Support

As explained in Causal Inference for Data Science

The support of a probability distribution is the range of values that can occur with positive probability.

The support of a probability distribution is the range of values that can occur with positive probability. For causal comparisons, compare the supports of propensity-score distributions for treated and untreated patients: overlap identifies patients with comparable treatment possibilities. section 5.3.3

Use support overlap to determine which causal effects are identifiable:

• No overlap means there are no matches, so an average treatment effect cannot be calculated. section 5.3.3
• Partial overlap restricts the average treatment effect to patients inside the common-support region. section 5.3.3
• Full overlap is the ideal setting for calculating average treatment effects. section 5.3.3

Figure 5.11 Partial overlap in a distribution’s supports. We can calculate the ATE only for patients within the common support region.

The partial-overlap diagram makes the common-support restriction visible: causal effects are estimated only where treated and untreated propensity-score distributions overlap. section 5.3.3

How Causal Inference for Data Science covers it

How deep it goes

Defines support through positive probability and applies overlap to determine where average treatment effects can be estimated.

Examples

Uses distributions with no overlap, full overlap, partial overlap, and overlap limited to treated patients.

What it assumes

Assumes treatment indicators, patient characteristics, propensity scores, and average treatment effects.

What you can do after

Evaluate causal-effect feasibility and restrict estimates to patients inside the common-support region.

How it connects

Connects propensity scores, positivity, matching, average treatment effect, and average treatment effect on the treated.

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Also explained in

• 

  liveBookmanning.com
  Fabulous Adventures in Data Structures and AlgorithmsThe support of a probability distribution is the set of values that can occur with positive probability.

Compare how 2 books explain support →

Related concepts

• uniform distributionused by · A uniform distribution assigns equal probability to each outcome in a discrete support or constant probability density across a continuous interval.
• continuous distributionpart of · A continuous distribution is a probability distribution for a variable whose possible values form a continuous range rather than a discrete set.

This explainer was generated by Manning's knowledge graph from the text of Causal Inference for Data Science. The section links point to the parts of the book it draws on.