Scalability over long traces, as well as comprehensibility and expressivity of results, are major challenges for dynamic analysis approaches to specification mining. In this work we present a novel use of object hierarchies over traces of inter-object method calls, as an abstraction/refinement mechanism that enables user-guided, top-down or bottom-up mining of layered scenario-based specifications, broken down by hierarchies embedded in the system under investigation. We do this using data mining methods that provide statistically significant sound and complete results modulo user-defined thresholds, in the context of Damm and Harel's live sequence charts (LSC); a visual, modal, scenario-based, inter-object language. Thus, scalability, comprehensibility, and expressivity are all addressed. Our technical contribution includes a formal definition of hierarchical inter-object traces, and algorithms for 'zooming-out' and 'zooming-in', used to move between abstraction levels on the mined specifications. An evaluation of our approach based on several case studies shows promising results.