Model Fitmentioning

confidence: 99%

Analyzing the Fit of IRT Models With the Hausman Test

Ranger

Much

2020

Front. Psychol.

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In this manuscript, the applicability of the Hausman test to the evaluation of item response models is investigated. The Hausman test is a general test of model fit. The test assesses whether for a model in question the parameter estimates of two different estimators coincide. The test can be implemented for item response models by comparing the parameter estimates of the marginal maximum likelihood estimator with the corresponding parameter estimates of a limited information estimator. For a correctly specified item response model, the difference of the two estimates is normally distributed around zero. The Hausman test can be used for the evaluation of item fit and global model fit. The performance of the test is evaluated in a simulation study. The simulation study suggests that the implemented versions of the test adhere to the nominal Type-I error rate well in samples of 1000 test takers and more. The test is also capable to detect misspecified item characteristic functions, but lacks power to detect violations of the conditional independence assumption. Keywords: item response theory, 2-PL model, model fit, item fit, Hausman test ANALYZING THE FIT OF IRT MODELS WITH THE HAUSMAN TESTItem response models are measurement models that allow inferring individual traits from responses given to the items of a standardized test. Core of item response models are precise assumptions about the relation between the traits and the response in a single item and the interrelation of the responses from different items. These assumptions then serve as a mathematical basis for deducing statements about a test taker's traits from his/her responses. The correctness of such inferential statements depends crucially on the validity of the item response model. As the results of psychological assessment often have important consequences, one has to guarantee that the conclusions drawn about the test takers have a sound basis. Therefore, it is indispensable to check the adequacy of the chosen item response model and its assumptions carefully. Such a check requires a powerful test of model fit.Several tests of model fit have been proposed in the past. A short overview over of the different tests is given in the following section. In doing so, the focus is mainly on the two-parameter logistic model. Nothing will be said about tests that were proposed exclusively for the Rasch model and cannot be used in general; for such tests see Glas and Verhelst (1995), Suaréz Falcón and Glas (2003), and Maydeu-Olivares and Montaño (2013. The review does also not cover the general approaches used in non-parametric item response theory (Sijtsma, 1998) or tests within the Bayesian framework (Sinharay, 2016). Tests of differential item functioning will also not be addressed (Magis et al., 2010). Having given this overview, an alternative test of model fit is Frontiers in Psychology | www.frontiersin.org 1 February 2020 | Volume 11 | Article 149 Ranger and Much Hausman Test for IRT Models Frontiers in Psychology | www.frontiersin.org

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Section: Tests Of Model Fitmentioning

confidence: 99%

Analyzing the Fit of IRT Models With the Hausman Test

Ranger

Much

2020

Front. Psychol.

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“…In this case, the numbers of parameters in β 0 and β * will not even be equal. Still, under misspecification,β will converge to a stationary population counterpart β * as sample size increases (e.g., Falk & Monroe, 2018).…”

Section: The Effect Of Model Misspecificationmentioning

confidence: 99%

Performance of Person‐Fit Statistics Under Model Misspecification

Hong

Monroe

Falk

2019

J Educational Measurement

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In educational and psychological measurement, a person‐fit statistic (PFS) is designed to identify aberrant response patterns. For parametric PFSs, valid inference depends on several assumptions, one of which is that the item response theory (IRT) model is correctly specified. Previous studies have used empirical data sets to explore the effects of model misspecification on PFSs. We further this line of research by using a simulation study, which allows us to explore issues that may be of interest to practitioners. Results show that, depending on the generating and analysis item models, Type I error rates at fixed values of the latent variable may be greatly inflated, even when the aggregate rates are relatively accurate. Results also show that misspecification is most likely to affect PFSs for examinees with extreme latent variable scores. Two empirical data analyses are used to illustrate the importance of model specification.

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“…MIRT models have become increasingly popular in the last decade [9,10]. This study is to expand the literature on MIRT software by examining the following details: (a) parameter specification, (b) screenshots to show step-by-step procedure for item calibrations, (c) comparisons on parameter recovery, as well as (d) the additional aspects (e.g., run time and cost).…”

Section: Research Goalmentioning

confidence: 99%

A Comparison between BMIRT and IRTPRO: A Simulation Study of a Multidimensional Item Response Model

Li¹

2019

EDUCATION

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The objective of this study is to provide comparative information on two software programs-IRTPRO version 2.1 for Windows and BMIRT. In educational measurement, software programs are being developed and updated rapidly. By using a small-scale simulation study on a two-parameter logistic model in multidimensional item response theory, this study is to examine the bias values and root mean square error values produced by both programs. Other than item parameter recovery, the comparisons about run time and user interface were also made. The results showed that BMIRT was better in estimating item slope parameters. However, in terms of run time, it is much slower than IRTPRO. In addition, IRTPRO's interface is much more user friendly than BMIRT's. Screenshots of conducting item calibrations for both programs are in Appendix A.

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On Lagrange Multiplier Tests in Multidimensional Item Response Theory: Information Matrices and Model Misspecification

Cited by 12 publications

References 42 publications

Analyzing the Fit of IRT Models With the Hausman Test

Analyzing the Fit of IRT Models With the Hausman Test

Performance of Person‐Fit Statistics Under Model Misspecification

A Comparison between BMIRT and IRTPRO: A Simulation Study of a Multidimensional Item Response Model

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