Orthogonality: Developing a structural/perspectival approach for improving theoretical models

Abstract

In order to create more useful theories we must attempt to choose better concepts (variables). Although we may strive to identify “independent” variables, that effort is problematic because we live in a world where everything is connected; also, attempting to obtain even nominally independent variables may require sophisticated analytical methodologies available only to well‐funded researchers and practitioners. To help resolve those problems, and so provide an improved path for developing more useful theories, we explore the notion of orthogonality as a tool for rethinking concepts in a theory, from a structural perspective, in a way that clarifies research opportunities (from a data perspective) and clarifies situational/theoretical perspectives (from a relevance perspective).

Understanding and improving the usefulness of conceptual systems: An Integrative Propositional Analysis‐based perspective on levels of structure and emergence

“…For example, it would be awkward to say something like 'having more apples causes us to have more fruit' because apples are a kind of fruit, thus suggesting a tautological aspect to the statement. Similarly, because there is an ontic overlap between apples and fruit, they should not be contained in the same theory due to the potential confusion of having a theory with non-orthogonal elements (Wallis, 2020d).…”

“…For example, a program model (also known as a program theory) may be nested (in some sense) within the larger program or policy. Within a theory, complex concepts may be said to have a number of sub-concepts (Wallis, 2020d) that may be thought of as a nested relationship. Social network analysis (Hawe, Webster, & Shiell, 2004;Neal & Neal, 2013) may be understood as looking at nested and/or networked relationships at multiple levels.…”

“…We may see concepts with causal connections between them as being ontologically similar, perhaps on some scale of abstraction (Wallis, 2014a) and/or some scale of orthogonality (Wallis, 2020d), whereas, in contrast, the properties/things/concepts/components that are emergent seem to be on ontologically different level than the concepts from which they emerged.…”

“…That theory represents some situation that is shared by different stakeholder groups. Each stakeholder group might look at that theory from a different perspective and, from each unique perspective, see their priorities as the parts of the whole that are perspectivally closer (Wallis, 2020d). Indeed, some concepts may appear so close and large that other concepts may appear to be 'hidden' behind them.…”

“…However, those also have limits. But by understanding our limits, we may learn to exceed them by gaining additional, perhaps orthogonal, insights (Pies, 2016;Wallis, 2020d). In this section, we will identify a few directions for future research and practice.…”