Theoretical and empirical validation of comprehensive complexity metric for multidimensional models for data warehouse

Abstract

Structural complexity metrics have been widely used to assess quality of an artefact. Researchers in past have defined complexity metrics to assess the quality of multidimensional models for data warehouse. These metrics have been defined considering various elements like facts, dimensions, dimension hierarchies etc., but have not taken into account the relationships among these elements of the models. In our previous work, a comprehensive complexity metric for multidimensional models for data warehouse has been proposed which not only considered complexity due to the elements but also structural complexity due to relationships among these elements. However, the proposal lacks theoretical and empirical validation of the metric. Hence, practical utility of the metric could not be established. This paper validates the proposed metric theoretically as well as empirically. The theoretical validation using Briand’s framework shows that the proposed metric satisfies most of the properties required for a complexity measure. Empirical validation is carried out to observe the relationship between the complexity metric and understandability-a sub-characteristic of maintainability of multidimensional models. The results show that the metric has significant positive correlation with understandability of multidimensional models. Predictive model based on Ordinal Regression proposed in this work indicates that the proposed complexity metric may act as objective indicator for understandability as accuracy of the model is 86.3 % which is quite high.