Quality metrics emphasizing dimension hierarchy sharing in multidimensional models for data warehouse: a theoretical and empirical evaluation

The quality of data warehouse (DW) depends largely on the multidimensional (MD) model quality. Few researchers have proposed metrics to evaluate the MD model quality based on facts, dimensions, hierarchy relationships, foreign keys, multiple hierarchies etc. However, some dimension hierarchy aspects like sharing of hierarchy levels within a dimension, sharing of hierarchy levels among various dimensions, relationship between dimension levels etc. have not been given due consideration. The aforementioned aspects may contribute to structural complexity of MD models, which in turn can affect its quality. Our previous study defined a set of quality metrics emphasizing dimension hierarchy sharing in MD models for DW. In this paper, we attempt to thoroughly validate a subset (six) of these metrics, theoretically as well as empirically. A careful study of the mathematical properties of defined metrics is done using Briand framework, which reveals that out of six metrics, two of them correspond to coupling measure, one metric is a cohesion measure and rest three are size/complexity measures. Further, an empirical validation consisting of Spearman’s Rho correlation analysis and linear regression analysis is conducted on 20 MD schemas and 28 subjects to determine the relationship between the metrics and understandability of MD models. The experimental study shows that four of our metrics are good indicators of understandability of MD models and can help in predicting the structural complexity of MD schemas for DW.