Bayesian Item Response Modeling: Theory and Applications by Jean-Paul Fox PDF

By Jean-Paul Fox

ISBN-10: 1441907416

ISBN-13: 9781441907417

This e-book offers an intensive remedy and unified insurance of Bayesian merchandise reaction modeling with purposes in various disciplines, together with schooling, drugs, psychology, and sociology. Breakthroughs in computing expertise have made the Bayesian method relatively necessary for plenty of reaction modeling difficulties. unfastened from computational constraints, life like and state of the art latent variable reaction versions are thought of for complicated overview and survey info to unravel real-world difficulties. The Bayesian framework defined presents a unified procedure for modeling and inference, facing (nondata) earlier info and data throughout a number of info assets. The booklet discusses equipment for examining merchandise reaction facts and the complicated relationships normally linked to human reaction habit and lines • Self-contained advent to Bayesian merchandise reaction modeling and a insurance of extending typical versions to address advanced overview facts • an intensive evaluation of Bayesian estimation and checking out tools for merchandise reaction types, the place MCMC tools are emphasised • quite a few examples that hide a variety of program components, together with schooling, medication, psychology, and sociology • Datasets and software program (S+, R, and WinBUGS code) of the versions and techniques provided within the ebook can be found on www.jean-paulfox.com Bayesian merchandise reaction Modeling is a superb e-book for study pros, together with utilized statisticians, psychometricians, and social scientists who research merchandise reaction info from a Bayesian standpoint. it's a advisor to the starting to be zone of Bayesian reaction modeling for researchers and graduate scholars, and also will serve them as an excellent reference. Jean-Paul Fox is affiliate Professor of dimension and information research, collage of Twente, The Netherlands. His major learn actions are in different parts of Bayesian reaction modeling. Dr. Fox has released various articles within the parts of Bayesian merchandise reaction research, statistical equipment for interpreting multivariate specific reaction info, and nonlinear combined results models.

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Example text

Both variance parameters are fixed to one. WinBUGS The model is implemented in WinBUGS for a response data matrix of N persons by K items. Each case i represents the responses of examinee i, and each column k represents all responses to item k. In the model description, all data points and parameters need to be specified. Therefore, the description contains a loop over observations (variable name Y ), examinees (variable name theta), and items (variable names a and b). 1. WinBUGS code: Two-parameter item response model.

The powerful simulation-based estimation methods (MCMC) will be discussed in Chapter 3. Without diminishing the importance of the estimation methods, attention is first focused on the Bayesian way of thinking and modeling. Until then, WinBUGS (Lunn, Thomas, Best and Spiegelhalter, 2000) is used in the exercises and examples and it will be assumed that samples from the posterior distributions (the common output of simulation-based estimation methods) are available that can be used for making Bayesian inferences.

4. 1) Each model parameter has a (posterior) density function, which makes it possible to compute (posterior) probability statements. (a) Compute the prior probability that the ability of examinee i = 1 is below the population average; that is, 0 P (θ1 < 0) = φ (x; µ = 0, σ = 1) dx. −∞ (b) Compute the posterior probability that the ability of examinee i = 1 is below the population average; that is, 0 P (θ1 < 0 | y) = p (θ1 | y) dθ1 . 3 or the sampled values from the posterior density to compute the posterior probability since the analytical form of the posterior density is unknown.

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Bayesian Item Response Modeling: Theory and Applications by Jean-Paul Fox


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