Çok Kategorili Madde Tepki Kuramı Modellerinin Örneklem Büyüklüğü Açısından İncelenmesi

Bu çalışmada Rosenberg Benlik Saygısı ölçeğinin madde tepki kuramındaki farklı çok kategorili modellerinde model veri uyumu kontrol edilip, madde parametreleri kestirimleri arasındaki ilişkilerin seçilen modele göre farklılaşıp farklılaşmadığı incelenmiştir. Araştırmada 47974 bireyin verdiği yanıtlar arasından kayıp veriler temizlendikten sonra rastgele seçilen Amerika Birleşik Devletli 500, 1000 ve 2000 bireyin tek boyutlu dört kategorili 10 maddelik ölçeğe verdiği yanıtlar kullanılmıştır. Genelleştirilmiş kısmi puan, 1 parametreli lojistik model gibi sınırlandırılmış genelleştirilmiş kısmi puan, kısmi puan ve aşamalı tepki modeliyle 500, 1000 ve 2000 kişilik örneklemlerden elde edilen verilerin analizinde -2log-olabilirlik, Akaike bilgi ölçütü ve Bayesian bilgi ölçütü model veri uyum katsayıları incelendiğinde en fazla uyumun her koşulda aşamalı tepki modeli ile gerçekleştiği bulunmuştur. Her modelden elde edilen madde parametreleri arasında manidar yüksek bir ilişkinin olduğu tespit edilmiştir. Farklı modellerden elde edilen bulgulara göre her üç örneklemden en yüksek ayırt ediciliğe sahip olan maddenin 6. madde, en az ayırt ediciliğe sahip olan maddenin ise 500 kişilik örneklem için 4. madde, 1000 ve 2000 kişilik örneklemler için ise genelde 8. madde olduğu görülmüştür.

Investigationof Polytomous Item Response Theory Modelsin Terms of Sample Size

In this study, we investigated whether the relations between the item parameter estimates differed according to the selected models by controlling the model datafit in the different polytomous models in the item response theory of the Rosenberg Self-Esteem scale. Among the answers given by 47974 individuals in the study, responses of randomly selected US 500, 1000 and 2000 individuals in a one-dimensional, four-categorical 10-item scale were used after the missing data were cleared. When the 2log-likelihood, AIC and BIC modeldata fit coefficients obtained from the data obtained from 500, 1000 and 2000 individuals into the generalized partial credit, restricted generalized partial credit such as 1-parameter logistic model, partial credit and graded response model were examined, it was found that the most adaptation was with graded response model in every condition. It was found that there was a high correlation between the item parameters obtained from each model. According to the findings obtained from different models, it was seen that item 6 had the highest discrimination from all three samples while item 4 had the least discrimination for 500 samples and item 8 for 1000 and 2000 samples in general.

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Akkermans, W. (1999). Polytomous item scores and Guttman dependence. British Journal of Mathematical and Statistical Psychology, 52(1), 39–62.
Baker, F. B. (2001). The basics of item response theory (Second edition). Washington DC.:ERIC.
Bıkmaz Bilgen, Ö., & Doğan, N. (2017). Çok Kategorili Parametrik ve Parametrik Olmayan Madde Tepki Kuramı Modellerinin Karşılaştırılması. Eğitimde ve Psikolojide Ölçme ve Değerlendirme Dergisi, 8(4), 354-372.
Cai, L., du Toit, S. H. C., & Thissen, D. (2011). IRTPRO: User guide. Lincolnwood, IL: Scientific Software International.
Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory(First edition). California: Thomson Learning.
Cook K.F., Dodd B.G.,& Fitzpatrick S.J. (1999). A comparison of three polytomous item response theory models in the context of testlet scoring.Journal of outcome measurement, 3(1), 1-20.
De Ayala, R. J. (2009). The theory and practice of item response theory (Methodology in the social sciences).New York: Guildford Press.
Doğan, N. ve Tezbaşaran, A.A. (2003). Klasik test kuramı ve örtük özellikler kuramının örneklemler bağlamındakarşılaştırılması. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 25(25), 58-67.
Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Erlbaum.
Fan, X. (1998). Item response theory and classical test theory: An empirical comparison of their item/person statistics. Educational and psychological measurement, 58(3), 357-381.
Hambleton, R. K., & Swaminathan, H. (1985). Item Response Theory: Principles and Applications. Boston: Kluwer Nijhoff.
Han, K. T., & Hambleton, R. K. (2014). User's manual for wingen 3: windows software that generates IRT model parameters and item responses(Center for Educational Assessment Report No. 642). Amherst, MA: University of Massachusetts.
Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991).Fundamentals of item response theory. London: Sage.
Hambleton, R. K. , & Jones, R. W. (1993). Comparison of classical test theory and item response theory and their applications to test development. Educational Measurement: Issues and Practice, 12(3), 38-47.
Hays, R. D., Morales, L. S., & Reise, S. P. (2000). Item response theory and health outcomes measurement in the 21st century. Medical care, 38(9 Suppl), II28. National Institutes of Health Public Access Author Manuscript. Retrieved 17/03/2017 from http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1815384/pdf/nihms14476.pdf
Hemker, B. T., Sijtsma, K., Molenaar, I. W., & Junker, B. W. (1996). Polytomous IRT models and monotone likelihood ratio of the total score. Psychometrika, 61(4), 679–693.
Hemker, B. T., Sijtsma, K., Molenaar, I. W., & Junker, B. W. (1997). Stochastic ordering using the latent trait and the sum score in polytomous IRT models. Psychometrika, 62(3), 331–347.
Jiao, H.,& Zhang, Y. (2014). Polytomous multilevel testlet models for testlet-based assessments with complex sampling designs. British Journal of Mathematical and Statistical Psychology, 68(1), 65-83.
Kang, T.,& Chen, T. T. (2008). Performance of the generalized S‐X2 ıtem fit ındex for polytomous IRT models. Journal of Educational Measurement, 45(4), 391-406.
Kline, T. J. B. (2005). Psychological testing: A practical approach to design and evaluation, Thousand Oaks, CA: Sage.
Koğar, H. (2015). Madde tepki kuramına ait parametrelerin ve model uyumlarının karşılaştırılması: Bir Monte Carlo çalışması. Eğitimde ve Psikolojide Ölçme ve Değerlendirme Dergisi, 6(1), 142-157
Köse, A. (2015). Aşamalı tepki modeli ve klasik test kuramı altında elde edilen test ve madde parametrelerinin karşılaştırılması. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 15(2), 184-197.
Macdonald, P., & Paunonen, S. V. (2002). A Monte Carlo comparison of item and person statistics based on item response theory versus classical test theory. Educational and psychological measurement, 62(6), 921-943.
Magno, C. (2009). Demonstrating the difference between classical test theory and item response theory using derived test data. The International Journal of Educational and Psychological Assessment, 1(1), 1-11.
Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149–174.
Maydeu-Olivares, A., Drasgow, F., & Mead, A. D. (1996). Distinguishing among parametric item response models for polytomous ordered data. Applied Psychological Measurement, 18(3), 245-256.
Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159–176.
Naumenko, O. (2014). Comparison of various polytomous ıtem response theory modeling approaches for task based simulation cpa exam data. AICPA 2014 Summer Internship Project. The University of North Carolina, Greensboro.
Ndalichako, J. L., & Rogers, W. T. (1997). Comparison of finite state score theory, classical test theory, and item response theory in scoring multiple-choice items. Educational and psychological measurement, 57(4), 580-589.
Ostini, R., & Nering, M. L. (2006). Polytomous item response theory models(No. 144). Thousand Oaks: Sage.
Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores (Psychometric Monograph No. 17). Richmond, VA: Psychometric Society. Retrieved 20.03.2017 from http://www.psychometrika.org/journal/online/MN17.pdf
Samejima, F. (1972). A general model for free-response data (Psychometric Monograph No. 18). Richmond, VA: Psychometric Society. Retrieved 18.03.2017 from http://www.psychometrika.org/journal/online/MN18.pdf
Samejima, F. (1995). Acceleration model in the heterogeneous case of the general graded response model. Psychometrika, 60(4), 549–572.
Samejima, F. (1996). The graded response model. In: van der Linden, W. J.,&Hambleton, R., (editors). Handbook of modern item response theory (p. 85-100). New York, NY: Springer.
Schermelleh-Engel, K., Moosbrugger, H., & Müler, H. (2003). Evaluating the fit of structural equation models: tests of significance and descriptive goodness-of-fit. Measures Of Psychological Research Online, 8(2), 23-74.
Sijtsma, K., & Hemker, B. T. (1998). Nonparametric polytomous IRT models for invariant item ordering, with results for parametric models. Psychometrika, 63(2), 183–200.
Sijtsma, K., & Hemker, B. T. (2000). A taxonomy of IRT models for ordering persons and items using simple sum scores. Journal of Educational and Behavioral Statistics, 25(4), 391–415.
Thissen, D., Pommerich, M., Billeaud, K., & Williams, V. S. (1995). Item response theory for scores on tests including polytomous items with ordered responses. Applied Psychological Measurement, 19(1), 39-49.
Uyar,Ş., Öztürk Gübeş, N. ve Kelecioğlu, H. (2013). PISA 2009 tutum anketi madde puanlarının aşamalı madde tepki modeli ile incelenmesi. Eğitim ve Öğretim Araştırmaları Dergisi, 2(4),125-134.
Van Der Ark, L. A. (2001). Relationships and properties of polytomous item response theory models. Applied Psychological Measurement, 25(3), 273-282.
Yurekli, H. (2010). The relationship between parameters from some polytomous item response theory models. (Unpublished Master’s thesis). The Florida State University, College Of Education, Florida.