14.3 Matching in Concept

What will our matching criteria be?

We want to minimize the distance between the treatment observations and the control observations.

Are we selecting matches or constructing a matched weighted sample?

• Distance matching
• Propensity matching
• Kernel matching

If we’re selecting matches, how many?

• One-to-one matching
• \(k\) nearest neighbors

If we’re constructing a matched weighted sample, how will weights decay with distance?

• Epanechnikov kernel

\[K(x) = \frac{3}{4}(1-x^{2}), \quad -1 \leq x \leq 1\]

• Inverse weighting

What is the worst acceptable match?

• Caliper or bandwidth
• Fewer, but better matches \(\rightarrow\) less bias, less precision
• More, but worse matches \(\rightarrow\) more bias, more precision