Meaningful metrics for multi-level modelling

One of the key enablers of further growth of multi-level modeling will be the development of objective ways to allow multi-level modeling approaches to be compared to one another and to two-level modeling approaches. While significant strides have been made regarding qualitative comparisons, there is currently no adequate way to quantitatively assess to what extent a multi-level model may be preferable over another model with respect to high-level qualities such as understandability, maintainability, and control capacity. In this paper, we propose deep metrics, as an approach to quantitatively measure high-level model concerns of multi-level models that are of interest to certain stakeholders. Beyond the stated goals, we see deep metrics as furthermore supporting the comparison of modeling styles and aiding modelers in making individual design decisions. We discuss what makes a metric "depth-aware" so that it can appropriately capture multi-level model properties, and present two concrete proposals for metrics that measure high-level multi-level model qualities.