Modified Bayesian Information Criterion for Item Response Models in Planned Missingness Test Designs
The Bayesian information criterion (BIC) is a widely used statistical tool originally derived for fully observed data. The BIC formula includes the sample size and the number of estimated parameters in the penalty term. However, not all variables are available for every subject in planned missingnes...
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MDPI AG
2024-11-01
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| Series: | Analytics |
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| Online Access: | https://www.mdpi.com/2813-2203/3/4/25 |
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| author | Alexander Robitzsch |
| author_facet | Alexander Robitzsch |
| author_sort | Alexander Robitzsch |
| collection | DOAJ |
| description | The Bayesian information criterion (BIC) is a widely used statistical tool originally derived for fully observed data. The BIC formula includes the sample size and the number of estimated parameters in the penalty term. However, not all variables are available for every subject in planned missingness designs. This article demonstrates that a modified BIC, tailored for planned missingness designs, outperforms the original BIC. The modification adjusts the penalty term by using the average number of estimable parameters per subject rather than the total number of model parameters. This new criterion was successfully applied to item response theory models in two simulation studies. We recommend that future studies utilizing planned missingness designs adopt the modified BIC formula proposed here. |
| format | Article |
| id | doaj-art-b49d4e13a3c44e9e9a5972efa2281ef9 |
| institution | Kabale University |
| issn | 2813-2203 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Analytics |
| spelling | doaj-art-b49d4e13a3c44e9e9a5972efa2281ef92024-12-27T14:05:26ZengMDPI AGAnalytics2813-22032024-11-013444946010.3390/analytics3040025Modified Bayesian Information Criterion for Item Response Models in Planned Missingness Test DesignsAlexander Robitzsch0IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, GermanyThe Bayesian information criterion (BIC) is a widely used statistical tool originally derived for fully observed data. The BIC formula includes the sample size and the number of estimated parameters in the penalty term. However, not all variables are available for every subject in planned missingness designs. This article demonstrates that a modified BIC, tailored for planned missingness designs, outperforms the original BIC. The modification adjusts the penalty term by using the average number of estimable parameters per subject rather than the total number of model parameters. This new criterion was successfully applied to item response theory models in two simulation studies. We recommend that future studies utilizing planned missingness designs adopt the modified BIC formula proposed here.https://www.mdpi.com/2813-2203/3/4/25Bayesian information criterionplanned missingness designitem response modeldifferential item functioningRasch model2PL model |
| spellingShingle | Alexander Robitzsch Modified Bayesian Information Criterion for Item Response Models in Planned Missingness Test Designs Analytics Bayesian information criterion planned missingness design item response model differential item functioning Rasch model 2PL model |
| title | Modified Bayesian Information Criterion for Item Response Models in Planned Missingness Test Designs |
| title_full | Modified Bayesian Information Criterion for Item Response Models in Planned Missingness Test Designs |
| title_fullStr | Modified Bayesian Information Criterion for Item Response Models in Planned Missingness Test Designs |
| title_full_unstemmed | Modified Bayesian Information Criterion for Item Response Models in Planned Missingness Test Designs |
| title_short | Modified Bayesian Information Criterion for Item Response Models in Planned Missingness Test Designs |
| title_sort | modified bayesian information criterion for item response models in planned missingness test designs |
| topic | Bayesian information criterion planned missingness design item response model differential item functioning Rasch model 2PL model |
| url | https://www.mdpi.com/2813-2203/3/4/25 |
| work_keys_str_mv | AT alexanderrobitzsch modifiedbayesianinformationcriterionforitemresponsemodelsinplannedmissingnesstestdesigns |