A Boundary Mixture Approach to Violations of Conditional Independence

Braeken, Johan

doi:10.1007/s11336-010-9190-4

Cited by 30 publications

(29 citation statements)

References 28 publications

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“…In the following, we concentrate on boundary mixture copula in which the distribution of these residuals is defined as a mixture of two distributions: One distribution Π indicates local independence while the other distribution M indicates maximal positive local dependence which implies that students will respond to items consistent with a Guttman scale. Thus, it is not possible that students solve a difficult item but fail at an easy item (see Braeken, ). Formally, for three items in a testlet the assumption can be written as

F (e_{p 1}, e_{p 2}, e_{p 3}) = (1 - δ_{t}) Π (e_{p 1}, e_{p 2}, e_{p 3}) + δ_{t} M (e_{p 1}, e_{p 2}, e_{p 3}),

where

δ_{t}

is a mixture parameter for testlet t , which takes a value between zero (local independence) and one (maximal positive dependence).…”

Section: Modeling Approaches To Handle Lidmentioning

confidence: 99%

A Comparison of Different Psychometric Approaches to Modeling Testlet Structures: An Example with C‐Tests

Schroeders

Robitzsch

Schipolowski

2014

J Educational Measurement

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F (e_{p 1}, e_{p 2}, e_{p 3}) = (1 - δ_{t}) Π (e_{p 1}, e_{p 2}, e_{p 3}) + δ_{t} M (e_{p 1}, e_{p 2}, e_{p 3}),

where

δ_{t}

is a mixture parameter for testlet t , which takes a value between zero (local independence) and one (maximal positive dependence).…”

Section: Modeling Approaches To Handle Lidmentioning

confidence: 99%

A Comparison of Different Psychometric Approaches to Modeling Testlet Structures: An Example with C‐Tests

Schroeders

Robitzsch

Schipolowski

2014

J Educational Measurement

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“…Graduate School of Education, The University of Tokyo/Japan Society for the Promotion of Science 113-0033 7-3-1 Tel 090-5229-5738 E-mail toudou@p.u-tokyo.ac.jp (Lord & Novick, 1968) , θ Lee, 2000;Sireci, Thissen, & Wainer, 1991;2010, 2012Bradlow, Wainer, & Wang (1999) Chen & Wang (2007 Bayesian testlet model BTM (Wainer, Bradlow, & Wang, 2007) constant interaction model (Hoskens & De Boeck, 1997) θ j P j (θ) 2 2PLM (Braeken, 2011;Braeken, Tuerlinckx, & De Boeck, 2007;Ip, 2010;Ip, Smith, & De Boeck, 2009) …”

Section: Item Response Theory Irt Local Independencementioning

confidence: 99%

“…(Braeken, 2011;Braeken et al, 2007;Ip et al, 2009) 2 BTM 2 BTM boundary mixture model (Braeken, 2011) (Braeken, et al, 2007) locally dependent linear logistic test model (Ip, et al, 2009) …”

mentioning

confidence: 99%

The Effect of Local Dependence on Item Parameter Estimation

Todo¹

2012

Kodo Keiryogaku

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In this study, we assessed the effect of local dependence on item parameter estimation based on comparable item parameters, using Markov Chain Monte Carlo method. The results showed that if we estimate item parameters ignoring local dependence, item parameter estimation will be more inaccurate than taking local dependence into account. Furthermore, it was supposed that the result of previous works, which were not based on comparable item parameters, was distorted.

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“…part is counted twice, and thus the measurement precision is overestimated 1 (e.g., Junker, 1991;Braeken, 2011;Baghaei and Ravand, 2016). To deal with these kinds of issues, testlet response theory (TRT; Wainer et al, 2007) models were proposed.…”

Section: Introductionmentioning

confidence: 99%

Robust Automated Test Assembly for Testlet-Based Tests: An Illustration with Analytical Reasoning Items

Veldkamp

Paap

2017

Front. Educ.

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In many high-stakes testing programs, testlets are used to increase efficiency. Since responses to items belonging to the same testlet not only depend on the latent ability but also on correct reading, understanding, and interpretation of the stimulus, the assumption of local independence does not hold. Testlet response theory (TRT) models have been developed to deal with this dependency. For both logit and probit testlet models, a random testlet effect is added to the standard logit and probit item response theory (IRT) models. Even though this testlet effect might make the IRT models more realistic, application of these models in practice leads to new questions, for example, in automated test assembly (ATA). In many test assembly models, goals have been formulated for the amount of information the test should provide about the candidates. The amount of Fisher Information is often maximized or it has to meet a prespecified target. Since TRT models have a random testlet effect, Fisher Information contains a random effect as well. The question arises as to how this random effect in ATA should be dealt with. A method based on robust optimization techniques for dealing with uncertainty in test assembly due to random testlet effects is presented. The method is applied in the context of a high-stakes testing program, and the impact of this robust test assembly method is studied. Results are discussed, advantages of the use of robust test assembly are mentioned, and recommendations about the use of the new method are given.

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A Boundary Mixture Approach to Violations of Conditional Independence

Abstract: Fréchet–Hoeffding bounds, copula function, local item dependencies, conditional independence,

Cited by 30 publications

References 28 publications

A Comparison of Different Psychometric Approaches to Modeling Testlet Structures: An Example with C‐Tests

A Comparison of Different Psychometric Approaches to Modeling Testlet Structures: An Example with C‐Tests

The Effect of Local Dependence on Item Parameter Estimation

Robust Automated Test Assembly for Testlet-Based Tests: An Illustration with Analytical Reasoning Items

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