Sketch recognition has been studied for decades, but it is far from solved. Drawing styles are highly variable across people and adapting to idiosyncratic visual expressions requires data-efficient learning. Explainability also matters, so that users can see why a system got confused about something. This paper introduces a novel part-based approach for sketch recognition, based on hierarchical analogical learning, a new method to apply analogical learning to qualitative representations. Given a sketched object, our system automatically segments it into parts and constructs multi-level qualitative representations of them. Our approach performs analogical generalization at multiple levels of part descriptions and uses coarse-grained results to guide interpretation at finer levels. Experiments on the Berlin TU dataset and the Coloring Book Objects dataset show that the system can learn explainable models in a data-efficient manner.