Data warehouse quality can be determined during the initial phases of data warehouse development by quantifying the structural complexity of multidimensional models using metrics. The structural complexity of a multidimensional model is guided by its elements, types, and relationships among those elements. So far, most of the researchers have dealt with metrics based on various elements (facts, dimensions, dimensional hierarchies, and hierarchy levels) existing in these models. However, not much consideration is given to different types of dimensions based on hierarchy types and different relationships among those elements. Therefore, this work proposes a comprehensive complexity metric for measuring multidimensional model complexity by taking into account various elements, their types and the relationships among the elements at various levels of granularity in these models. The theoretical validation of the proposed metric using the property-based framework given by Briand et al . characterises it as a complexity measure. Furthermore, the empirical study, employing statistical techniques (correlation and multinomial regression), on 26 multidimensional models and 20 subjects proved that the authors’ proposed metric is strongly correlated with multidimensional model understandability. Hence, this metric can be considered as a good predictor for data warehouse multidimensional model understandability.

中文翻译：

---

数据仓库多维模型可理解性的综合复杂性度量

可以在数据仓库开发的初始阶段，通过使用指标量化多维模型的结构复杂性来确定数据仓库的质量。多维模型的结构复杂性由其元素，类型以及这些元素之间的关系决定。到目前为止，大多数研究人员已经根据这些模型中存在的各种要素（事实，维度，维度层次结构和层次结构级别）来处理度量标准。但是，基于层次结构类型以及这些元素之间的不同关系，并未对不同类型的维度给予太多考虑。因此，这项工作提出了一种综合的复杂性指标，用于通过考虑各种因素来测量多维模型的复杂性，这些模型中各个粒度级别的元素的类型和元素之间的关系。使用Briand给出的基于属性的框架对拟议指标进行理论验证等 。将其表征为复杂性度量。此外，使用统计技术（相关性和多项式回归）对26个多维模型和20个主题进行的实证研究证明，作者提出的度量标准与多维模型的可理解性密切相关。因此，该度量标准可以被视为数据仓库多维模型可理解性的良好预测指标。