Recent feasibility studies involving children with autism spectrum disorders (ASD) interacting with socially assistive robots have shown that some children have positive reactions to robots, while others may have negative reactions. It is unlikely that children with ASD will enjoy any robot 100% of the time. It is therefore important to develop methods for detecting negative child behaviors in order to minimize distress and facilitate effective human-robot interaction. Our past work has shown that negative reactions can be readily identified and classified by a human observer from overhead video data alone, and that an automated position tracker combined with human-determined heuristics can differentiate between the two classes of reactions. This paper describes and validates an improved, non-heuristic method for determining if a child is interacting positively or negatively with a robot, based on Gaussian mixture models (GMM) and a naive-Bayes classifier of overhead camera observations. The approach achieves a 91.4% accuracy rate in classifying robot interaction, parent interaction, avoidance, and hiding against the wall behaviors and demonstrates that these classes are sufficient for distinguishing between positive and negative reactions of the child to the robot.