Since electronic devices have become an integral part of life, there has been a need to bring the communication between a human and a machine closer to being as similar as possible to that between two people. As interpersonal relationships are built on the basis of feelings and empathy, training machines to understand emotions and to provide responses in accordance with the emotional state of the user, i.e. human, has become an interesting area for technology development. To gain a more comprehensive understanding of a person's emotional state, simultaneous utilization of different modalities such as audio, text, and video and their further processing using a graph neural network, recently became popular due to its suitability for tracking a conversation. However, small IoT devices commonly have constrained computational capabilities, memory resources and lower power consumption, and running such a complex multimodal algorithm in real-time may be difficult. In this research, we examine utilization of binarization and 8-bit floating point arithmetic for compressing state-of-the-art GNN-based model COGMEN. We demonstrate that in the case of the multimodal emotion recognition task, such constrained models can provide significant data savings while maintaining relatively high performance, as shown through experiments processing data from the IEMOCAP dataset.