Parametrik ve Parametrik Olmayan Madde Tepki Kuramı Modellerinden Çeşitli Faktörlere Göre Elde Edilen Madde ve Yetenek Kestirimlerinin Karşılaştırılması
Öz
Bu
araştırmada, Madde Tepki Kuramı kapsamında yer alan iki farklı yaklaşım olan
Parametrik Madde Tepki Kuramı (PMTK) ve Parametrik Olmayan Madde Tepki Kuramı
(POMTK) modellerinden kestirilen madde ve yetenek parametrelerinin test
uzunluğu, örneklem büyüklüğü ve maddelerin psikometrik nitelikleri faktörlerine
göre karşılaştırılması amaçlanmıştır. Temel araştırma niteliğinde olan
araştırmanın verileri Uluslararası Matematik ve Fen Eğilimleri
Araştırması’nın (Trends of International
Mathematics and Science-TIMSS) 2011 yılındaki uygulamasından elde edilmiştir.
Çeşitli kriterler dikkate alınarak oluşturulan veri setinden çalışmanın
amaçları ve incelemeye alınan faktörlerin koşulları gözetilerek 16 ayrı veri
seti oluşturulmuştur. Elde edilen sonuçlar incelendiğinde, her iki yaklaşıma
göre farklı örneklem büyüklüğünden kestirilen madde parametreleri arasında
yüksek düzeyde ve manidar bir uyum olduğu belirlenmiştir. Test uzunluğu ve
örneklem büyüklüğü koşullarının birlikte incelendiği veri setleri için ise PMTK
ve POMTK modellerinden kestirilen madde parametreleri arasında yüksek düzeyde
ve manidar ilişkiler olduğu bulunmuştur. Özetle her iki yaklaşıma göre farklı
koşullar altında kestirilen madde ve yetenek parametreleri birbirleri ile
yüksek düzeyde ve manidar ilişkiler göstermiştir. Böylelikle PMTK modellerinin
varsayımları veri setleri için yeterli düzeyde karşılanmadığında, incelenen
koşullara uygun durumlarda POMTK yaklaşımının tercih edilebileceği sonucuna
ulaşılmıştır.
Anahtar Kelimeler
Parametrik madde tepki kuramı parametrik olmayan madde tepki kuramı Mokken ölçekleme örneklem büyüklüğü test uzunluğu
Kaynakça
- Baker, F. B. and Kim. S.H. (2004). Item response theory: Parameter estimation techniques (2nd Edition). New York: Marcel Dekker. Christensen, K. and Kreiner, S. (2010). Monte Carlo tests of the Rasch model based on scalability coefficients. British Journal of Mathematical and Statistical Psychology, 63, 101-111. Dyehouse, M. A. (2009). A comparison of model-data fit for parametric and nonparametric item response theory models using ordinal-level ratings. Purdue University. Embretson, S. E. and Reise, S. P. (2000). Item response theory for psychologists. Mahwah. NJ: Erlbaum. Hambleton, R. K. and Swaminathan, H. (1985). Item response theory. Principles and applications. Boston: Kluwer. Junker, B. (2000). Some topics in nonparametric and parametric IRT. with some thougts about the future. Carnegie Mellon University: Department of Statistics. Koğar, H. (2014). Madde tepki kuramının farklı uygulamalarından elde edilen parametrelerin ve model uyumlarının örneklem büyüklüğü ve test uzunluğu açısından karşılaştırılması. Yayımlanmamış doktora tezi. Hacettepe Üniversitesi Eğitim Bilimleri Enstitüsü. Kujipers, R. E., Van der Ark, L. A., Croon, M. A. and Sijtsma, K. (2016). Bias in point estimates and standard errors of Mokken’s scalability coefficients. Applied Pyschological Measurement. 40 (5), 331-345. Loevinger, J. (1947). A systematic approach to the construction and evaluation of tests of ability. Psychological Monographs. 61 (A). Loevinger, J. (1948). The technic of homogeneous tests compared with some aspects of "scale analysis" and factor analysis. Psychological Bulletin. 45 (6). 507-529. Meijer, R. R., Sijtsma, K and Smidt, N. G. (1990). Theoretical and empirical comparison of the Mokken and the Rasch approach to IRT. Applied Psychological Measurement. 14. 283–298. Meijer, R. R., Sijtsma, K., and Molenaar, I. W. (1995). Reliability estimation for single dichotomous items based on Mokken's IRT model. Applied Psychological Measurement, 19 (4), 323-335. Meijer, R.R., and Baneke, J.J. (2004). Analyzing psychopathlogy items: a case for nonparametric item response theory modeling. Pyschological Methods, 9 (3), 354-368. Meijer, R. R., Egberink, I.J.L.,Emmons, W.H.M. and Sijtsma, K. (2008). Detection and valiaditon of unscalable item score patterns usingitem response theory: an isllustration with Harter’s self-perception profile for children. Journal of Personality Assessment, 90 (3), 227-238. Meijer, R. R., Tendeiro, J. N., & Wanders, R. B. (2014). The use of nonparametric item response theory to explore data quality. In Handbook of Item Response Theory Modeling (s. 103-128). New York: Routledge. Mislevy, R. J. & Stocking, M. L. (1989). A consumer’s guide to LOJIST and BILOG. Applied Psychological Measurement. 13. 57-75. Mokken. R. J. and Lewis. C. (1982). A nonparametric approach to the analysis of dichotomous item responses. Applied Psychological Measurement, 6 (A), 417-430. Molenaar, I.W. veSijtsma. K. (1984).Internalconisistency and realibility in Mokken’s nonparametric item response model. Tijdshriftvoor onderwijsresearch.9 (5). 257-268. Molenaar, I. W. (1991). A weighted Loevinger H coefficient extending Mokken scaling to multicategory items. KwantitatieMeMethoden. 37. 97– 117. Molenaar. I. W. (1997). Nonparametric models for polytomous responses. In W.J. Man der Linden and R.K. Hambleton (Ed.). Handbook of modern item response theory (s. 369–380). NewYork: Springer. Molenaar, I. W. (2001). Thirty years of nonparametric item response theory. Applied Psychological Measurement, 25 (3), 295-299. Mokken, R. J. (1971). A theory and procedure of scale analysis with applications in political research. New York. Berlin: Walter de Gruyter. Mouton. Molenaar. I. W. (1997). Nonparametric models for polytomous responses. In W.J. Man der Linden and R.K. Hambleton (Ed.). Handbook of modern item response theory (s. 369–380). NewYork: Springer. Sijtsma, K. and Junker, B.W. (2006). Item Response Theory: Past Performance. Present Developments and Future Expectations. Behaviormetrika, 1, 75–102. Sijtsma, K. and Meijer, R. R. (2007). Nonparametric item response theory. C. R. Rao. & S. Sinharay (Ed.) Handbook of statistics26: psychometrics. (s.719-746). Amsterdam: Elsevier. Sijtsma, K., and Molenaar, I. W. (2002). Introduction to nonparametric item response theory. Newbury Park. CA: Sage. Straat, J. H., Van der Ark, L.A. and Sijtsma, K. (2014). Minimum sample size requirements for Mokken scale analysis. Educational and Psychological Measurement, 74, 809-822. Şengül Avşar, A., & Tavşancil, E. (2017). Examination of Polytomous Items' Psychometric Properties According to Nonparametric Item Response Theory Models in Different Test Conditions. Educational Sciences: Theory and Practice, 17(2), 493-514. Van Schuur, W. H. (2011). Ordinal item response theory: Mokken scale analysis. Los Angeles: Sage Publications
The Comparison of Item And Ability Estimations Calculated From The Parametric and Non-Parametric Item Response Theory According to The Several Factors
Öz
This study
aimed to compare the item and ability parameters estimated from two different
approaches of Item Response Theory, which are parametric and non-parametric,
according to the factors of test length, sample size and the item psychometric
qualities. The study was prepared in a basic research method and the data of
the study is obtained from the Trends of International Mathematics and Science
(TIMSS) 2011 application. From the main data set, 16 different data sets were
formed according to the research questions and the conditions of the factors.
The results showed that all of the item parameters estimated according to the
parametric and non-parametric models from the data sets which are composed of
different number of items and sample sizes were correlated significantly and
highly. Among of the abilities estimated by non-parametric models in all sample
size and test length factors, it was concluded that ability parameters are
significantly and highly correlated. To
sum up, it was found that both approaches had resulted in so highly and
significantly correlated item and ability parameters. This finding showed that
if the assumptions of parametric item response theory models are not met as a
required level, the non-parametric alternative models can be used in the
conditions that studied in this research.
Anahtar Kelimeler
Parametric item response theory non-parametric item response theory Mokken scaling sample size test length
Kaynakça
- Baker, F. B. and Kim. S.H. (2004). Item response theory: Parameter estimation techniques (2nd Edition). New York: Marcel Dekker. Christensen, K. and Kreiner, S. (2010). Monte Carlo tests of the Rasch model based on scalability coefficients. British Journal of Mathematical and Statistical Psychology, 63, 101-111. Dyehouse, M. A. (2009). A comparison of model-data fit for parametric and nonparametric item response theory models using ordinal-level ratings. Purdue University. Embretson, S. E. and Reise, S. P. (2000). Item response theory for psychologists. Mahwah. NJ: Erlbaum. Hambleton, R. K. and Swaminathan, H. (1985). Item response theory. Principles and applications. Boston: Kluwer. Junker, B. (2000). Some topics in nonparametric and parametric IRT. with some thougts about the future. Carnegie Mellon University: Department of Statistics. Koğar, H. (2014). Madde tepki kuramının farklı uygulamalarından elde edilen parametrelerin ve model uyumlarının örneklem büyüklüğü ve test uzunluğu açısından karşılaştırılması. Yayımlanmamış doktora tezi. Hacettepe Üniversitesi Eğitim Bilimleri Enstitüsü. Kujipers, R. E., Van der Ark, L. A., Croon, M. A. and Sijtsma, K. (2016). Bias in point estimates and standard errors of Mokken’s scalability coefficients. Applied Pyschological Measurement. 40 (5), 331-345. Loevinger, J. (1947). A systematic approach to the construction and evaluation of tests of ability. Psychological Monographs. 61 (A). Loevinger, J. (1948). The technic of homogeneous tests compared with some aspects of "scale analysis" and factor analysis. Psychological Bulletin. 45 (6). 507-529. Meijer, R. R., Sijtsma, K and Smidt, N. G. (1990). Theoretical and empirical comparison of the Mokken and the Rasch approach to IRT. Applied Psychological Measurement. 14. 283–298. Meijer, R. R., Sijtsma, K., and Molenaar, I. W. (1995). Reliability estimation for single dichotomous items based on Mokken's IRT model. Applied Psychological Measurement, 19 (4), 323-335. Meijer, R.R., and Baneke, J.J. (2004). Analyzing psychopathlogy items: a case for nonparametric item response theory modeling. Pyschological Methods, 9 (3), 354-368. Meijer, R. R., Egberink, I.J.L.,Emmons, W.H.M. and Sijtsma, K. (2008). Detection and valiaditon of unscalable item score patterns usingitem response theory: an isllustration with Harter’s self-perception profile for children. Journal of Personality Assessment, 90 (3), 227-238. Meijer, R. R., Tendeiro, J. N., & Wanders, R. B. (2014). The use of nonparametric item response theory to explore data quality. In Handbook of Item Response Theory Modeling (s. 103-128). New York: Routledge. Mislevy, R. J. & Stocking, M. L. (1989). A consumer’s guide to LOJIST and BILOG. Applied Psychological Measurement. 13. 57-75. Mokken. R. J. and Lewis. C. (1982). A nonparametric approach to the analysis of dichotomous item responses. Applied Psychological Measurement, 6 (A), 417-430. Molenaar, I.W. veSijtsma. K. (1984).Internalconisistency and realibility in Mokken’s nonparametric item response model. Tijdshriftvoor onderwijsresearch.9 (5). 257-268. Molenaar, I. W. (1991). A weighted Loevinger H coefficient extending Mokken scaling to multicategory items. KwantitatieMeMethoden. 37. 97– 117. Molenaar. I. W. (1997). Nonparametric models for polytomous responses. In W.J. Man der Linden and R.K. Hambleton (Ed.). Handbook of modern item response theory (s. 369–380). NewYork: Springer. Molenaar, I. W. (2001). Thirty years of nonparametric item response theory. Applied Psychological Measurement, 25 (3), 295-299. Mokken, R. J. (1971). A theory and procedure of scale analysis with applications in political research. New York. Berlin: Walter de Gruyter. Mouton. Molenaar. I. W. (1997). Nonparametric models for polytomous responses. In W.J. Man der Linden and R.K. Hambleton (Ed.). Handbook of modern item response theory (s. 369–380). NewYork: Springer. Sijtsma, K. and Junker, B.W. (2006). Item Response Theory: Past Performance. Present Developments and Future Expectations. Behaviormetrika, 1, 75–102. Sijtsma, K. and Meijer, R. R. (2007). Nonparametric item response theory. C. R. Rao. & S. Sinharay (Ed.) Handbook of statistics26: psychometrics. (s.719-746). Amsterdam: Elsevier. Sijtsma, K., and Molenaar, I. W. (2002). Introduction to nonparametric item response theory. Newbury Park. CA: Sage. Straat, J. H., Van der Ark, L.A. and Sijtsma, K. (2014). Minimum sample size requirements for Mokken scale analysis. Educational and Psychological Measurement, 74, 809-822. Şengül Avşar, A., & Tavşancil, E. (2017). Examination of Polytomous Items' Psychometric Properties According to Nonparametric Item Response Theory Models in Different Test Conditions. Educational Sciences: Theory and Practice, 17(2), 493-514. Van Schuur, W. H. (2011). Ordinal item response theory: Mokken scale analysis. Los Angeles: Sage Publications