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Im Januar legt die Ständige Wissenschaftliche Kommission der Kultusministerkonferenz ein Impulspapier zu „Large Language Models und ihre Potenziale im Bildungssystem“ vor mit Anregungen für den Einsatz im Unterricht, Forschungs- und Entwicklungsaufgaben sowie bildungspolitische Diskussionen.
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The Rasch model has the desirable property that item parameter estimation can be separated from person parameter estimation. This implies that no assumptions about the ability distribution are required when estimating item difficulties. Pairwise estimation approaches in the Rasch model exploit this principle by estimating item difficulties solely from sample proportions of respondents who answer item i correctly and item j incorrectly. A recent contribution by Tutz introduced Tutz’s pairwise separation estimator (TPSE) for the more general class of homogeneous monotone (HM) models, extending the idea of pairwise estimation to this broader setting. The present article examines the asymptotic behavior of the TPSE within the Rasch model as a special case of the HM framework. It should be emphasized that both analytical derivations and a numerical illustration show that the TPSE yields asymptotically biased item parameter estimates, rendering the estimator inconsistent, even for a large number of items. Consequently, the TPSE cannot be recommended for empirical applications.
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Robust mean–geometric mean (MGM) linking is a method for comparing the performance of two groups on a test involving dichotomous items and is particularly suited to settings with fixed and sparse differential item functioning (DIF). However, robust MGM linking has been shown to yield biased estimates in finite samples because the estimated item parameters are affected by sampling error, which in turn induces bias in the estimated linking parameters. To address this issue, the simulation extrapolation (SIMEX) method is applied to robust MGM linking to reduce bias in the linking parameter estimates. Results from a simulation study demonstrate that SIMEX reduces bias in robust MGM linking. Moreover, SIMEX with a linear extrapolation function also reduces the variance of the parameter estimates in the absence of DIF effects. These findings indicate that the application of SIMEX in robust MGM linking methods can be generally recommended for empirical research aimed at removing DIF items from group comparisons.
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The Rasch model has the desirable property that item parameter estimation can be separated from person parameter estimation. This implies that no assumptions about the ability distribution are required when estimating item difficulties. Pairwise estimation approaches in the Rasch model exploit this principle by estimating item difficulties solely from sample proportions of respondents who answer item i correctly and item j incorrectly. A recent contribution by Tutz introduced Tutz’s pairwise separation estimator (TPSE) for the more general class of homogeneous monotone (HM) models, extending the idea of pairwise estimation to this broader setting. The present article examines the asymptotic behavior of the TPSE within the Rasch model as a special case of the HM framework. It should be emphasized that both analytical derivations and a numerical illustration show that the TPSE yields asymptotically biased item parameter estimates, rendering the estimator inconsistent, even for a large number of items. Consequently, the TPSE cannot be recommended for empirical applications.
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Moderated Nonlinear Latent Factor Analysis (MNLFA) has been introduced as a flexible approach for testing measurement invariance among categorical and continuous covariates. Equipped with Bayesian shrinkage priors, MNLFA can handle large numbers of covariates and potentially invariant item parameters. The present study extends the capabilities of the Bayesian MNLFA to multilevel and longitudinal confirmatory factor analysis. We show how a Bayesian hierarchical MNLFA (BH-MNLFA) can be implemented and provide two simulation studies to demonstrate its functionality. Focusing on invariance explorations in experience sampling data as a potential use case in the context of longitudinal data analysis, we showcase the utility of BH-MNLFA with data from educational psychology, and test invariance of state self-concepts measures across time and school subjects.
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