IRT Linking and Equating

Lee, Won‐Chan; Lee, Guemin

doi:10.1002/9781118489772.ch21

Cited by 30 publications

(24 citation statements)

References 32 publications

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“…, G) are sufficient conditions for ensuring identifiability. In the linking approach see [27][28][29][30][31], the sets of identified group-specific item parametersλ g,0 = (λ 1g,0 , . .…”

Section: Full Invariance Partial Invariance and Linking Methodsmentioning

confidence: 99%

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Lp Loss Functions in Invariance Alignment and Haberman Linking with Few or Many Groups

Robitzsch

2020

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The comparison of group means in latent variable models plays a vital role in empirical research in the social sciences. The present article discusses an extension of invariance alignment and Haberman linking by choosing the robust power loss function ρ(x)=|x|p(p>0). This power loss function with power values p smaller than one is particularly suited for item responses that are generated under partial invariance. For a general class of linking functions, asymptotic normality of estimates is shown. Moreover, the theory of M-estimation is applied for obtaining linking errors (i.e., inference with respect to a population of items) for this class of linking functions. In a simulation study, it is shown that invariance alignment and Haberman linking have comparable performance, and in some conditions, the newly proposed robust Haberman linking outperforms invariance alignment. In three examples, the influence of the choice of a particular linking function on the estimation of group means is demonstrated. It is concluded that the choice of the loss function in linking is related to structural assumptions about the pattern of noninvariance in item parameters.

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“…, G) are sufficient conditions for ensuring identifiability. In the linking approach see [27][28][29][30][31], the sets of identified group-specific item parametersλ g,0 = (λ 1g,0 , . .…”

Section: Full Invariance Partial Invariance and Linking Methodsmentioning

confidence: 99%

“…We can now use (29) and the estimating Equation ( 28) to show asymptotic normality of the estimateγ. Note thatγ is only implicitly given as the root of Ψ(γ,β) = 0.…”

Section: Asymptotic Normality: Standard Errorsmentioning

confidence: 99%

Lp Loss Functions in Invariance Alignment and Haberman Linking with Few or Many Groups

Robitzsch

2020

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“…The scaling models described above resulted in country-specific item discriminations a ic and item difficulties b ic . To enable a comparison of country means, the corresponding ability distributions can be obtained by linking approaches that establish a common ability metric [72,73]. In this article, Haberman linking [74] in its original proposal is used (see also [75,76]).…”

Section: Linking Proceduresmentioning

confidence: 99%

On the Treatment of Missing Item Responses in Educational Large-scale Assessment Data: The Case of PISA 2018 Mathematics

Robitzsch¹

2021

Preprint

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Missing item responses are prevalent in educational large-scale assessment studies like the programme for international student assessment (PISA). The current operational practice scores missing item responses as wrong, but several psychometricians advocated a model-based treatment based on latent ignorability assumption. In this approach, item responses and response indicators are jointly modeled conditional on a latent ability and a latent response propensity variable. Alternatively, imputation-based approaches can be used. The latent ignorability assumption is weakened in the Mislevy-Wu model that characterizes a nonignorable missingness mechanism and allows the missingness of an item to depend on the item itself. The scoring of missing item responses as wrong and the latent ignorable model are submodels of the Mislevy-Wu model. This article uses the PISA 2018 mathematics dataset to investigate the consequences of different missing data treatments on country means. Obtained country means can substantially differ for the different scaling models. In contrast to previous statements in the literature, the scoring of missing item responses as incorrect provided a better model fit than a latent ignorable model for most countries. Furthermore, the dependence of the missingness of an item from the item itself after conditioning on the latent response propensity was much more pronounced for constructed-response items than for multiple-choice items. As a consequence, scaling models that presuppose latent ignorability should be refused from two perspectives. First, the Mislevy-Wu model is preferred over the latent ignorable model for reasons of model fit. Second, we argue that model fit should only play a minor role in choosing psychometric models in large-scale assessment studies because validity aspects are most relevant. Missing data treatments that countries can simply manipulate (and, hence, their students) result in unfair country comparisons.

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“…In practice, it is not known which items serve as anchor items for group g. The choice can be based on a substantive basis (e.g., considerations outside of psychometrics, see [14]) or using psychometric methods. In this article, the identification of group means and group standard deviations is conducted using psychometric methods, namely linking methods (see [15][16][17][18][19] for overviews). Linking methods rely on separate scalings for all groups.…”

Section: Pl Model With Partial Invariance: Presence Of Uniform Dif Ementioning

confidence: 99%

Robust Haebara Linking for Many Groups: Performance in the Case of Uniform DIF

Robitzsch

2020

Psych

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The comparison of group means in item response models constitutes an important issue in empirical research. The present article discusses a slight extension of the robust Haebara linking approach of He and Cui [Appl. Psychol. Meas., 44, 296–310, 2020] by proposing a flexible class of robust Haebara linking functions for comparisons of many groups. These robust linking functions are robust against violations of invariance. In this article, we investigate the performance of robust Haebara linking in the presence of uniform DIF effects. In an analytical derivation, it is shown that the robust Haebara linking approach provides unbiased estimates of group means in the limiting case p=0. In a simulation study, it is demonstrated that the proposed variant of the Haebara linking approach outperforms existing implementations of Haebara linking to some extent. In an empirical application using PISA data, it is illustrated that country means can be sensitive to the choice of linking functions.

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IRT Linking and Equating

Cited by 30 publications

References 32 publications

Lp Loss Functions in Invariance Alignment and Haberman Linking with Few or Many Groups

Lp Loss Functions in Invariance Alignment and Haberman Linking with Few or Many Groups

On the Treatment of Missing Item Responses in Educational Large-scale Assessment Data: The Case of PISA 2018 Mathematics

Robust Haebara Linking for Many Groups: Performance in the Case of Uniform DIF

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