Department of Human Development and Quantitative Methodology, University of Maryland, 3304R Benjamin Bldg, 3942 Campus Dr, College Park, MD, 20742, USA.
Psychometrika. 2024 Jun;89(2):386-410. doi: 10.1007/s11336-023-09936-3. Epub 2023 Nov 16.
It is widely believed that a joint factor analysis of item responses and response time (RT) may yield more precise ability scores that are conventionally predicted from responses only. For this purpose, a simple-structure factor model is often preferred as it only requires specifying an additional measurement model for item-level RT while leaving the original item response theory (IRT) model for responses intact. The added speed factor indicated by item-level RT correlates with the ability factor in the IRT model, allowing RT data to carry additional information about respondents' ability. However, parametric simple-structure factor models are often restrictive and fit poorly to empirical data, which prompts under-confidence in the suitablity of a simple factor structure. In the present paper, we analyze the 2015 Programme for International Student Assessment mathematics data using a semiparametric simple-structure model. We conclude that a simple factor structure attains a decent fit after further parametric assumptions in the measurement model are sufficiently relaxed. Furthermore, our semiparametric model implies that the association between latent ability and speed/slowness is strong in the population, but the form of association is nonlinear. It follows that scoring based on the fitted model can substantially improve the precision of ability scores.
人们普遍认为，对项目反应和反应时间（RT）进行联合因素分析可能会产生比仅基于反应预测更准确的能力分数。为此，通常更喜欢简单结构因素模型，因为它仅需要为项目级 RT 指定一个附加的测量模型，而不改变原始项目反应理论（IRT）模型的反应。项目级 RT 指示的附加速度因素与 IRT 模型中的能力因素相关联，允许 RT 数据携带有关受访者能力的附加信息。然而，参数简单结构因素模型通常是限制性的，并且与经验数据拟合不良，这促使人们对简单因素结构的适用性缺乏信心。在本文中，我们使用半参数简单结构模型分析了 2015 年国际学生评估计划（PISA）的数学数据。我们得出的结论是，在进一步放宽测量模型中的参数假设后，简单因素结构可以达到良好的拟合。此外，我们的半参数模型表明，潜在能力与速度/缓慢之间的关联在人群中很强，但关联的形式是非线性的。因此，基于拟合模型的评分可以大大提高能力分数的精度。
