The integration of computational modelling in science classrooms provides a unique opportunity to promote key 21st century skills including computational thinking (CT) and collaboration. The open-ended, problem-solving nature of the task requires groups to grapple with the combination of two domains (science and computing) as they collaboratively construct computational models. While this approach has produced significant learning gains for students in both science and CT in K-12 settings, the collaborative learning processes students use, including learner regulation, are not well understood. In this paper, we present a systematic analysis framework that combines natural language processing (NLP) of collaborative dialogue, log file analyses of students' model-building actions, and final model scores. This analysis is used to better understand students' regulation of collaborative problem solving (CPS) processes over a series of computational modelling tasks of varying complexity. The results suggest that the computational modelling challenges afford opportunities for students to a) explore resource-intensive processes, such as trial and error, to more systematic processes, such as debugging model errors by leveraging data tools, and b) learn from each other using socially shared regulation (SSR) and productive collaboration. The use of such SSR processes correlated positively with their model-building scores. Our paper aims to advance our understanding of collaborative, computational modelling in K-12 science to better inform classroom applications.