Rasch Modelinde Gibbs Örnekleme Yönteminin Uygulanması

Year 2018, Volume: 9 Issue: 3, 258 - 276, 29.09.2018

Sedat Şen , Tuğba Karadavut , Hyo Jin Eom Allan Cohen Seock-ho Kım

https://doi.org/10.21031/epod.408451

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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