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.).