Common support (positivity)

Option	Description
Required	Strict overlap needed for valid comparison.
Recommended	Strongly advised.
Desirable	Improves precision.
Relaxes assumption	Methods can tolerate some lack of overlap (e.g., regularization).

Definition

The method requires overlap in the covariate distributions of the treated and control units, which is also known as the positivity assumption.

Explanation

Lack of overlap (regions with only treated or only control units) forces models to extrapolate beyond data, risking bias. Some methods strictly require common support; others can tolerate limited gaps.

Tools/rationale for helping assessment

1. Tabulate key covariates (e.g. canopy cover, slope) by treatment group / compute propensity scores; check if ranges overlap.
2. If there’s overlap across the full range, mark Required; if minor gaps, Recommended; if some extrapolation but acceptable, Desirable; if severe gaps, Relaxes assumption to specifically study this assumption’s influence or try limiting the study scope to recover overlapping covariate range.

Example

After matching on slope and elevation, treated and control plots overlap only in slope ∈ [5,25°], so I restrict analysis to that band and mark Required.