Matrix-variate logistic regression is useful in facilitating the relationship between the binary response and matrix-variates, which arise commonly from medical imaging research. However, such a model is impaired by the presence of response misclassification. It is imperative to account for the misclassification effects when employing matrix-variate logistic regression to handle such data. In this article, we develop two inferential methods that account for the misclassification effects. The first method, called an imputation method, has roots in the score function derived from the misclassification-free context, and replaces the involved response variable with an unbiased pseudo-response variable, i.e., expressed in terms of the observed surrogate measurement. The second method is to directly derive the likelihood function for the observed response surrogate and then conduct estimation accordingly. Our development is carried out for two settings where misclassification rates are either known or estimated from validation data. The proposed methods are justified both theoretically and empirically. We analyze the Breast Cancer Wisconsin (Prognostic) data with the proposed methods.

中文翻译：

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具有响应错误分类的矩阵变量逻辑回归的插补和似然方法

矩阵变量逻辑回归有助于促进二元响应和矩阵变量之间的关系，这通常来自医学成像研究。然而，这种模型会因响应错误分类的存在而受损。在使用矩阵变量逻辑回归处理此类数据时，必须考虑错误分类的影响。在本文中，我们开发了两种解释错误分类影响的推理方法。第一种方法，称为插补方法，源于从无误分类上下文中导出的评分函数，并用无偏的伪响应变量替换所涉及的响应变量，即用观察到的替代测量表示。第二种方法是直接导出观察到的响应代理的似然函数，然后进行相应的估计。我们的开发是针对错误分类率已知或从验证数据估计的两种设置进行的。所提出的方法在理论上和经验上都是合理的。我们使用所提出的方法分析威斯康星州乳腺癌（预后）数据。