An application of hierarchical linear modeling: OKS-2006 science test achievement

Problem Durumu: Son yıllarda iç içe geçmiş veri yapısı sergileyen verilerde aşamalı doğrusal modelleme (ADM) sıkça kullanılmaktadır. Veriler iç içe geçmiş veri yapıları sergiledikleri zaman, klasik doğrusal modellere ilişkin başlıca varsayımların (veri grubundaki gözlemlerin, veri grubundaki diğer gözlemlerle olan bağımsızlığı) ihlal edildiği bir yapıya sahip olurlar. Örneğin, eğitimde sıkça öğrencilerin çeşitli alanlardaki başarı puanları incelenir ve eğitim sisteminde öğrenciler sınıflardan (eğitim aldıkları ortamlardan), sınıflarda içinde bulundukları okullardan bağımsız olarak düşünülemez. Öğrenciler, aynı sınıfın içinde ortak bir öğretmeni, ortak bir öğretme sitilini ve ortak bir öğrenme deneyimlerini paylaşırlar. Bu ortak deneyimler nedeniyle, öğrenci başarı puanları, aynı sınıfın içindeki diğer öğrencilerin başarı puanlarıyla doğrudan ilişkilidir ve bağımsız olarak düşünülemez. Aşamalı ya da iç içe geçmiş verilere standart regresyon eşitlikleri uygulandığında da bazı problemlerle karşılaşılır. En temel problem gözlemlerin bağımsızlığı sorunudur. Standart regresyon modellerinde değişkenlerin birbirinden bağımsız olma koşulu hiyerarşik verilerde bozulduğundan hiyerarşik yapılarda bulunan gözlemler, birbirlerine, tesadüfî yolla örneklenen gözlemlerden daha çok benzer olma eğilimindedirler. ADM’de değişkenler birkaç şekilde modellenebilir. Bu çalışmada ADM’de değişkenlerin 3 farklı şekilde modellemesi açıklanmıştır. 1-ADM’de Koşulsuz Modelleme Ya Da Tesadüfî Etkili ANOVA 2- Düzey 1 Denklemine Kestiriciler Ekleme 3- Düzey 1 ve 2 Denklemine Kestiriciler Ekleme

Aşamalı doğrusal modellemede bir uygulama: OKS–2006 fen testi başarısı

Problem Statement: Recent research has commonly used hierarchical linear models (HLMs). Also known as multilevel models, HLMs can be used to analyze a variety of questions with either categorical or continuous dependent variables. With hierarchical linear models, each level (e.g., student, classroom, and school) is formally represented by its own submodel. This study presents detailed descriptions of practical procedures to conduct nested data analysis using HLM. Purpose of Study: The purpose of this study was to illustrate the use of HLMs to identify the effects of school districts and students’ gender on students’ science achievement. Methods: A stratified random sampling method was used for the study, and the data was gathered from 10,727 students nested in 81 school districts. HLM 6.02 was used in order to build a two-level HLM model. In the analysis, a one-way ANOVA with random effects model was used first, followed by a Random-Coefficients Regression Model and finally the addition of a Level-1 and a Level-2 Predictor. Results: According to the results of the one-way random effects ANOVA model, considerable variations were observed in the school means. 0.004 of the variability in science achievement was observed between school districts. According to the results of the Random-Coefficients Regression Model, a significant difference was observed in the gender slope (i.e., the effect of gender on science scores) across schools. According to the results of the contextual model with gender in level 1 and socio-economic status (SES) in level 2, SES had a significant effect on the means of school science achievement. The effect of gender on science achievement in schools with the average percentage of SES was statistically different from zero. Further, no significant effect by SES on the gender slope was observed. Recommendations: Since the national exams show nested data structures, our recommendation is to use statistical models containing the hierarchies in which the student is classified, the characteristics belonging to these hierarchies, and the characteristics belonging to the student in the analyses concerning the factors that affect the success of the student.

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Acar, T. (2005). OKÖSYS Sosyal Bilimler Test Başarı Puanlarının Diğer Alt Test Başarı Puanları ve Cinsiyet Değişkeni İle Karşılaştırılması. Egitim Arastirmalari- Eurasian Journal of educational Research,21.
Bryke, A. S. & Raudenbush, S.W. (1992). Hierarchical linear models. Thousand Oaks, CA: Sage.
Franks, M.E. and others (1996, April). An analysis of NEAP trial state assessment data concerning the effects of computers on Mathematics achievement. Paper presented at the annual meeting of the American Educational Research Association, New York.
Koopmans, M. (1998, April). Application of HLM to the evaluation of the effects of basic skills programs on Math achievement. Paper presented at the annual meeting of the American Educational Research Association, San Diego (ERIC Document Reproduction Service No. ED 419 843).
Liu, X. (2004, October). Applying HLM to estimate reading achievement. Paper presented at the 35th annual Conference of the Northheastern Educational Research Association, New York
Novy, D.M., & Francis, D.J. (1989, August). An application of hierarchical linear modeling to group research. Paper presented at the 1989 annual meeting of the American Psychological Association, New Orleans
Opdenakker, M.& Van Damme, J. (1998, April). The impotances of indentifinglevels in multilevel analysis. Paper presented at the annual meeting of the American Educational Research Association, San Diago. (ERIC Document Reproduction Service No. ED 422 400).
Osborne, J.W. (2000). Advantages of hierarchical linear modeling. Practical Assessment, Research, and Evaluation, 7(1). Retrieved 26 November 2007 from http://www4.ncsu.edu/~jwosbor2/otherfiles/MyResearch/PARE2000- HLM.pdf
Park, S. (2005). Student engagement and classroom variables in improving mathemetics achievement. Asia Pacific Education Review. Vol. 6, No. 1, 87-97.
Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods. Sage Publications.
Subedi, B.R. (2005) Demonstratıon of the three-level hierarchical generalized linear model applied to educational research. Unpublished doctoral dissertation, The Florida State University (UMI No. 3183114).
Tamada, M. (2002, June). Predictors of graduation rates: Why they can be expected to have greater predictive value at the national level than at the intuitional research. Paper presented at the annual forum of the Association for intuitional Research, Toronto.(ERIC Document Reproduction Service No. ED 472 474).
Wang, J. (2000, April).Relevance of the hierarchical linear model to TIMSS data analysis. Paper presented at the annual meeting of the American Educational Research Association, New Orleans. (ERIC Document Reproduction Service No. ED 441 432).
Webster, W. J. and others (1996, April). The applicability of selected regression and hierarchical linear models to the estimation of school and teacher effects. Paper presented at the annual meeting of the National Council or Measurement in Education, New York. (ERIC Document Reproduction Service No. ED 400 320).
Williams, N. J. (2003). Item and Person Parameter Estimation using Hierarchical Generalized Linear Models and Polytomous Item Response Theory Models, Doctor of Philosophy: Unpublished doctoral dissertation, The University of Texas at Austin.(UMI No. 3116234).
Willms, J.D. (1999). Basic Concepts in Hierarchical Linear Modeling with Applications for Policy Analysis. In G. Cizek (Ed.), Handbook of educational policy. San Diego, CA: Academic Press. Retrieved 10 February 2008 from http://www.unb.ca/crisp/pdf/9806land.pdf
Zhang, Y.&Zhang, L. (2002, April). Modeling school and district effect in the Math achievenment of delaware students measured by DSTP: A preliminary application of hierarchical linear modeling in accountability study. Paper presented at the annual meeting of the American Educational Research Association, New Orleans. (ERIC Document Reproduction Service No. ED 468 962).