Bayesian estimation of a multilevel IRT model using gibbs sampling

Fox, Jean-Paul; Glas, Cornelis A.W.

doi:10.1007/bf02294839

Cited by 320 publications

(346 citation statements)

References 30 publications

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“…It can be seen that the magnitudes of the fixed effects in the MLIRT model were larger than the analogous estimates in the ML model. This finding is in line with the other findings (Fox & Glas, 2001Shalabi, 2002), which indicates that the MLIRT model has more power to detect effects in hierarchical data where some variables are measured with error. …”

Section: Multilevel Irtsupporting

confidence: 91%

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Item response theory in educational assessment and evaluation

Glas

2014

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Item response theory provides a useful and theoretically well-founded framework for educational measurement. It supports such activities as the construction of measurement instruments, linking and equating measurements, and evaluation of test bias and differential item functioning. It further provides underpinnings for item banking and flexible test administration designs, such as multiple matrix sampling, flexi-level testing, and computerized adaptive testing. First, a concise introduction to the principles of IRT models is given. The models discussed pertain to dichotomous items (items that are scored as either correct or incorrect) and polytomous items (items with partial credit scoring, such as most types of openended questions and performance assessments). Second, it is shown how an IRT measurement model can be enhanced with a structural model, such as, for instance, an analysis of variance model, to relate data from achievement and ability tests to students’ background variables, such as socio-economic status, intelligence or cultural capital, to school variables, and to features of the schooling system. Two applications are presented. The first one pertains to equating and linking of assessments, and the second one to a combination of an IRT measurement model and a multilevel linear model useful in school effectiveness research.La théorie de réponse à l’item (TRI) fournit un cadre utile et théoriquement bien fondé pour la mesure en éducation. Elle soutient des activités telles que la construction d’instruments de mesure, les procédures de mise en relation et de vérification d’équivalence des mesures, l’évaluation du biais d’un test et le fonctionnement différentiel d’items. Elle prévoit la base pour des banques d’items et des designs flexibles pour l’administration d’un test, comme les méthodes d’échantillonnage multicritérié, « flexi-level testing », et la méthode du test adaptatif par ordinateur. Tout d’abord, une brève introduction aux principes de modèles TRI est donnée. Les modèles discutés concernent des items dichotomiques (items qui sont corrects ou incorrects) et des items polytomiques (items à un crédit partiel, comme la plupart des questions ouvertes et questions de l’évaluation des compétences). Deuxièmement, on montre comment un modèle de mesure TRI peut être amélioré en utilisant un modèle structurel, par exemple, un modèle d’analyse de la variance, pour établir un lien entre les données provenant de tests pour mesurer le rendement et la capacité des élèves à des variables, tels leur statut socio-économique, leur niveau d’intelligence ou leur capital culturel, et à des variables caractérisant l’école et le système scolaire. Deux applications sont présentées. La première se rapporte aux procédures de type mise en parallèle (equating et linking), et la seconde à une combinaison d’un modèle de mesure TRI et d’un modèle linéaire multiniveaux utilisé dans la recherche relative à l’efficacité de l’école.A teoria de resposta ao item (TRI) fornece um quadro útil e teoricamente bem fundamentado para a...

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Section: Multilevel Irtsupporting

confidence: 91%

“…It is assumed that only the intercept β 0j is random, so the Level 2 predictors are only related to this random intercept. The parameters in the MLIRT model are estimated in a Bayesian framework (Fox & Glas, 2001.…”

Section: Multilevel Irtmentioning

confidence: 99%

Item response theory in educational assessment and evaluation

Glas

2014

mee

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“…An EM algorithm for unbalanced continuous two-level data has recently been implemented in EQS (e.g., Liang & Bentler, 2003). For binary data, MCMC methods have been proposed by Ansari and Jedidi (2000) and Fox and Glas (2001). BUGS can be used to estimate general models by MCMC (Spiegelhalter, Thomas, Best, & Gilks, 1996), although model specification and monitoring of stationarity require some expertise.…”

Section: Discussionmentioning

confidence: 99%

“…In the unidimensional case, this model represents an obvious generalization of item response theory (IRT) models useful if, for example, children's mean latent abilities vary randomly between schools (see, e.g., Fox & Glas, 2001). Such a model is illustrated in path diagram form in Figure 1 outer frame labeled "cluster k" vary between clusters and have a k subscript and variables also inside the inner frame labeled "unit j" vary between units and have both the j and k subscripts.…”

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confidence: 99%

Generalized multilevel structural equation modeling

2004

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A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent variables. The response model generalizes GLMMs to incorporate factor structures in addition to random intercepts and coefficients. As in GLMMs, the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower-level units in the higher-level units and missing data. A wide range of response processes can be modeled including ordered and unordered categorical responses, counts, and responses of mixed types. The structural model is similar to the structural part of a SEM except that it may include latent and observed variables varying at different levels. For example, unit-level latent variables (factors or random coefficients) can be regressed on cluster-level latent variables. Special cases of this framework are explored and data from the British Social Attitudes Survey are used for illustration. Maximum likelihood estimation and empirical Bayes latent score prediction within the GLLAMM framework can be performed using adaptive quadrature in gllamm, a freely available program running in Stata.

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“…The MCMC algorithm is straightforwardly implemented with the introduction of the continuous latent variable that underlies each binary response. This approach follows the procedure of Albert (1992), which builds on the Data Augmentation algorithm of Tanner and Wong (1987), and has been extensively used in other missing data problems (see, for example, Beguin, 2000;Fox & Glas, 2000;Johnson & Albert, 1999, pp. 194-202;Maris, 1995;Robert & Casella, 1999, pp.…”

Section: Estimation Using Gibbs Samplingmentioning

confidence: 99%