We propose a model of eye-tracking data to understand information acquisition patterns on attribute-by-product matrices, which are common in online choice environments such as comparison websites. The objective is to investigate how consumers gather product and attribute information from moment to moment. We propose a hierarchical hidden Markov model that consists of three connected layers: a lower layer that describes the eye movements, a middle layer that identifies information acquisition processes, and an upper layer that captures strategy switching. The proposed model accounts for the data better than several alternative models. The results show that consumers switch frequently between acquisition strategies, and they obtain information on only two or three attributes or products in a particular acquisition strategy before switching. Horizontal and contiguous eye movements play an important role in information acquisition. Furthermore, our results shed new light on the phenomenon of gaze cascades during choice. We discuss the implications for Web design, online retailing, and new directions for research on online choice.