data augmentation;
Gibbs sampler;
Markov chain Monte Carlo;
model choice;
likelihood ratio statistic;
predictive distribution;
three parameter model;
D O I:
10.1080/00949650212387
中图分类号:
TP39 [计算机的应用];
学科分类号:
081203 ;
0835 ;
摘要:
Item response models are essential tools for analyzing results from many educational and psychological tests. Such models are used to quantify the probability of correct response as a function of unobserved examinee ability and other parameters explaining the difficulty and the discriminatory power of the questions in the test. Sonic of these models also incorporate a threshold parameter for the probability of the correct response to account for the effect of guessing the correct answer in multiple choice type tests. In this article we consider fitting of such models using the Gibbs sampler. A data augmentation method to analyze a normal-ogive model incorporating a threshold guessing parameter is introduced and compared with a Metropolis-Hastings sampling method, The proposed method is an order of magnitude more efficient than the existing method, Another objective of this paper is to develop Bayesian model choice techniques for model discrimination. A predictive approach based oil a variant of the Bayes factor is used and compared with another decision theoretic method which minimizes in expected loss function oil the predictive space. A classical model choice technique based on a modified likelihood ratio test statistic is shown as one component of the second criterion. As a consequence the Bayesian methods proposed in this paper are contrasted with the classical approach based on the likelihood ratio test, Several examples are given to illustrate the methods.
机构:
Univ Sao Paulo, Luiz de Queiroz Coll Agr ESALQ, BR-13418900 Piracicaba, BrazilUniv Sao Paulo, Luiz de Queiroz Coll Agr ESALQ, BR-13418900 Piracicaba, Brazil
da Silva, Marcelo A.
Liu, Ren
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机构:
Univ Calif Merced, Sch Social Sci Humanities & Arts, Merced, CA USAUniv Sao Paulo, Luiz de Queiroz Coll Agr ESALQ, BR-13418900 Piracicaba, Brazil
Liu, Ren
Huggins-Manley, Anne Corinne
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机构:
Univ Florida, Coll Educ, Gainesville, FL USAUniv Sao Paulo, Luiz de Queiroz Coll Agr ESALQ, BR-13418900 Piracicaba, Brazil
Huggins-Manley, Anne Corinne
Bazan, Jorge L.
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h-index: 0
机构:
Univ Sao Paulo, Inst Math & Comp Sci, Sao Carlos, BrazilUniv Sao Paulo, Luiz de Queiroz Coll Agr ESALQ, BR-13418900 Piracicaba, Brazil
机构:
Loyola Univ, Chicago, IL 60611 USA
Loyola Univ, Sch Educ, Program Res Methodol, 820N Michigan Ave, Chicago, IL 60611 USALoyola Univ, Chicago, IL 60611 USA
Fujimoto, Ken A. A.
Falk, Carl F. F.
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h-index: 0
机构:
McGill Univ, Montreal, PQ, CanadaLoyola Univ, Chicago, IL 60611 USA