Rasch-ZINB及其相關模式在計數資料上之應用

Rasch-ZINB Modeling for Testing Count Data

洪來發(Lai-Fa Hung)

負二項迴歸模式 ； 試題反應理論 ； 過度離散 ； 零膨脹迴歸模式 ； item response theory ； negative binomial regression model ； over-dispersion ； zero-inflated regression model

測驗學刊

63卷1期（2016 / 03 / 01）

31 - 57

繁體中文

在統計分析方法中，計數模式（例如：Poisson Regression Model、Negative Binomial Regression Model、Zero-inflated Regression Model）已被廣泛應用於心理學、管理學，以及其他社會科學等領域。不過，國內相關研究一直未將現代測驗理論之試題反應理論（Item Response Theory, IRT）模式與這些計數模式相結合，也就是未能以IRT的觀點：受試者潛在特質和試題難度，對於計數資料過度離散（Over-dispersion）或零膨脹（Zero-inflated）等異常現象提出解釋與處理。因此，本研究結合Rasch模式與計數模式提出Rasch-ZINB迴歸模式、Rasch-ZIG迴歸模式，以及Rasch-ZIP迴歸模式，並以某學科考試結果做為模式分析之實例。整體而言，本研究提出的結合模式，針對資料異常現象，可以藉由受試者潛在特質和試題難易度加以解釋。最後，進行模擬分析以更確認研究結果的可信度，並提出未來研究的一些建議。

Count data models (for example, Poisson regression model, negative binomial regression model, and zero-inflated regression model) have been widely applied in psychology, management and other social science fields. However, related studies in Taiwan have been failed to make connection between item response theory (IRT) and count data models which means those studies can't propose explanation from IRT approaches under the over-dispersion and zero-inflated count data. As a result, this study integrate Rasch model with count data model in order to propose a Rasch-ZINB regression model, Rasch-ZIG regression model, and Rasch-ZIP regression model. Various statistical tests for model evaluation are illustrated through an example of statistic testing. Overall, the integration model proposed in this study can make further explanations on data's skew phenomenon by means of item psychmetric features and individual traits. Finally, some suggestions for future research are provided.

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