International Journal on New Trends in Education and Their Implications July 2013 Volume: 4 Issue: 3 Article: 19 ISSN 1309-6249 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org 188 9 AN INVESTIGATION OF GOODNESS OF MODEL DATA FIT: EXAMPLE OF PISA 2009 MATHEMATICS SUBTEST Res. Assist. Gülden KAYA UYANIK Sakarya University Education Faculty Department of Measurement and Evaluation in Education Sakarya, TURKEY Inst. Gülşen TAŞDELEN TEKER Sakarya University, Education Faculty Department of Measurement and Evaluation in Education Sakarya, TURKEY Assist. Prof. Dr. Neşe GÜLER Sakarya University, Education Faculty Department of Measurement and Evaluation in Education Sakarya, TURKEY ABSTRACT Although Classical Test Theory (CTT) has been used for test development, Item Response Theory (IRT) is beginning to major theoretical source. However, the model-data fit should be verified as a prerequisite. Therefore, in this study it is aimed to investigate which IRT model will provide the best fit to the data obtained from PISA 2009 mathematics subtest. For goodness-of-fit analysis, first the model assumptions and then the expected model features were tested. The model assumptions unidimensionality, local independence and non- speeded test administration were investigated. In the expected model features part the invariance of ability parameter estimates and invariance of item parameter estimates were analyzed. In addition, item characteristics curves and item information functions were analyzed. To determine the best model, two different ways were followed: first number of items which fits with the model and then the results of the ki- square statistics of -2 log likelihood values of models were compared. The results suggested that two parameter logistic model is the most appropriate model for data fit. Key Words: Item response theory, model data fit analysis, person and item statistics. INTRODUCTION One of the advantages of Item Response Theory (IRT) compared to Classical Test Theory (CTT ) is that item and test parameters can be predicted independently of the group and the group members’ properties. The advantages of IRT is true only when the model-data fit is achieved at a satisfactory level. When the concordance is low, invariance of item and ability parameters cannot be attained. The model-data fit is achieved by satisfying the primary assumptions. The assumptions necessary for all IRT models are: assuring unidimensionality and local independence, and making sure that the test is not a speed test (Hambleton, Swaminathan and Rogers, 1991; Baker, 2001; Embretson and Reise, 2000). This study examines firstly the model assumptions and then the invariance of the predictions for item and ability parameters- the expected model properties. One of the suppositions of IRT is “unidimensionality”. What is meant by the term unidimensionality is the measurement of one single ability with one test, and it is too difficult to meet this assumption exactly. In order