A Comprehensive Simulation Study of Estimation Methods for the Rasch Model
The Rasch model is one of the most prominent item response models. In this article, different item parameter estimation methods for the Rasch model are systematically compared through a comprehensive simulation study: Different alternatives of joint maximum likelihood (JML) estimation, different alt...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Stats |
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| Online Access: | https://www.mdpi.com/2571-905X/4/4/48 |
| _version_ | 1797500498720325632 |
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| author | Alexander Robitzsch |
| author_facet | Alexander Robitzsch |
| author_sort | Alexander Robitzsch |
| collection | DOAJ |
| description | The Rasch model is one of the most prominent item response models. In this article, different item parameter estimation methods for the Rasch model are systematically compared through a comprehensive simulation study: Different alternatives of joint maximum likelihood (JML) estimation, different alternatives of marginal maximum likelihood (MML) estimation, conditional maximum likelihood (CML) estimation, and several limited information methods (LIM). The type of ability distribution (i.e., nonnormality), the number of items, sample size, and the distribution of item difficulties were systematically varied. Across different simulation conditions, MML methods with flexible distributional specifications can be at least as efficient as CML. Moreover, in many situations (i.e., for long tests), penalized JML and JML with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula> adjustment resulted in very efficient estimates and might be considered alternatives to JML implementations currently used in statistical software. Moreover, minimum chi-square (MINCHI) estimation was the best-performing LIM method. These findings demonstrate that JML estimation and LIM can still prove helpful in applied research. |
| first_indexed | 2024-03-10T03:04:42Z |
| format | Article |
| id | doaj.art-48d50023d79d48a4afccae0a2074d67b |
| institution | Directory Open Access Journal |
| issn | 2571-905X |
| language | English |
| last_indexed | 2024-03-10T03:04:42Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Stats |
| spelling | doaj.art-48d50023d79d48a4afccae0a2074d67b2023-11-23T10:34:57ZengMDPI AGStats2571-905X2021-10-014481483610.3390/stats4040048A Comprehensive Simulation Study of Estimation Methods for the Rasch ModelAlexander Robitzsch0IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, GermanyThe Rasch model is one of the most prominent item response models. In this article, different item parameter estimation methods for the Rasch model are systematically compared through a comprehensive simulation study: Different alternatives of joint maximum likelihood (JML) estimation, different alternatives of marginal maximum likelihood (MML) estimation, conditional maximum likelihood (CML) estimation, and several limited information methods (LIM). The type of ability distribution (i.e., nonnormality), the number of items, sample size, and the distribution of item difficulties were systematically varied. Across different simulation conditions, MML methods with flexible distributional specifications can be at least as efficient as CML. Moreover, in many situations (i.e., for long tests), penalized JML and JML with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula> adjustment resulted in very efficient estimates and might be considered alternatives to JML implementations currently used in statistical software. Moreover, minimum chi-square (MINCHI) estimation was the best-performing LIM method. These findings demonstrate that JML estimation and LIM can still prove helpful in applied research.https://www.mdpi.com/2571-905X/4/4/48Rasch modelestimation methodsnonnormality |
| spellingShingle | Alexander Robitzsch A Comprehensive Simulation Study of Estimation Methods for the Rasch Model Stats Rasch model estimation methods nonnormality |
| title | A Comprehensive Simulation Study of Estimation Methods for the Rasch Model |
| title_full | A Comprehensive Simulation Study of Estimation Methods for the Rasch Model |
| title_fullStr | A Comprehensive Simulation Study of Estimation Methods for the Rasch Model |
| title_full_unstemmed | A Comprehensive Simulation Study of Estimation Methods for the Rasch Model |
| title_short | A Comprehensive Simulation Study of Estimation Methods for the Rasch Model |
| title_sort | comprehensive simulation study of estimation methods for the rasch model |
| topic | Rasch model estimation methods nonnormality |
| url | https://www.mdpi.com/2571-905X/4/4/48 |
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