Bloklanmış Üç Düzeyli Regresyon Süreksizlik Tasarımlarının Tasarım ve Analizinde Bir Düzeyinin Yok Sayılmasının Sonuçları: Güç ve Tip I Hata Oranları

Öz

Çok düzeyli regresyon süreksizliği tasarımları, politika ve programların etkililiğini değerlendirme amacıyla eğitim araştırmalarında giderek daha fazla kullanılmaktadır. Üç düzeyli bir veri yapısında (öğrenciler sınıflarda/öğretmenlerde, sınıflar/öğretmenler okullarda kümelenmiştir) bir düzeyin, ister veri analizi sırasında farkında olmadan ister planlama aşamasında kaynak kısıtlamaları nedeniyle göz ardı edilmesi yaygın bir sorundur. Bu çalışma, veri analizi ve planlama sırasında bloke edilmiş üç düzeyli regresyon süreksizlik tasarımlarında (BIRD3; müdahale 1. seviyededir) orta veya üst düzeyin göz ardı edilmesinin sonuçlarını araştırmaktadır. Monte Carlo simülasyon sonuçları, analiz sırasında bir düzeyin göz ardı edilmesinin müdahale etkisi tahminlerinin doğruluğunu etkilemediğini ancak standart hata, güç ve Tip I hata oranlarını etkilediğini göstermiştir. Orta düzeyin göz ardı edilmesi analiz aşamasında önemli bir sorun yaratmamıştır. Güç oranları nispeten daha küçük olsa bile Tip I hata oranları sabit kalmıştır. Buna karşılık, üst düzeyi göz ardı etmek daha büyük güç oranlarının elde edilmesine yardımcı olurken öte yandan Tip I hatada ciddi bir artışa yol açmaktadır. Tasarım aşamasına gelince, orta düzey göz ardı edildiğinde bir BIRD3 tasarımını planlamak için iki düzeyli bloke edilmiş regresyon süreksizlik modelinden (BIRD2) gelen parametreleri kullanmak uygundur. Ancak BIRD3 tasarımında, BIRD2 modelindeki 2. düzeye ait parametreleri 3. düzey parametrelerinin yerine kullanmak gerekir. Üst düzey göz ardı edildiğinde, bir BIRD3 tasarımını planlamak için BIRD2 modelindeki parametreleri kullanmaktan kaçınılması gerekmektedir.

Anahtar Kelimeler

• bloke edilmiş regresyon süreksizlik tasarımları
• bir yuvalama seviyesinin göz ardı edilmesi
• güç analizi
• çok düzeyli modeller
• hiyerarşik lineer modeller

Consequences of Ignoring a Level of Nesting on Design and Analysis of Blocked Three-level Regression Discontinuity Designs: Power and Type I Error Rates

Abstract

Multilevel regression discontinuity designs have been increasingly used in education research to evaluate the effectiveness of policy and programs. It is common to ignore a level of nesting in a three-level data structure (students nested in classrooms/teachers nested in schools), whether unwittingly during data analysis or due to resource constraints during the planning phase. This study investigates the consequences of ignoring intermediate or top level in blocked three-level regression discontinuity designs (BIRD3; treatment is at level 1) during data analysis and planning. Monte Carlo simulation results indicated that ignoring a level during analysis did not affect the accuracy of treatment effect estimates; however, it affected the precision (standard errors, power, and Type I error rates). Ignoring the intermediate level did not cause a significant problem. Power rates were slightly underestimated, whereas Type I error rates were stable. In contrast, ignoring a top-level resulted in overestimated power rates; however, severe inflation in Type I error deemed this strategy ineffective. As for the design phase, when the intermediate level was ignored, it is viable to use parameters from a two-level blocked regression discontinuity model (BIRD2) to plan a BIRD3 design. However, level 2 parameters from the BIRD2 model should be substituted for level 3 parameters in the BIRD3 design. When the top level was ignored, using parameters from the BIRD2 model to plan a BIRD3 design should be avoided.

Keywords

• blocked regression discontinuity designs
• ignoring a level of nesting
• power analysis
• multilevel models
• hierarchical linear models

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