Language is shaped by the relationships between the speaker/writer and the audience, the object of discussion, and the talk itself. In turn, language is used to reshape these relationships over the course of an interaction. Computational researchers have succeeded in operationalizing sentiment, formality, and politeness, but each of these constructs captures only some aspects of social and relational meaning. Theories of interactional stancetaking have been put forward as holistic accounts, but until now, these theories have been applied only through detailed qualitative analysis of (portions of) a few individual conversations. In this article, we propose a new computational operationalization of interpersonal stancetaking. We begin with annotations of three linked stance dimensions—affect, investment, and alignment—on 68 conversation threads from the online platform Reddit. Using these annotations, we investigate thread structure and linguistic properties of stancetaking in online conversations. We identify lexical features that characterize the extremes along each stancetaking dimension, and show that these stancetaking properties can be predicted with moderate accuracy from bag-of-words features, even with a relatively small labeled training set. These quantitative analyses are supplemented by extensive qualitative analysis, highlighting the compatibility of computational and qualitative methods in synthesizing evidence about the creation of interactional meaning.