edgenum: Computes the number of edges in the reduced bipartite graph.

In DiPs: Directional Penalties for Optimal Matching in Observational Studies

Computes the number of edges in the reduced bipartite graph.

Description

Computes the number of edges in the reduced bipartite graph after applying the caliper and number of nearest neighbors (constant). Equivalently, this is the number of candidate pairs for matching in the observational study.

This function can provide users some idea of the required computation time. Smaller caliper and constant removes more edges, hence accelarates computation, but risks infeasibility.

Usage

edgenum(z, p, caliper, constant=NULL, exact=NULL, ties.all=TRUE)

Arguments

z	A vector whose ith coordinate is 1 for a treated unit and is 0 for a control.
p	A vector of length(z)=length(p) giving the variable used to define the caliper. Typically, p is the propensity score or its rank.
caliper	If two individuals differ on p by more than caliper, we will not calculate the distance for this pair.
constant	If the number of pairs within a caliper is greater than constant, we will select the constant closest ones.
exact	If not NULL, then a vector of length(z)=length(p) giving variable that need to be exactly matched.
ties.all	If ties.all is True, include all ties while choosing nearest neighbors. In this case, some treated may have more than constant controls. Otherwise, randomly select one or several controls to make sure there are not more than constant controls for each treated.

Details

A given choice of caliper and number of nearest neighbors (constant) removes candidate pairs, so there exists a corresponding reduced bipartite graph.

Smaller caliper and constant removes more edges from the original dense graph, hence the computation is faster. However, this risks infeasibility. A smallest caliper that permits a feasible match and its corresponding smallest number of nearest neighbors can be computed by functions optcal() and optconstant().

Value

Number of edges in the reduced bipartite graph with the constraints on caliper and number of nearest neighbors (constant).

References

Yu, R., Silber, J. H., & Rosenbaum, P. R. (2020). Matching methods for observational studies derived from large administrative databases (with Discussion). Statistical Science, 35(3), 338-355.

Examples

data(nh0506Homocysteine)
attach(nh0506Homocysteine)
p<-glm(z ~ female + age + black + education + povertyr + bmi,
        family = binomial)$fitted.values
edgenum(z, p, 0.2)
edgenum(z, p, 0.2, 10, exact=female)
detach(nh0506Homocysteine)

DiPs documentation built on Aug. 7, 2022, 5:13 p.m.