Multivariate Datasets for Inference of Order: Some Considerations and Explorations

Ideal formulation of a multi-indicator system (MIS) would be to define, design, and acquire the entire construct with complete consensus among all concerned. However, such would be an extreme rarity in actuality. Experts have differing views. Factors may not express monotonically, as when either extreme is unfavorable. The entirety cannot be assessed and must be sampled. Empirical experience to validate expectations is inadequate. Consequently, exploratory examination of any available datasets collected for collateral purposes can augment insights relative to suitable surrogates for ideal indicators, with particular attention to ordering relations for subsets of quantifiers and ensembles of entities (objects, cases, instances, etc.). Multivariate datasets are comprised of several quantifiers (variates or variables) as columns recorded for multiple entities as rows. The data matrix thus realized is not necessarily directly useful nor fully informative for analytically inferring order among entities. In this chapter, some approaches are discussed which may be helpful in extracting insights on ordering properties that are embodied in multivariate datasets and applicable in configuring suites of indicators. These procedures may be particularly helpful in finding suitable surrogates and applying partial order theory when expediency is essential. We consider orientation, crispness of data, and culling of candidates according to importance in respect of some desirable criteria.