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Constructing a Misspecified Item Response Model That Yields a Specified Estimate and a Specified Model Misfit Value

Sun, Yinghao
http://rave.ohiolink.edu/etdc/view?acc_num=osu1449097866

Abstract Details

2015, Doctor of Philosophy, Ohio State University, Psychology.
Item response theory (IRT) models are usually built on a set of statistical assumptions which may not necessarily hold in real data. Understanding the behavior of IRT models in response to deviations from these assumptions can provide valuable information as how to apply IRT models in practice and how to interpret results. One way to study the behavior of IRT models when their assumptions do not hold exactly is through simulations, where data can be generated from a model constructed by deliberately violating some of the IRT model assumptions. This dissertation presents a method to perturb an IRT model so that its particular structure only holds approximately. The departure of the original IRT model from the perturbed model is operationalized by an exact value of model misfit. Meanwhile, maximum likelihood estimates (MLEs) of parameters in the original IRT model given data generated from the perturbed model converge almost surely to specified values. Therefore, starting from an IRT model with a set of specified parameter values, the proposed method allows us to construct a perturbed (or misspecified) IRT model such that MLEs remain unchanged and yet there is a specified degree of model misfit. It is then possible to construct a simulated environment where the original IRT model only holds approximately through generating data from the perturbed model. The proposed perturbation method can be formulated as a constrained optimization problem, which can be solved by several commonly available optimization routines, such as the interior-point method. Illustrated through a few simulation studies using the 1- and 2-parameter logistic model, it is shown that the perturbation method is working as expected, yielding specified estimates and specified model misfit values. Despite its application to IRT models in this dissertation, the perturbation method is generic and can be applied to a wide range of statistical models with different measures of model misfit.
Michael Edwards (Advisor)
Paul De Boeck (Committee Member)
Minjeong Jeon (Committee Member)
Steven MacEachern (Committee Member)
Quantitative Psychology

Recommended Citations

Citations

  • Sun, Y. (2015). Constructing a Misspecified Item Response Model That Yields a Specified Estimate and a Specified Model Misfit Value [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1449097866

    APA Style (7th edition)

  • Sun, Yinghao. Constructing a Misspecified Item Response Model That Yields a Specified Estimate and a Specified Model Misfit Value. 2015. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1449097866.

    MLA Style (8th edition)

  • Sun, Yinghao. "Constructing a Misspecified Item Response Model That Yields a Specified Estimate and a Specified Model Misfit Value." Doctoral dissertation, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1449097866

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.