Semiparametric Item Response Model

As the theory most widely used in modern educational measurement, item response theory (IRT) recently focus on the study of Model Robustness, the computer adaptive test and multi-dimensional item response model.This thesis starts from Model Robustness, combining a semi-parametric two-stage estimation with good statistical property and IRT, and obtains a new semi-parametric item response model (SIRM). It is easy to see that the new SIRM obtains the merits of both the parametric item response model (PITM ) and non-parametric item response model (NIRM).As a representative of modern mental measurement, PIRT ended the rule of the classical measurement theory and True Score Theory and marked a new epoch in mental measurement. In the subsequent decades, many scholars put forward numbers of parametric models based on different assumptions.In practice, item analyzers can choose different models flexibly using the historical information and professional experiences, which reflects the flexibility of PIRT. In addition, item parameters, which describe the property of items effectively with clearly and visible meaning, such as item difficulty parameter, item discrimination parameter and item guessing parameter .etc are offered by PIRT.However, with the advance of the study of PIRM, many scholars found that for some examinations it was not able to fit the test data well. This made an urgent requirement of a more robust model. NIRM, which expand the range of use of IRT as a combination of nonparametric method and IRT, was raised in this context. NIRM gets better fitting for small samples and short exam. And it could be used to test the fit of PIRM because of the Robustness. However, there's no the concept of item parameter in NIRT, which became one of the reasons that item analyzers are unwilling to use it.New SIRM estimates IRF with parametric model as the first-stage estimator, which is then adjusted by nonparametric method. In this way, the new estimator could make historical data and empirical information in use as PIRM, and simultaneously hold excellent robustness as NIRM. In addition, the new estimator can get more reliable estimation of item parameters than PIRM, whereas NIRM can not offer it at all.The new SIRM starts from the parametric model, adjusts with nonparametric methods and ends in the new semi-parametric model. It fills the blank of semi-parametric application in IRT.In the first chapter of this thesis, the history and status of mental measurement, IRT and NIRM are briefly introduced. The introduction of the background of the problem and the brief of the new SIRM are also in this chapter. In the second chapter, PIRM and the methods dealing with them are introduced. NIRM is mentioned in chapter three. The explanation of SIRM and the algorithm will be in the fourth chapter. In the fifth chapter, the new estimation will be promoted. The property of the new estimation will be studied using the simulation in the sixth chapter and other discussions and conclusions are mentioned in the last chapter.