دورية أكاديمية
أعرض في EDS

A Bayesian nonparametric approach for handling item and examinee heterogeneity in assessment data.

التفاصيل البيبلوغرافية
العنوان: A Bayesian nonparametric approach for handling item and examinee heterogeneity in assessment data.
المؤلفون: Pan T; Department of Statistics, University of California, Irvine, California, USA., Shen W; Department of Statistics, University of California, Irvine, California, USA., Davis-Stober CP; Department of Psychological Sciences, University of Missouri - Columbia, Columbia, Missouri, USA., Hu G; Department of Biostatistics and Data Science, Center for Spatial Temporal Modeling for Applications in Population Sciences, The University of Texas Health Science Center at Houston, Houston, Texas, USA.
المصدر: The British journal of mathematical and statistical psychology [Br J Math Stat Psychol] 2024 Feb; Vol. 77 (1), pp. 196-211. Date of Electronic Publication: 2023 Sep 20.
نوع المنشور: Journal Article
اللغة: English
بيانات الدورية: Publisher: Wiley-Blackwell Country of Publication: England NLM ID: 0004047 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 2044-8317 (Electronic) Linking ISSN: 00071102 NLM ISO Abbreviation: Br J Math Stat Psychol Subsets: MEDLINE
أسماء مطبوعة: Publication: <2012-> : Chichester : Wiley-Blackwell
Original Publication: London : British Psychological Society
مواضيع طبية MeSH: Algorithms* , Students*, Humans ; Bayes Theorem ; Cluster Analysis
مستخلص: We propose a novel nonparametric Bayesian item response theory model that estimates clusters at the question level, while simultaneously allowing for heterogeneity at the examinee level under each question cluster, characterized by a mixture of binomial distributions. The main contribution of this work is threefold. First, we present our new model and demonstrate that it is identifiable under a set of conditions. Second, we show that our model can correctly identify question-level clusters asymptotically, and the parameters of interest that measure the proficiency of examinees in solving certain questions can be estimated at a n rate (up to a log term). Third, we present a tractable sampling algorithm to obtain valid posterior samples from our proposed model. Compared to the existing methods, our model manages to reveal the multi-dimensionality of the examinees' proficiency level in handling different types of questions parsimoniously by imposing a nested clustering structure. The proposed model is evaluated via a series of simulations as well as apply it to an English proficiency assessment data set. This data analysis example nicely illustrates how our model can be used by test makers to distinguish different types of students and aid in the design of future tests.
(© 2023 British Psychological Society.)
References: Alexeev, N., Templin, J., & Cohen, A. S. (2011). Spurious latent classes in the mixture Rasch model. Journal of Educational Measurement, 48(3), 313-332.
Andrich, D., & Marais, I. (2019). A course in Rasch measurement theory. In D. Andrich & I. Marais (Coords.), Measuring in the educational, social and health sciences (pp. 41-53). Springer.
Bartolucci, F., Farcomeni, A., & Scaccia, L. (2017). A nonparametric multidimensional latent class IRT model in a Bayesian framework. Psychometrika, 82(4), 952-978.
Bell, R. C., Pattison, P. E., & Withers, G. P. (1988). Conditional independence in a clustered item test. Applied Psychological Measurement, 12(1), 15-26.
Bolt, D. M., Cohen, A. S., & Wollack, J. A. (2002). Item parameter estimation under conditions of test speededness: Application of a mixture Rasch model with ordinal constraints. Journal of Educational Measurement, 39(4), 331-348.
Dahl, D. B. (2006). Model-based clustering for expression data via a Dirichlet process mixture model. Bayesian inference for gene expression and proteomics, 4, 201-218.
Doob, J. L. (1949). Application of the theory of martingales. Le calcul des probabilites et ses applications [The calculus of probabilities and its applications] (pp. 23-27). CNRS International Colloquia 13. Centre National de la Recherche Scientifique.
Ghosal, S., & Van der Vaart, A. (2017). Fundamentals of nonparametric Bayesian inference (Vol. 44). Cambridge University Press.
Green, P. J., & Richardson, S. (2001). Modelling heterogeneity with and without the Dirichlet process. Scandinavian Journal of Statistics, 28(2), 355-375.
Guha, A., Ho, N., & Nguyen, X. (2019). On posterior contraction of parameters and interpretability in Bayesian mixture modeling. arXiv preprint. arXiv:1901.05078.
Ho, N., & Nguyen, X. (2016). On strong identifiability and convergence rates of parameter estimation in finite mixtures. Electronic Journal of Statistics, 10(1), 271-307.
Hu, G., Ma, Z., & Paek, I. (2020). A nonparametric Bayesian item response modeling approach for clustering items and individuals simultaneously. arXiv preprint. arXiv:2006.00105.
Ishwaran, H., & James, L. F. (2001). Gibbs sampling methods for stick-breaking priors. Journal of the American Statistical Association, 96(453), 161-173.
Jain, S., & Neal, R. M. (2004). A split-merge Markov chain Monte Carlo procedure for the Dirichlet process mixture model. Journal of Computational and Graphical Statistics, 13(1), 158-182.
Jang, Y., Kim, S.-H., & Cohen, A. S. (2018). The impact of multidimensionality on extraction of latent classes in mixture Rasch models. Journal of Educational Measurement, 55(3), 403-420.
Keith, R. A. (1987). The functional independence measure: a new tool for rehabilitation. Advances in Clinical Rehabilitation, 2, 6-18.
Kreiner, S., & Christensen, K. B. (2007). Validity and objectivity in health-related scales: Analysis by graphical loglinear Rasch models. In Multivariate and mixture distribution Rasch models (pp. 329-346). Springer.
Marais, I., & Andrich, D. (2008). Formalizing dimension and response violations of local independence in the unidimensional Rasch model. Journal of Applied Measurement, 9(3), 200-215.
Miller, J. W., & Harrison, M. T. (2018). Mixture models with a prior on the number of components. Journal of the American Statistical Association, 113(521), 340-356.
Mislevy, R. J., & Verhelst, N. (1990). Modeling item responses when different subjects employ different solution strategies. Psychometrika, 55(2), 195-215.
Miyazaki, K., & Hoshino, T. (2009). A bayesian semiparametric item response model with Dirichlet process priors. Psychometrika, 74(3), 375-393.
Muraki, E. (1992). A generalized partial credit model: Application of an em algorithm. ETS Research Report Series, 1992(1), 1-30.
Neal, R. M. (2000). Markov chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics, 9(2), 249-265.
Neal, R. M. (2003). Slice sampling. The Annals of Statistics, 31(3), 705-767.
Nobile, A. (1994). Bayesian analysis of finite mixture distributions. Carnegie Mellon University.
Pitman, J. (2006). Combinatorial stochastic processes: Ecole d'eté de probabilités de saint-flour xxxii-2002. Springer.
Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336), 846-850.
Rasch, G. (1993). Probabilistic models for some intelligence and attainment tests. ERIC.
Reckase, M. D. (2009). Multidimensional item response theory models. Springer.
Rost, J. (1990). Rasch models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14(3), 271-282.
Rouse, S. V., Finger, M. S., & Butcher, J. N. (1999). Advances in clinical personality measurement: An item response theory analysis of the mmpi-2 psy-5 scales. Journal of Personality Assessment, 72(2), 282-307.
Sen, S., Cohen, A. S., & Kim, S.-H. (2019). Model selection for multilevel mixture Rasch models. Applied Psychological Measurement, 43(4), 272-289.
Shen, W., Tokdar, S. T., & Ghosal, S. (2013). Adaptive Bayesian multivariate density estimation with Dirichlet mixtures. Biometrika, 100(3), 623-640.
Teicher, H. (1963). Identifiability of finite mixtures. The Annals of Mathematical Statistics, 34(4), 1265-1269.
Thomas, M. L. (2011). The value of item response theory in clinical assessment: a review. Assessment, 18(3), 291-307.
Zumbo, B. D., Pope, G. A., Watson, J. E., & Hubley, A. M. (1997). An empirical test of Roskam's conjecture about the interpretation of an ICC parameter in personality inventories. Educational and Psychological Measurement, 57(6), 963-969.
فهرسة مساهمة: Keywords: IRT model; Rasch model; model averaging; nonparametric Bayesian method; posterior contraction rate
تواريخ الأحداث: Date Created: 20230920 Date Completed: 20240115 Latest Revision: 20240115
رمز التحديث: 20240115
DOI: 10.1111/bmsp.12322
PMID: 37727141
قاعدة البيانات: MEDLINE
الوصف
تدمد:2044-8317
DOI:10.1111/bmsp.12322