University of Giessen, Germany.
Br J Math Stat Psychol. 2012 May;65(2):334-49. doi: 10.1111/j.2044-8317.2011.02032.x. Epub 2011 Oct 19.
For computer-administered tests, response times can be recorded conjointly with the corresponding responses. This broadens the scope of potential modelling approaches because response times can be analysed in addition to analysing the responses themselves. For this purpose, we present a new latent trait model for response times on tests. This model is based on the Cox proportional hazards model. According to this model, latent variables alter a baseline hazard function. Two different approaches to item parameter estimation are described: the first approach uses a variant of the Cox model for discrete time, whereas the second approach is based on a profile likelihood function. Properties of each estimator will be compared in a simulation study. Compared to the estimator for discrete time, the profile likelihood estimator is more efficient, that is, has smaller variance. Additionally, we show how the fit of the model can be evaluated and how the latent traits can be estimated. Finally, the applicability of the model to an empirical data set is demonstrated.
对于计算机管理的测试，可以同时记录响应时间和相应的响应。这拓宽了潜在建模方法的范围，因为可以分析响应时间，除了分析响应本身。为此，我们提出了一种新的测试响应时间的潜在特质模型。该模型基于 Cox 比例风险模型。根据该模型，潜在变量改变了基线风险函数。描述了两种不同的项目参数估计方法：第一种方法使用离散时间的 Cox 模型的变体，而第二种方法基于轮廓似然函数。在模拟研究中，将比较每个估计器的属性。与离散时间的估计器相比，轮廓似然估计器更有效，即具有更小的方差。此外，我们展示了如何评估模型的拟合度以及如何估计潜在特质。最后，演示了该模型在实际数据集上的适用性。
