关键词: 项目反应理论, Rasch模型, 模型选择, 参数和维度

Abstract: There are various analysis models of item response theory (IRT). Based on their quantitative differences in parameters and dimensions, they fall into two schools: the atypical IRT school with Rasch model proposed by Georg Rasch as the research orientation and the typical IRT school with Three-parameter Logistic (3PL) model proposed by Birnbaum as the research orientation. The former emphasizes the one-parameter and unidimensional research paradigm, while the latter emphasizes the multi-parameter and multi-dimensional research development direction. The multi-parameter and multi-dimensional IRT model is a measurement method which advocates "model fits data". It focuses on the interpretability of data, and sets multiple parameters to achieve the goals of better fitting data and more sufficient interpretation of data. In a multidimensional case, researchers pay attention to the distinction and connection between dimensions from an integrated perspective. They attach importance to the influence of the interaction between different dimensions, and the influence of the interaction between dimensions and objects on parameter estimation as well. However, the multi-parameter and multi-dimensional IRT model exhibits strong sample dependence, and the relationship between model parameters is complicated and more susceptible to additional factors. In contrast, Rasch model is a "simple" model. It adheres to the one-parameter and unidimensional research paradigm, and focuses on the corresponding relationship between measurement objectives and measurement tools. It is designed on the basis of the relationship between objects and instruments. In Rasch model, difficulty parameters and ability parameters are symmetrical to each other; the estimation of item difficulty parameters does not depend on the difficulty distribution of items, and the estimation of person ability parameters does not depend on the ability distribution of persons. Besides, Rasch model can transform the non-linear data matrix composed of responses into two symmetrical columns of interval data reflecting ability parameters and difficulty parameters respectively. These features of Rasch model make it have two major advantages in practical applications. First, the essential advantage of Rasch model is that it can base on low-level data (Nominal Data or Ordinal Data) to construct a higher level of linear measurement, which provides more useful metrical information. Second, in the process of constructing or revising measurement tools, Rasch model places persons and items conjointly, and it is helpful for researchers to evaluate and explain the adaptability between the measured objects and the measurement tools more accurately. In the multi-dimensional research, Rasch model and MIRT model are applicable to different groups of research cases and can also complement each other in certain cases. Rasch model is suitable for the research with high correlation between dimensions or only one dominant factor. On the one hand, it requires the elimination of non-unidimensional items in the data to maintain the unidimensional nature of the original measurement. The objective of this practice is to ensure that each test only focuses on one variable or feature. On the other hand, it focuses on the explanatory power of the dominant dimension generated by the integration of different dimensions, and also on the analysis of whether deviant indicators indicate the existence of secondary dimensions. In general, Rasch model emphasizes two principles — "Theory drives research" and "Data matches model". Its core is the one-parameter and unidimensional measurement model can minimize the influence and interference of additional variables on the actual measurement goal, and ensure the objectivity and accuracy of measurement accordingly.

Key words: Item response theory(IRT), Rasch model, Model selection, Parameter and Dimensionality