Validating dimension hierarchy metrics for the understandability of multidimensional models for data warehouse

Structural properties including hierarchies have been recognised as important factors influencing quality of a software product. Metrics based on structural properties (structural complexity metrics) have been popularly used to assess the quality attributes like understandability, maintainability, fault-proneness etc. of a software artefact. Although few researchers have considered metrics based on dimension hierarchies to assess the quality of multidimensional models for data warehouse, there are certain aspects of dimension hierarchies like those related to multiple hierarchies, shared dimension hierarchies among various dimensions etc. which have not been considered in the earlier works. In the authors' previous work, they identified the metrics based on these aspects which may contribute towards the structural complexity and in turn the quality of multidimensional models for data warehouse. However, the work lacks theoretical and empirical validation of the proposed metrics and any metric proposal is acceptable in practice, if it is theoretically and empirically valid. In this study, the authors provide thorough validation of the metrics considered in their previous work. The metrics have been validated theoretically on the basis of Briand's framework - a property-based framework and empirically on the basis of controlled experiment using statistical techniques like correlation and linear regression. The results of these validations indicate that these metrics are either size or length measure and hence, contribute significantly towards structural complexity of multidimensional models and have considerable impact on understandability of these models.