Factor analysis is a statistical technique for data reduction and structure detection that traditionally relies on the normality assumption for factors. However, due to the presence of non-normal features such as asymmetry and heavy tails in many practical situations, the first two moments cannot adequately explain the factors. An extension of the factor analysis model is introduced by assuming a generalization of the multivariate restricted skew-normal distribution for the vector of unobserved factors. An efficient and computationally tractable EM-type algorithm is adopted for computing the maximum likelihood estimates by presenting a hierarchical representation of the proposed model. Finally, the efficiency and advantages of the proposed novel methodology are demonstrated through both simulated and real benchmark datasets.

因子分析是一种用于数据缩减和结构检测的统计技术，传统上依赖于因子的正态性假设。但是，由于在许多实际情况下都存在非正常特征（例如不对称和粗尾），因此前两个时刻不足以解释这些因素。通过假设未观察因素向量的多元受限偏正态分布的一般化，引入了因素分析模型的扩展。通过呈现所提出模型的分层表示，采用一种高效且易于计算的EM类型算法来计算最大似然估计。最后，通过模拟和真实基准数据集展示了所提出的新颖方法的效率和优势。