Rasch Modelinde Gibbs Örnekleme Yönteminin Uygulanması

Abstract

Rasch modelinde, madde güçlük ve ayırt edicilik parametrelerinin Bayes kestirimlerini elde etmek için, Gibbs örnekleme yönteminin reddetme örneklemesi yoluyla uygulanmasının kısa bir açıklaması sunulmuştur. Reddetme örneklemesi yoluyla Gibbs örnekleme yöntemi, OpenBUGS bilgisayar programı ile birlikte kullanılmıştır. Bu çalışmada reddetme örneklemesine dayanan kestirim metodu ile veri artırmaya (data augmentation) dayanan başka bir Gibbs örnekleme metodu, koşullu, marjinal ve ortak maksimum olabilirlik kestirim metotları örnek veriler üzerinden karşılaştırılmıştır. Önsel belirlemelerin madde güçlük ve kişi yetenek tahminleri üzerindeki etkileri ampirik veri setleri ile gösterilmiştir. Madde tepki kuramında Bayes kestirimi ile ilgili konular hakkında bir tartışma sunulmuştur. 

Keywords

• Bayes kestirimi,veri artırma,Gibbs örneklemesi,reddetme örneklemesi,Rasch modeli

An Implementation of the Gibbs Sampling Method Under the Rasch Model

Abstract

A brief explication of the implementation of the Gibbs sampling method via rejection sampling to obtain Bayesian estimates of difficulty and ability parameters under the Rasch model is presented. The Gibbs sampling method via rejection sampling was used in conjunction with the computer program OpenBUGS. Examples that compared the estimation method with another Gibbs sampling method via data augmentation as well as conditional, marginal, and joint maximum likelihood estimation methods are presented using empirical data sets. The effects of prior specifications on the difficulty and ability estimates are illustrated with the empirical data sets. A discussion is presented for related issues of Bayesian estimation in item response theory.  

Keywords

• Bayesian estimation,data augmentation,Gibbs sampling,rejection sampling,Rasch model

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