Process compliance measurement is getting increasing attention in companies due to stricter legal requirements and market pressure for operational excellence. In order to judge on compliance of the business processing, the degree of behavioural deviation of a case, i.e., an observed execution sequence, is quantified with respect to a process model (referred to as fitness, or recall). Recently, different compliance measures have been proposed. Still, nearly all of them are grounded on state-based techniques and the trace equivalence criterion, in particular. As a consequence, these approaches have to deal with the state explosion problem. In this paper, we argue that a behavioural abstraction may be leveraged to measure the compliance of a process log - a collection of cases. To this end, we utilise causal behavioural profiles that capture the behavioural characteristics of process models and cases, and can be computed efficiently. We propose different compliance measures based on these profiles, discuss the impact of noise in process logs on our measures, and show how diagnostic information on non-compliance is derived. As a validation, we report on findings of applying our approach in a case study with an international service provider.