We consider linear dynamical systems, particularly coupled linear oscillators, where the parameters represent meaningful values in a domain theory, and thus learning what affects them contributes to explanation. Rather than allow perturbations of latent states, we assume that temporal variation beyond noise is explained by parameter drift, and variation across coupled systems is a function of moderating variables. This change in model structure reduces opportunities for efficient inference, and we propose sampling procedures to learn and fit the models. We test our approach on a real dataset of self-recalled emotional experience measurements of heterosexual couples engaged in a conversation about a potentially emotional topic, with body mass index (BMI) being considered as a moderator. We evaluate several models on their ability to predict future conversation dynamics (the last 20% of the data for each test couple), with shared parameters being learned using held out data. We validate the hypothesis that BMI affects the conversation dynamic in the experimentally chosen topic.