Bayesian Estimation for an Item Response Theory Tree Model

• Main Authors: TU,JYUN-YE, 涂俊曄
• Other Authors: CHANG,YU-WEI
• Format: Others
• Language: zh-TW
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/jqedt6

碩士 === 逢甲大學 === 統計學系統計與精算碩士班 === 107 === Under the Item Response Theory (IRT) models framework, the latent factor of an examinee can be inferred by the correctness/incorrectness of each item of the examinee. If we are further interested in the underlying process of each examinee, we can incorporate IRT models into tree models to form the so-called IRTree models. While the non-response/response is also recorded, instead of simply correctness/incorrectness for every item, we can use an existing IRTree model with four end nodes (TR4) to analyze testing or questionnaire data. To get more information from data and to provide teacher more message about how items function, the current study also targets two special cases of the TR4 model: TR3 and TR3-v2. We hope that we would have proper parameter estimates under TR4 fittings for the TR3 and TR3-v2 scenarios. However, the TR3-v2 data cannot be identified in the TR4 model. Therefore, the penalized quasi-likelihood estimation for the TR4 model in the literature does not work for the TR3-v2 data. In the current study, we propose an Bayesian estimation procedure for the TR4 model. Through proper settings of prior distributions, the above identifiability problem can be solved. There are many parameters in the models and the posterior distribution is not a known distribution. Therefore, the Markov chain Monte Carlo technique is adopted in our Bayesian estimation. We conduct some simulation studies to demonstrate the estimation performance and the efficiency of submodel selection. Last, the proposed method is applied to the OECD's Programme for International Student Assessment data for illustration.