Censored data arise frequently in diverse applications in which observations to be measured may be subject to some upper and lower detection limits due to the restriction of experimental apparatus such that they are not exactly quantifiable. Mixtures of factor analyzers with censored data (MFAC) have been recently proposed for model-based density estimation and clustering of high-dimensional data in the presence of censored observations. In this paper, we consider an extended version of MFAC by considering regression equations to describe the relationship between covariates and multiply censored dependent variables. Two analytically feasible EM-type algorithms are developed for computing maximum likelihood estimates of model parameters with closed-form expressions. Moreover, we provide an information-based method to compute asymptotic standard errors of mixing proportions and regression coefficients. The utility and performance of our proposed methodology are illustrated through a simulation study and two real data examples.

删失数据经常出现在不同的应用中，在这些应用中，由于实验设备的限制，要测量的观测值可能会受到一些检测上限和下限的限制，因此它们不能完全量化。最近提出了因子分析器与删失数据 (MFAC) 的混合，用于在存在删失观察的情况下对高维数据进行基于模型的密度估计和聚类。在本文中，我们通过考虑回归方程来描述协变量和乘法删失因变量之间的关系来考虑 MFAC 的扩展版本。开发了两种分析上可行的 EM 类型算法，用于计算具有封闭形式表达式的模型参数的最大似然估计。而且，我们提供了一种基于信息的方法来计算混合比例和回归系数的渐近标准误差。通过模拟研究和两个真实数据示例说明了我们提出的方法的实用性和性能。