Quaternion representation (QR) has been shown to be an effective tool for image processing by modelling color images as quaternion matrices. However, previous QR based classification (QRC) methods overlook the labels of training data and may lead to sub-optimal results. In this article, we propose a Probabilistic Quaternion Collaborative Representation (ProQCR) method based on maximum likelihood estimation with application to color face identification. The proposed ProQCR method has the following merits: (1) Full supervision: In the representation and classification processes, the ProQCR method exploits the label information of training data, in contrast to prior methods using such supervision information only in the classification step. (2) Multi-channel integrality: ProQCR represents multiple color channels of each test color image as a quaternion linear combination of training data in a holistic manner. (3) Robustness: Equipped with the quaternion Huber loss function, ProQCR is robust against gross corruption in the test data. Experiments on benchmark databases demonstrate the effectiveness and robustness of ProQCR for color face identification.