By Clement A. Stone, Xiaowen Zhu
Written specially for psychometricians, scale builders, and practitioners drawn to functions of Bayesian estimation and version checking of merchandise reaction idea (IRT) versions, this publication teaches you ways to complete all of this with the SAS MCMC Procedure. due to its instructional constitution, Bayesian research of merchandise reaction concept versions utilizing SAS might be of instant sensible use to SAS clients with a few introductory heritage in IRT types and the Bayesian paradigm.
operating via this book’s examples, you are going to how you can write the PROC MCMC programming code to estimate a variety of uncomplicated and extra advanced IRT types, together with the alternative and specification of previous distributions, specification of the chance version, and interpretation of effects. particularly, you'll study PROC MCMC programming code for estimating specific versions and how you can interpret effects that illustrate convergence diagnostics and inferences for parameters, in addition to effects that may be utilized by scale developers—for instance, the plotting of merchandise reaction services. additionally, you are going to easy methods to examine competing IRT types for an software, in addition to evaluation the healthy of types with using posterior predictive version checking equipment.
quite a few courses for undertaking those analyses are supplied and annotated that you should simply adjust them to your purposes.
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Additional info for Bayesian Analysis of Item Response Theory Models Using SAS
The ideal rating variables are random variables that depend on examinee ability and these in turn may be modeled using any item response function in another level of the model. For example, a K category PC model may be used, where [j corresponds to the ideal rating of item j for an examinee: ೣ ܲ ൫ߦ ൯ ൌ ݁ σೖసబ൫ஞೕ ିೕ ିఛೕೖି ൯ σೖసబ൫ஞೕ ିೕ ିதೕೖ ି ൯ σ ୀ ݁ and T, bj, Wjk, and Or are defined as in the MFRM model. In addition, Patz et al. (2002) discussed how covariates introduced to predict rater behaviors can be incorporated into the HR model.
In this model, slope parameters (or factor loadings) are estimated for each item on the general factor as well a single secondary factor. For example, in a 6-item test, slope parameters (aj1) for Items 16 are estimated for Factor 1, slope parameters (aj2) for Items 14 are estimated for Factor 2, and slope parameters (aj3) for Items 5-6 are estimated for Factor 3. In matrix notation this would be displayed as follows: Ƚଵ ۇȽଶ ۈȽଷ ۈȽ ۈସ Ƚହ ۉȽ Ƚଵଵ Ƚଶଵ Ƚଷଵ Ƚସଵ ۊ ۋ ۋ ۋ Ƚହଶ Ƚଶ ی The bifactor model can be considered a constrained case of a compensatory MIRT model where the first factor is defined as a general factor, and slope parameters for subsets of items are constrained to be 0 on secondary factors.
However, in some testing applications that reflect a nested structure of item responses within clusters of persons, within clusters of items, or both, this assumption may not be reasonable. For example, in testing applications where students are clustered within schools, the responses of the students in a school (cluster) are likely to be more related than is accounted for by their latent traits alone. Persons can also come from clusters of neighborhoods, and the neighborhood context could influence responses to behavioral assessments.
Bayesian Analysis of Item Response Theory Models Using SAS by Clement A. Stone, Xiaowen Zhu