The Study And Application Of Partially Linear Models In Item Response Theory

As an advanced theory of psychology and educational measurement, Item Response Theory (IRT) develops rapidly in recent decades of years. The researches on traditional IRT turn to model robustness, since Computerized Adaptive Test, which builds on IRT brings great changes to practical examinations. The researches towards model robustness include those on Multi-dimensional IRT, Nonparametric IRT and Diagnostic Test for Cognition.As one of the leading theories in measurement, IRT explains how the probability of answering correctly relates to item characters and testers' latent traits. Compared to the classical test theory, IRT clarifies item difficulty, item discrimination and item guessing factor, also it grasps the essence of tests, measures both of item characters and testers' abilities in the same scale, and avoids the limitation of sample dependence when people evaluate the items and testers. From this point of view, IRT demonstrates its advantages in wide use especially in constructing practical tests designed for different testers.However, it is the sample dependence of IRT models that hinders its application. When it comes to those test models which do not satisfy assumptions, Parametric IRT (PIRT) results in the bias when fits test data from these models. Nonparametric IRT (NIRT) which applies classical smoothing methods of nonparametric statistics to IRT models serves as a vital supplement. NIRT is more stable in tests of small scale. But, NIRT is lack of description of item characters. The explanation of items and tests is so vague that the NIRT is of less use than PIRT.This thesis represents the new Semi-parametric IRT (SIRT) model, combining traditional PIRT model and NIRT model. That is, SIRT changes PIRT models which determine the probability of answering correctly only by testers' latent traits and item characters. It introduces nonparametric function as other unknown factors which might affect the results of the probability. Compared to those single models such as parametric and nonparametric models, the new semi-parametric models improve greatly in evaluating both items and testers. SIRT model continues providing clear information from its parametric part; it also keeps the robustness of model as nonparametric models do. These two advantages ensure flexibility of the new model in practical use. Furthermore, the design of SIRT is more reasonable. It conveys more information of items and tests, since it takes other unknown factors into consideration as part of this new model. In sum, SIRT model is more close to actual tests.The first chapter introduces the background knowledge about psychological measurement theory and the recent developments and researches on Item Response Theory. The second chapter introduces Parametric IRT models and their assumptions, and Nonparametric IRT models and smoothing methods. The third chapter introduces the Semi-parametric IRT models together with the method and algorithm for estimation. The fourth chapter discusses some issues that come along with SIRT models. The fifth chapter is to simulate the new model and render the conclusion about it. The last chapter is the conclusion about SIRT.