Entrainment is the tendency of speakers engaged in conversation to align different aspects of their communicative behavior. In this study we explore in more detail a measure of prosodic entrainment defined in previous work, which uses a discrete parametrization of intonational contours defined by the ToBI conventions for prosodic description. We divide this measure into two asymmetric variants: backward mimicry (in which a speaker uses a contour used previously by the interlocutor) and forward influence (in which a speaker's contour appears later in the speech of the interlocutor). This distinction sheds new light on significant correlations with a number of social variables related to the level of engagement of speakers in a corpus of task-oriented dialogues in Standard American English.