Tanımlayıcı ve açıklayıcı madde tepki modellerinin TIMSS 2007 Türkiye matematik verisine uyarlanması

Rasch modeli, bir, iki veya üç parametreli lojistik modeller gibi madde tepki kuramı (MTK) modelleri, bireylerin ölçülmek istenen örtük özelliklerinin tahmin edilmesinde kullanılan ölçme modelleridirler. MTK modellerinin geleneksel formülasyonları, bireysel farklılıkların açıklanmasına olanak vermemektedirler. Ancak bu modeller genelleştirilmiş doğrusal ve doğrusal olmayan karma modeller çerçevesinde ele alndığı zaman istatistiksel modeller olarak da kullanılabilmektedirler. Genelleştirilmiş doğrusal ve doğrusal olmayan modeller çerçevesinde, tanımlayıcı madde tepki modelleri olarak formüle edilen geleneksel MTK modellerine, bireysel farklılıkları açıklamak üzere birey özelliklerinin ve/veya maddesel farklılıkları açıklamak üzere madde özelliklerinin eklenmesiyle açıklayıcı madde tepki modelleri elde edilir. Bu çalışmada, dört temel tanımlayıcı ve açıklayıcı madde tepki modelinin - Rasch modeli, örtük regresyon Rasch modeli, doğrusal lojistik test modeli ve örtük regresyon doğrusal lojistik test modeli -TIMSS 2007 Türkiye sekizinci smıf matematik verisi üzerinde uygulanması gösterilmiştir.

An application of descriptive and explanatory item response models to TIMSS 2007 Turkey mathematics data

Item response theory (IRT) models such as the Rasch model, one, two, or three parameter logistic models are measurement models that are used to estimate the latent trait of individuals. Traditional formulations of IRT models do not allow explaining individual differences. However, it is possible to use these models as statistical models when they are formulated under the generalized linear and nonlinear mixed models (GLMM and NLMM) framework. Including person properties to explain the differences among person abilities and/or item properties to explain the differences among item difficulties into traditional IRT models that are formulated as descriptive item response models under the generalized linear and nonlinear mixed models framework, explanatory item response models (EIRM) are obtained. In this study, the application of four basic descriptive and explanatory item response models - Rasch model, latent regression Rasch model, linear logistic test model (LLTM), and latent regression LLTM - was illustrated using TIMSS 2007 mathematics data for eight grade Turkish students.

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