Download Bayesian Analysis of Item Response Theory Models Using SAS by Clement A. Stone, Xiaowen Zhu PDF
By Clement A. Stone, Xiaowen Zhu
Written in particular for psychometricians, scale builders, and practitioners drawn to purposes of Bayesian estimation and version checking of merchandise reaction conception (IRT) versions, this e-book teaches you ways to complete all of this with the SAS MCMC Procedure. due to its educational constitution, Bayesian research of merchandise reaction thought versions utilizing SAS can be of speedy sensible use to SAS clients with a few introductory historical past in IRT types and the Bayesian paradigm.
operating via this book’s examples, you'll how you can write the PROC MCMC programming code to estimate numerous uncomplicated and extra advanced IRT types, together with the alternative and specification of earlier distributions, specification of the possibility version, and interpretation of effects. in particular, you are going to research PROC MCMC programming code for estimating specific types and how one 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 features. furthermore, you are going to the right way to examine competing IRT types for an program, in addition to overview the healthy of versions with using posterior predictive version checking tools.
quite a few courses for engaging in those analyses are supplied and annotated so you might simply adjust them to your purposes.
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Additional info for Bayesian Analysis of Item Response Theory Models Using SAS
However, if estimation of the trait or ability is the focus, then the minimum dimensionality that provides the greatest information and most meaningful interpretation is the objective. If dimensionality is overestimated, more parameters are estimated, and in turn estimation error may increase. Factor analytic or cluster-based methods have been used to explore the dimensionality in test item responses because these methods attempt to explain the associations among a set of variables (items) in terms of a smaller number of factors (dimensions).
For example, a parameter, θ, may be assumed to be distributed as Normal(μθ, σθ), and the parameters μθ and σθ also have assumed distributions. Hierarchical prior structures will be discussed further in Chapter 3 and in the context of specific IRT models to be estimated (Chapters 4–6). 30 Bayesian Analysis of Item Response Theory Models Using SAS Computing the Posterior and Drawing Inferences Continuing with the example, consider 10 balls are drawn at random from a bag of golf balls, and 4 white balls are observed.
In other words, the assumed IRT model and model parameter estimates have uncertain validity for a specific examinee because they should not be used in combination with an examinee’s item responses (response pattern) to estimate his or her ability or trait. Because IRT models afford predictions of expected item response for each examinee, E[uj] = Pj(Z, T), and predictions of expected test score across items in a test for each examinee, 6E[uj] = 6Pj(Z, T), these predictions may be summarized across examinees and compared with observed results.