The Bayesian Multilevel Trifactor Item Response Theory Model.
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ABSTRACT:
SUBMITTER: Fujimoto KA
PROVIDER: S-EPMC6506989 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:Although item response theory (IRT) models such as the bifactor, two-tier, and between-item-dimensionality IRT models have been devised to confirm complex dimensional structures in educational and psychological data, they can be challenging to use in practice. The reason is that these models are multidimensional IRT (MIRT) models and thus are highly parameterized, making them only suitable for data provided by large samples. Unfortunately, many educational and psychological studies are conducted on a small scale, leaving the researchers without the necessary MIRT models to confirm the hypothesized structures in their data. To address the lack of modeling options for these researchers, we present a general Bayesian MIRT model based on adaptive informative priors. Simulations demonstrated that our MIRT model could be used to confirm a two-tier structure (with two general and six specific dimensions), a bifactor structure (with one general and six specific dimensions), and a between-item six-dimensional structure in rating scale data representing sample sizes as small as 100. Although our goal was to provide a general MIRT model suitable for smaller samples, the simulations further revealed that our model was applicable to larger samples. We also analyzed real data from 121 individuals to illustrate that the findings of our simulations are relevant to real situations.
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Project description:In educational and psychological testing, individuals are often repeatedly measured to assess the changes in their abilities over time or their latent trait growth. If a test consists of several subtests, the latent traits may have a higher order structure, and traditional item response theory (IRT) models for longitudinal data are no longer applicable. In this study, various multilevel higher order item response theory (ML-HIRT) models for simultaneously measuring growth in the second- and first-order latent traits of dichotomous and polytomous items are proposed. A series of simulations conducted using the WinBUGS software with Markov chain Monte Carlo (MCMC) methods reveal that the parameters could be recovered satisfactorily and that latent trait estimation was reliable across measurement times. The application of the ML-HIRT model to longitudinal data sets is illustrated with two empirical examples.
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Project description:In educational and psychological research, the logit and probit links are often used to fit the binary item response data. The appropriateness and importance of the choice of links within the item response theory (IRT) framework has not been investigated yet. In this paper, we present a family of IRT models with generalized logit links, which include the traditional logistic and normal ogive models as special cases. This family of models are flexible enough not only to adjust the item characteristic curve tail probability by two shape parameters but also to allow us to fit the same link or different links to different items within the IRT model framework. In addition, the proposed models are implemented in the Stan software to sample from the posterior distributions. Using readily available Stan outputs, the four Bayesian model selection criteria are computed for guiding the choice of the links within the IRT model framework. Extensive simulation studies are conducted to examine the empirical performance of the proposed models and the model fittings in terms of "in-sample" and "out-of-sample" predictions based on the deviance. Finally, a detailed analysis of the real reading assessment data is carried out to illustrate the proposed methodology.
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Project description:BackgroundComputer and paper examinations in our days are constructed from an item pool which is regularly updated. Given the way that exams are created, one of the major concerns is the security of the items that are being used in order to ensure a good estimation of abilities. The aim of this study is to measure the prevalence of item pre-knowledge in our medical school.MethodsThe Deterministic, Gated Item Response Theory Model (DGM) was applied to estimate the prevalence of students who have had item pre-knowledge from six multiple choice examinations of the Clinical Anatomy course at the Faculty of Medicine of University of Porto. Each examination consisted of 100 items with an average of 200 students and 20% repeated items per examination. The estimation of the sensitivity and specificity was based on a simulation study. The sensitivity and specificity estimates, and apparent prevalence were used to estimate true prevalence of cheating students in the examinations under study.ResultsThe specificity in the DGM for different simulation scenarios was between 68 and 98%, while the sensitivity ranged from 60 to 91%. The apparent prevalence was between 0.0 and 3.4%, while the true prevalence ranged from 1.2 to 3.7%.ConclusionsThe true prevalence was much lower compared to the students self-reported copying of responses from other students; however, it is important to keep monitoring the pre-knowledge prevalence in order to enforce measures in case an increase occurs.
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