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进行联合因素分析，能比仅基于反应的传统预测方法获得更精确的能力分数。为此，简单结构因素模型通常更受青睐，因为它只需为项目级反应时间额外指定一个测量模型，同时保留原有的项目反应理论（IRT）模型用于反应数据。由项目级反应时间指示的附加速度因子与IRT模型中的能力因子相关，使得反应时间数据能携带关于被试能力的额外信息。然而，参数化简单结构因素模型往往具有限制性，且对经验数据拟合不佳，导致对简单因子结构适用性的信心不足。本文采用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。我们得出结论：在进一步放宽测量模型中的参数假设后，简单因子结构能够实现良好的拟合。此外，我们的半参数模型表明，在总体中潜在能力与速度/迟缓性之间关联较强，但这种关联形式是非线性的。因此，基于拟合模型的评分能显著提高能力分数的精度。