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 (PISA) 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.

翻译：普遍认为，对项目反应与反应时间（RT）进行联合因子分析，可能比传统仅基于反应数据的预测获得更精确的能力分数。为此，简单结构因子模型常被优先采用，因其仅需为项目层次的RT额外指定测量模型，而保留原始项目反应理论（IRT）模型中反应数据的结构。由项目层次RT表征的速度因子与IRT模型中的能力因子相关，使RT数据能携带关于被试能力的额外信息。然而，参数化简单结构因子模型往往限制性强，且对实证数据拟合欠佳，导致对简单因子结构适用性的信心不足。本文基于半参数简单结构模型分析了2015年国际学生评估项目（PISA）数学数据，发现：在充分放宽测量模型中附加参数假设后，简单因子结构能实现良好拟合。此外，半参数模型表明，潜在能力与速度/迟缓性的群体关联强度较高，但关联形式呈非线性。据此，基于拟合模型进行评分可显著提升能力分数的精度。