Madde Tepki Teorisinde Ölçeklerin Ortak Değişkenler ile İlişkilendirilmesi

Öz

Bir biriyle eşit özelliklere sahip olmayan farklı gruplara test formları uygulandığı ve sonuçlar madde tepki kuramına (MTT) göre puanlandırıldığı zaman, iki grup için ayrı ayrı tahmin edilen madde parametrelerinin aynı ölçeğe yerleştirilmesi gerekmektedir. Test edilenlerle ilgili değişkenleri içeren MTT modellerinde, aynı skalaya koyulması gereken, düzgün olan ve düzgün olmayan değişken madde fonksiyonunu (DMF)  modelleyen iki farklı parametre vardır. Bu çalışma düzgün olan ve düzgün olmayan DMF parametrelerini aynı skalaya yerleştiren dönüşüm denklemlerini önermeyi amaçlamaktadır. Dönüşüm denklemlerinin katsayılarını tahmin etmek amacıyla bu çalışmada şu dört yöntem kullanılmıştır: ortalama/ortalama, ortalama/sigma, Haebara ve Stocking-Lord. Araştırmamızda bir simülasyon çalışması ve deneysel bir örnek vermekteyiz. Bu simülasyon çalışmasının sonuçları bizlere eşitlik denklemlerinin katsayılarının büyük ölçüde Haebara ve Stocking-Lord yöntemleri için aynı olduğunu göstermiş olsa da, diğer yöntemler için farklı olduğunu göstermiştir. Deneysel örneğimizin sonuçları ise yüksek beceri değerleri için değişkenlerle birlikte olan MTT’nin değişkenler olmaksızın uygulanan MTT’den daha bilgilendirici bir sonuç ürettiğini göstermiştir. Bunun yanında ortalama/ortalama ve ortalama/sigma yöntemleri kullanıldığında eş zamanlı kalibrasyon yöntemine göre daha aydınlatıcı sonuçlar elde edilmiştir.  

Anahtar Kelimeler

• MTT,Ortak değişkenler,Birleştirme,DMF

Linking Scales in Item Response Theory with Covariates

Abstract

When test forms are administered to different non-equivalent groups of examinees and are scored by item response theory (IRT), it is necessary to put item parameters estimated separately on two groups on the same scale. In the IRT models which include covariates about the examinees, we have two parameters which model uniform and non-uniform differential item functioning (DIF) and that have to be put on the same scale. The aim of this study is to propose conversion equations, which are used to put the uniform and non-uniform DIF parameters on the same scale. To estimate the coefficients of the conversion equations we will use four methods: mean/mean, mean/sigma, Haebara and Stocking-Lord. We give a simulation study and an empirical example. The results of the simulation study show that the coefficients of the conversion equations are substantially equal for the Haebara and Stocking-Lord methods, while they are different for the other methods. The results of the empirical example is that IRT with covariates produces a more informative test than using IRT without covariates for high abilities’ values and, when the mean-mean and the mean-sigma methods are used, we obtain more informative tests than when using concurrent calibration.

Keywords

• IRT,Covariates,Linking,DIF

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