Abstract: With the popularity of computer-based testings, it is easier to collect item response times (RTs) in psychological and educational assessments. RTs can provide an important source of information for respondents and tests. Accordingly, RTs can help in evaluating the speed of respondents, detecting cheating behaviors and designing better tests. RTs can also be used for improving the accuracy of parameter estimation and others. To full use of RTs, researchers have invested substantial effort in developing statistical models of RTs. Most of the proposed models posit a unidimensional latent speed to account for RTs in tests. However, there are many multidimensional tests in psychological and educational assessments. Based on the assumption that each latent speed should be paired with a specific latent ability in multidimensional tests, a multidimensional lognormal response time model (MLRT) model was proposed with extended the unidimensional lognormal response time model (ULRTM). In multidimensional tests, there are between-item and within-item multidimensionality. There may be effects between different latent speeds in the between-item multidimensionality. MLRTM may not be appropriate for this situation. To capture the effect between different latent speeds, this study proposed higher-order lognormal response time model (HO-LRTM) and bifactor lognormal response time model (Bi-LRTM) based on the corresponding response model. Model parameters in the HO-LRTM and Bi-LRTM can be estimated via maximum likelihood estimation in Mplus. In the simulation study, the results showed that the parameters of HO-LRTM and Bi-LRTM can be accurately estimated. In empirical data, three sets (A, C and D) were chose from the Raven’s Standard Progressive Matrices. Each set has 12 items. Firstly, RTs were explored the structure of latent speed by the empirical kaiser criterion (EKC) and exploratory factor analysis (EFA). The results of the EKC and EFA indicated that the latent structure of RTs is a three-dimensional structure. Secondly, according to the different fit indices, the Bi-LRTM fits better than other models. Furthermore, it is necessary to free speed-slope parameters in the response time models by comparing the fitting effect of fixed and free the parameters. Finally, this study assessed unidimensionality of Bi-LRTM based on some statistical indices. These statistical indices showed the necessity of general and specific latent speed in the Bi-LRTM. Overall, the proposed Bi-LRTM works well in simulation study and empirical data. That is, considering the effect on multidimensional latent speeds meets the need for analyzing the between-item multidimensional response time.

Key words: response time, the between-item multidimensionality, higher-order lognormal response time model, bifactor lognormal response time model

摘要： 随着计算机测验使用的普及化，被试在心理与教育测验上的作答反应时的获取也越发便利。为了充分利用项目反应时信息，单维与多维的反应时模型相继被提出。然后，在项目间多维反应时数据中，潜在特质速度之间可能存在共同关系（比如，层阶关系），此时现有的反应时模型并不能适用。基于此，本研究提出了高阶对数正态反应时模型与双因子对数正态反应时模型。在模拟研究中，高阶对数正态反应时模型与双因子对数正态反应时模型的各参数都能被准确估计。在瑞文标准推理测验的三组测验项目的反应时数据中，双因子对数正态反应时模型表现出更为优秀的拟合效果，同时基于多个统计量说明了局部与全局潜在特质速度同时存在的必要性。因此，在项目间多维测验反应时数据分析中，非常有必要考虑多维潜在特质速度之间的共同效应。

关键词: 反应时, 项目间多维, 高阶对数正态反应时模型, 双因子对数正态反应时模型