There is much interest in computer vision to utilize commodity hardware for gaze estimation. A number of papers have shown that algorithms based on deep convolutional architectures are approaching accuracies where streaming data from mass-market devices can offer good gaze tracking performance, although a gap still remains between what is possible and the performance users will expect in real deployments. We observe that one obvious avenue for improvement relates to a gap between some basic technical assumptions behind most existing approaches and the statistical properties of the data used for training. Specifically, most training datasets involve tens of users with a few hundreds (or more) repeated acquisitions per user. The non i.i.d. nature of this data suggests better estimation may be possible if the model explicitly made use of such 'repeated measurements' from each user as is commonly done in classical statistical analysis using so-called mixed effects models. The goal of this paper is to adapt these 'mixed effects' ideas from statistics within a deep neural network architecture for gaze estimation, based on eye images. Such a formulation seeks to specifically utilize information regarding the hierarchical structure of the training data-each node in the hierarchy is a user who provides tens or hundreds of repeated samples. This modification yields an architecture that offers state of the art performance on various publicly available datasets improving results by 10-20%.