Van der Linden's (2007, Psychometrika, 72, 287) hierarchical model for responses and response times in tests has numerous applications in psychological assessment. The success of these applications requires the parameters of the model to have been estimated without bias. The data used for model fitting, however, are often contaminated, for example, by rapid guesses or lapses of attention. This distorts the parameter estimates. In the present paper, a novel estimation approach is proposed that is robust against contamination. The approach consists of two steps. In the first step, the response time model is fitted on the basis of a robust estimate of the covariance matrix. In the second step, the item response model is extended to a mixture model, which allows for a proportion of irregular responses in the data. The parameters of the mixture model are then estimated with a modified marginal maximum likelihood estimator. The modified marginal maximum likelihood estimator downweights responses of test‐takers with unusual response time patterns. As a result, the estimator is resistant to several forms of data contamination. The robustness of the approach is investigated in a simulation study. An application of the estimator is demonstrated with real data.

中文翻译：

---

响应和响应时间的层次模型的鲁棒估计。

范德林登（2007，Psychometrika，72，287）用于测试中响应和响应时间的分层模型在心理评估中具有许多应用。这些应用程序的成功需要对模型的参数进行估计而不会产生偏差。但是，用于模型拟合的数据通常会受到例如快速猜测或注意力不集中的影响。这会使参数估计值失真。在本文中，提出了一种新颖的估计方法，该方法对污染具有鲁棒性。该方法包括两个步骤。第一步，在协方差矩阵的稳健估计的基础上拟合响应时间模型。在第二步中，项目响应模型扩展为混合模型，该模型允许数据中出现一定比例的不规则响应。然后，使用修改的边际最大似然估计器来估计混合模型的参数。修改后的边际最大似然估计量可降低具有异常响应时间模式的应试者的响应。结果，估计器可以抵抗多种形式的数据污染。在仿真研究中研究了该方法的鲁棒性。真实数据演示了估算器的应用。