Toolkit: When to Reach for Theory (and how to find a new dimension)
Toolkit: When to Reach for Theory ← you are here
Not every research problem needs a new theory. Some need better measurement, clearer framing, or more careful modelling. But sometimes, none of those suffice, because the question we’re asking lacks the right dimension to express it.
This post is about knowing when you’ve reached that point, and what to do next.
Do You Actually Need a New Theory? A Quick Triage
Reach for a new theoretical construct when:
Structured residuals remain after reasonable models are fit, something large and patterned is unexplained.
People disagree about constructs, not just coefficients, there’s contention over what to include, not just how much it matters.
You see paradoxes or incompatible cases that a new dimension might resolve or unify.
Interventions can’t be ranked—you can’t say what works best without adding a new axis of variation.
If two or more of these hold, it’s time to theorise. Otherwise, measure better or engineer a fix.
Finding a Missing Dimension: A Short Protocol
Theory doesn’t come from nowhere. It comes from structured failures, carefully interrogated. Here’s a method:
Parameterise what you think matters, and do it explicitly: list the constructs and dimensions your current model uses. Include units, signs, and expected invariances (e.g., scale-free? additive? threshold effects?).
Assemble exemplars and edge cases: both where the model works and where it fails. Look for differences it cannot explain.
Visualise residuals, don’t just minimise them, study their shape. Where is the model systematically wrong?
Hypothesise a new dimension that would dissolve the failure. Name it. Define its scope, direction, and expected effect.
Test for portability by analogy and evolution. Can this dimension be reused in nearby domains or extended from a narrower case?
Re-parameterise minimally, add the dimension without bloating the model. Hold other structures constant.
Stress-test the new dimension out-of-sample, out-of-domain, and across subgroups. Keep what survives.
That’s the high-level version. But if you want your new construct to last, across papers, domains, or policy cycles, you’ll need a stronger scaffold.
Name It Properly (Or It Won’t Travel)
Every proposed dimension deserves a short passport:
Definition (1–2 sentences).
Scope and boundaries. When won’t this matter?
Units and admissible range. Direction of expected effect?
Operational measures. Primary and fallback proxy, with expected biases.
Functional form. Should the effect diminish, reverse, saturate?
Policy levers. What interventions could plausibly change it?
Analogies. Other fields where the idea already appears in disguise?
Retirement criteria. What evidence would make you drop or reframe it?
This isn’t red tape, it’s what makes a dimension reusable. Done well, it becomes a node in a Theory Graph, not just a tweak in a regression.
A Minimal Test Suite (to Avoid Fooling Yourself)
You’ve named your new parameter. Now show it earns its keep:
Ablation test: Does adding it to your base model improve explanation or decision ranking (not just AIC)?
Structure test: Does it reduce the residual pattern you observed? Show before/after plots.
Orthogonality test: Is it distinct from interactions or collinear combinations of what you already had?
Transportability test: Hold out one domain where it should work, and one where it shouldn’t.
Invariance test: Is its effect stable across unit choices and data normalisations?
Predictive heterogeneity: Register subgroups where you expect the effect to flip, amplify, or vanish. Then test.
A dimension that doesn’t pass at least three of these is probably not worth embedding into a theory. At best it’s a feature. At worst, a tautology.
Example: Adding Synchrony to Access
Suppose a city speeds up buses. Commute times drop, but job access barely improves for night-shift workers. Residuals cluster by time-of-day and occupation. You suspect that travel speed is no longer the bottleneck.
You hypothesise a new dimension: temporal synchrony: the overlap between a traveller’s available time, a destination’s opening hours, and service span.
You define it:
[latex]s_{ij} = \frac{|W_i \cap A_j \cap S_{ij}|}{|W_i|}[\latex]
where Wi is the person’s available window, Aj is destination hours, Sij is service availability.
You add it to the cumulative opportunity model:
[latex]A_i = \sum_j [t_{ij} \le T] \cdot s_{ij} \cdot O_j[\latex]
Predictions:
Night workers gain more from extended span than from faster speeds.
Weekend retail access depends more on synchrony than reliability.
Synchrony has low correlation with speed and headway, but explains large residuals.
You test it. It improves explanatory power, changes the policy ranking, and replicates in unrelated domains (clinics, freight). It’s not collinear, not tautological, and can be influenced by schedule planning.
Synchrony becomes a stable parameter. You add it to your theory, not as a gimmick, but as a dimension.
What Not to Do
Some things look like theory, but aren’t:
Tautologies: Defining the construct using the outcome (“people go where they go because they want to go” (also known as Utility Theory)).
Overfit proxies: Using high-cardinality interactions or black-box scores in place of a transparent dimension.
Rebrandings: Introducing a “new” parameter that’s just a relabelled linear combination of known inputs.
Passive descriptors: Proposing something you can’t act on or interpret.
Fit-first logic: Keeping a dimension just because it improves R², without changing understanding or decisions.
Making It Durable: Theory Graph Hooks
If your new dimension is real, it belongs in a reusable structure:
A Construct node (e.g., synchrony)
One or more Measures (e.g., overlap metric)
A Model variant that uses it
Claims derived from the model
Evidence that supports or refutes those claims
Context to scope its validity
Optional: retirement criteria and analogies to other domains
That’s a Theory Graph fragment. You can add it to your research programme and inspect it later. You don’t just “have a hunch” anymore. You have a structured bet.
In Short
Good theories don’t just fit the data. They name the right dimensions.
When your model fails predictably, and your interventions can’t be ranked, it may be time to theorise. But don’t just reach for big words. Reach for structured variation.
Parameterise explicitly. Test ruthlessly. Generalise carefully. And keep a record of what changed.
That’s how new dimensions earn their place.
That’s how theory moves forward.
