Recent work on measuring growth with categorical outcome variables has combined the item response theory (IRT) measurement model with the latent growth curve model and extended the assessment of growth to multidimensional IRT models and higher order IRT models. However, there is a lack of synthetic studies that clearly evaluate the strength and limitations of different multilevel IRT models for measuring growth. This study aims to introduce the various longitudinal IRT models, including the longitudinal unidimensional IRT model, longitudinal multidimensional IRT model, and longitudinal higher order IRT model, which cover a broad range of applications in education and social science. Following a comparison of the parameterizations, identification constraints, strengths, and weaknesses of the different models, a real data example is provided to illustrate the application of different longitudinal IRT models to model students’ growth trajectories on multiple latent abilities.

中文翻译：

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纵向项目反应理论模型的研究

最近使用分类结果变量测量增长的工作已将项目响应理论（IRT）测量模型与潜在增长曲线模型相结合，并将对增长的评估扩展到多维IRT模型和高阶IRT模型。然而，缺乏综合的研究来清楚地评估不同的多级IRT模型用于测量生长的强度和局限性。本研究旨在介绍各种纵向IRT模型，包括纵向一维IRT模型，纵向多维IRT模型和纵向高阶IRT模型，它们涵盖了教育和社会科学领域的广泛应用。在比较了不同模型的参数设置，识别约束，优势和劣势之后，