Hierarchical Rasch Model for Written Examinations in Anesthesiology
碩士 === 國立臺灣大學 === 流行病學與預防醫學研究所 === 101 === Background: The relationship between the predictors and the response in biomedical field is often characterized by a non-linear function. One of classical examples is the application of the logistic regression model to dealing with the data on threshold-bas...
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| Format: | Others |
| Language: | zh-TW |
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2013
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| Online Access: | http://ndltd.ncl.edu.tw/handle/61653280899077309419 |
| Summary: | 碩士 === 國立臺灣大學 === 流行病學與預防醫學研究所 === 101 === Background: The relationship between the predictors and the response in biomedical field is often characterized by a non-linear function. One of classical examples is the application of the logistic regression model to dealing with the data on threshold-based response outcomes, such as the Rasch model. The conventional Rasch model based on likelihood-based theory requires the assumption of local independence (conditional independence) and cannot deal with covariate affecting ability and hierarchical data structure. It is therefore interesting to relax the assumption of local independence and consider the heterogeneity due to covariates or correlated property from hierarchical structure by developing new statistical methods for the Rasch model.
Aims: We proposed the nonlinear mixed and Bayesian hierarchical regression model to fit the empirical data on the written test of board certification examination for anesthesiologists to demonstrate the feasibility of using the two innovative Rasch models. Estimates obtained from both methods were compared with the conventional maximum likelihood method.
Material and Methods: The Rasch model was first framed by a non-linear mixed regression underpinning to analyze the examinee ability (θ) and item difficulty (β) by treating the parameters of θ as a random effect following a normal distribution. This non-linear mixed regression was further extended to accommodate the data with hierarchical structures on examinees from training hospitals and items developed by raters. We also developed Bayesian hierarchical Rasch model for the same purpose. The data used for applications are the numbers of examinees distributed from 34 to 37 in 4 consecutive years from 2007 to 2010. There were 100 questions related to anesthesiology in each test. Hierarchical data structured on individuals and hospitals or items under raters and also covariates on age and gender were considered in our illustration. We used Statistical Analysis System (SAS) to estimate the parameters of the Rasch model by using PROC NLIN and NLMIXED. WinBUGS software was used for Bayesian hierarchical Rasch model.
Results: Our results show the two sets of estimates (θ and β) and standard error from maximum likelihood method were very close to those from non-linear mixed regression model. This suggests the data may obey the assumption of local independence. However, the standard errors were inflated when Bayesian hierarchical Rasch model was fitted to data.
Conclusion: The nonlinear mixed regression model and Bayesian hierarchical Rasch model provides alternative ways of estimating parameters with flexibility, particularly for hierarchical data. The feasibility is demonstrated with the application of the Rasch model to written examinations in anesthesiology.
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