A Bayesian random effects model for testlets

Bradlow, Eric T.; Wainer, Howard; Wang, Xiaohui

doi:10.1007/bf02294533

Cited by 328 publications

(345 citation statements)

References 24 publications

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“…Albert and Chib (1993) expanded the work of Albert to incorporate polytomous data. A number of studies have compared MCMC estimation with other popular estimation methods (Baker, 1998;Bradlow, Wainer, & Wang, 1999;Kim, 2001;Patz & Junker, 1999;Sahu, 2002;Wollack, Bolt, Cohen, & Lee, 2002) for some of the most commonly found unidimensional IRT models. Although there are differences in the various findings reported in these studies, the typical finding is that MCMC and more standard methods (such as MML/EM) provide estimates of similar quality.…”

Section: Markov Chain Monte Carlomentioning

confidence: 99%

Item factor analysis: Current approaches and future directions.

Wirth

Edwards

2007

Psychological Methods

779

613

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The rationale underlying factor analysis applies to continuous and categorical variables alike; however, the models and estimation methods for continuous (i.e., interval or ratio scale) data are not appropriate for item-level data that are categorical in nature. The authors provide a targeted review and synthesis of the item factor analysis (IFA) estimation literature for ordered-categorical data (e.g., Likert-type response scales) with specific attention paid to the problems of estimating models with many items and many factors. Popular IFA models and estimation methods found in the structural equation modeling and item response theory literatures are presented. Following this presentation, recent developments in the estimation of IFA parameters (e.g., Markov chain Monte Carlo) are discussed. The authors conclude with considerations for future research on IFA, simulated examples, and advice for applied researchers. Keywordsitem factor analysis; parameter estimation; categorical data; confirmatory factor analysis; item response theory Item-level data within the social and behavioral sciences are often categorical in nature. Dichotomous (e.g., disagree vs. agree) or polytomous (e.g., strongly disagree, disagree, neither, agree, and strongly agree) item response formats may fail to maintain the scale and distributional properties assumed by models such as ordinary least squares regression or common linear factor analysis. Traditional regression techniques describe the outcome variable as an optimal linear function of observed predictors. The proper implementation of these techniques requires assumptions such as independent and normally distributed residuals, a continuous conditionally normal outcome, and that the model is correctly specified (i.e., a linear relationship exists between the outcome and predictors). The common linear factor model, which describes the covariances among observed variables as a function of a smaller number of latent factors, makes many of the same assumptions. It is assumed that the unique factors (those that affect only one measured variable) are normally distributed, the outcomes are continuous and conditionally normally distributed, and a linear relationship exists between the observed and latent variables. Although this list of assumptions is not exhaustive, it does represent assumptions that are easily violated with itemlevel ordered-categorical data. Attempting to estimate model parameters, for example, NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript with dichotomous outcomes within the standard confirmatory factor model (as described by Jöreskog, 1969) results in parameter estimates that are biased and impossible to interpret accurately (Di-Stefano, 2002). However, all is not lost; just as logistic and ordinal regression techniques offer appropriate alternatives to linear regression when modeling dichotomous or polytomous (e.g., ordinal, Likert-type scales) outcomes, item factor analysis (IFA) offers an appropriate alternative to the common line...

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Section: Markov Chain Monte Carlomentioning

confidence: 99%

Item factor analysis: Current approaches and future directions.

Wirth

Edwards

2007

Psychological Methods

779

613

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“…For instance, the dependency structure defi ned by Formula (1) is quite simple. IRT models with much more complicated dependence structures could be incorporated, such as the testlet model by Bradlow, Wainer and Wang (1999) and the models for ratings by Patz and Junker (1999). Also on the side of the structural model, much was left out of consideration.…”

Section: Resultsmentioning

confidence: 99%

Item response theory in educational assessment and evaluation

Glas

2014

mee

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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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“…Another solution is to use the sum of the dependent items as a so-called 'subtest' (Andrich, 1985). Alternatively, a testlet model (Bradlow et al, 1999;Wang & Wilson, 2005) or other models taking account of local dependence (Hoskens & De Boeck, 1997;Ip, 2002) can be applied. In Rasch models, a simple way of quantifying local dependence has been proposed (Andrich and Kreiner, 2010).…”

Section: Discussionmentioning

confidence: 99%

“…Another formalization of local dependence in IRT models is the notion of testlets, i.e., groups of items that are placed on a test as a unit, typically reading passages followed by a group of questions (Bradlow et al, 1999;Wang & Wilson, 2005). When evidence of local dependence turns up, constructing testlets post hoc can be a solution that permits the use of conventional unidimensional IRT models even in the presence of local dependence (Yen, 1993).…”

Section: Introductionmentioning

confidence: 99%

Modeling local dependence in longitudinal IRT models

Olsbjerg

2015

Behav Res

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Measuring change in a latent variable over time is often done using the same instrument at several time points. This can lead to dependence between responses across time points for the same person yielding within person correlations that are stronger than what can be attributed to the latent variable. Ignoring this can lead to biased estimates of changes in the latent variable. In this paper we propose a method for modeling local dependence in the longitudinal 2PL model. It is based on the concept of item splitting, and makes it possible to correctly estimate change in the latent variable.

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A Bayesian random effects model for testlets

Abstract: Gibbs sampler, Data augmentation, Testlets,

Cited by 328 publications

References 24 publications

Item factor analysis: Current approaches and future directions.

Item factor analysis: Current approaches and future directions.

Item response theory in educational assessment and evaluation

Modeling local dependence in longitudinal IRT models

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