In this paper we present a dialogue system and response model that allows a robot to act as an active listener, encouraging users to tell the robot about their travel memories. The response model makes a combined decision about when to respond and what type of response to give, in order to elicit more elaborate descriptions from the user and avoid non-sequitur responses. The model was trained on human-robot dialogue data collected in a Wizard-of-Oz setting, and evaluated in a fully autonomous version of the same dialogue system. Compared to a baseline system, users perceived the dialogue system with the trained model to be a significantly better listener. The trained model also resulted in dialogues with significantly fewer mistakes, a larger proportion of user speech and fewer interruptions.