Institute of Epidemiology and Preventive Medicine, National Taiwan University, Taipei, Taiwan.
Biostatistics. 2013 Jan;14(1):189-202. doi: 10.1093/biostatistics/kxs023. Epub 2012 Jul 2.
Logistic regression has been widely applied in the field of biomedical research for a long time. In some applications, the covariates of interest have a natural structure, such as that of a matrix, at the time of collection. The rows and columns of the covariate matrix then have certain physical meanings, and they must contain useful information regarding the response. If we simply stack the covariate matrix as a vector and fit a conventional logistic regression model, relevant information can be lost, and the problem of inefficiency will arise. Motivated from these reasons, we propose in this paper the matrix variate logistic (MV-logistic) regression model. The advantages of the MV-logistic regression model include the preservation of the inherent matrix structure of covariates and the parsimony of parameters needed. In the EEG Database Data Set, we successfully extract the structural effects of covariate matrix, and a high classification accuracy is achieved.
逻辑回归在生物医学研究领域已经得到了广泛的应用。在某些应用中，感兴趣的协变量在收集时具有自然的结构，例如矩阵的形式。协变量矩阵的行和列具有一定的物理意义，并且必须包含有关响应的有用信息。如果我们简单地将协变量矩阵堆叠为一个向量，并拟合一个常规的逻辑回归模型，相关信息可能会丢失，并且会出现效率低下的问题。基于这些原因，我们在本文中提出了矩阵变量逻辑（MV-logistic）回归模型。MV-logistic 回归模型的优点包括保留协变量的固有矩阵结构和所需参数的简约性。在 EEG 数据库数据集，我们成功地提取了协变量矩阵的结构效应，并实现了较高的分类准确性。
