Functional form
| Option | Description |
|---|---|
Linear | Assumes straight‐line relationships between predictors and outcomes. |
Quadratic | Incorporates second‐degree terms to capture simple non‑linearity. |
Non-linear | Allows arbitrary shape; may use kernels or neural networks. |
Additivity | Effects sum without interaction terms. |
Assumption-free | No explicit functional form assumed. |
Rule-based | Uses decision or logic rules. |
Log-linear | Models on a logarithmic scale. |
Definition
The mathematical flexibility of the model’s structure, ranging from strictly linear or quadratic relationships to fully non‑parametric, additive, or rule‑based formulations.
Explanation
Choosing an appropriate functional form balances bias and interpretability: simpler linear forms offer transparency but may miss curvature, whereas flexible non‑parametric or rule‑based models capture complex patterns at the cost of more demanding data and potential over‑fitting.
Tools/rationale for helping assessment
- List your mechanistic or theoretical expectations: do you expect a straight‐line, simple curvature, additive effects, or entirely unknown shape?
- Match explicitly your belief to the best option available
Example
You know from field experiments that tree‐growth response to sunlight saturates (levels off). You therefore expect a non-linear form over a strictly linear one, based on that a priori assumption.