Modeling visitor engagement is a key challenge in informal learning environments, such as museums and science centers. Devising predictive models of visitor engagement that accurately forecast salient features of visitor behavior, such as dwell time, holds significant potential for enabling adaptive learning environments and visitor analytics for museums and science centers. In this paper, we introduce a multimodal early prediction approach to modeling visitor engagement with interactive science museum exhibits. We utilize multimodal sensor data including eye gaze, facial expression, posture, and interaction log data captured during visitor interactions with an interactive museum exhibit for environmental science education, to induce predictive models of visitor dwell time. We investigate machine learning techniques (random forest, support vector machine, Lasso regression, gradient boosting trees, and multi-layer perceptron) to induce multimodal predictive models of visitor engagement with data from 85 museum visitors. Results from a series of ablation experiments suggest that incorporating additional modalities into predictive models of visitor engagement improves model accuracy. In addition, the models show improved predictive performance over time, demonstrating that increasingly accurate predictions of visitor dwell time can be achieved as more evidence becomes available from visitor interactions with interactive science museum exhibits. These findings highlight the efficacy of multimodal data for modeling museum exhibit visitor engagement.