题目因素分析:基于SEM和基于IRT的两类方法

Item Factor Analysis: Approaches Based SEM and IRT

心理和教育测量一般只能达到顺序量表的水平,其测量数据与被测因子间并非简单线性关系。题目因素分析是用来描述测量题目与因子间非线性关系的统计模型。题目因素分析主要有基于结构方程模型和基于项目反应理论两类方法,两类方法之间存在紧密的联系,甚至可以看作是同一模型的两种表现形式。本文详细阐述了该关系,同时对两类方法在参数估计、模型拟合指标、测量一致性检验和支撑软件等方面的特点进行了分析和比较,以便研究者选择最为适合其研究的方法。

In psychological and educational measurement, the relationship between measurement data and latent variable cannot be present by linear regression since the data are ordinal in nature. Item factor analysis （IFA） is used to model non-linear relationship of ordinal-categorical item data and factors. Item factor analysis models and estimation methods are constructed under structural equation modeling （SEM） and item response theory （IRT） frame- work. They are mathematically equivalent, and one is aherative form of each other. The current study compares the two approaches to show the strengths and weaknesses of them on parameter estimation, model fit indexes, testing measurement invariance and statistical software. The strength of SEM-hased method is more familiar by psychologist and more flexible on measurement and structural model. At the same time, IRT-based method has unique advances on scoring and person fit test.