threshold: Smallest threshold for thick description.

In thickmatch: Threshold Matching for Thick Description for Optimal Matching in Observational Studies

Description

Finds the smallest threshold on such that a treated-control matching with that at least select_num matched pairs having distance not exceeding the threshold exists.

Usage

threshold(z,X,p,caliper,dat,ncontrol=1,exact=NULL,nearexact=NULL,fine=NULL,
penalty=1000,nearexpenalty=100,rank=FALSE,select_num=0,tol=0.1)

Arguments

z	A vector whose ith coordinate is 1 for a treated unit and is 0 for a control.
X	A matrix with length(z) rows giving the covariates. X should be of full column rank.
p	A vector of with length(z)=length(p) giving the variable used to define the caliper. For instance, p might be the propensity score.
caliper	If the treated-minus-control difference (in the scale of sd(p)) in p is < -caliper or > caliper, then penalty is added to the distance.
dat	A data frame with length(z) rows. If the match is feasible, the matched portion of dat is returned with additional columns that define the match.
ncontrol	A positive integer giving the number of controls to be matched to each treated subject. If ncontrol is too large, the match will be infeasible.
exact	If not NULL, then a vector of length(z)=length(p) giving variable that need to be exactly matched.
nearexact	If not NULL, then a vector of length length(z) giving variable that need to be exactly matched.
fine	A vector of with length(z)=length(fine) giving the nominal levels that are to be nearly-finely balanced.
penalty	A numeric penalty imposed for each violation of fine balance.
nearexpenalty	The penalty for a mismatch on nearexact.
rank	If rank=TRUE, a rank-based Mahalanobis distance will be calculated. Otherwise (with default value FALSE), a traditional Mahalanobis distance will be computed.
select_num	A positive number giving the required number of matched pairs with distance not exceeding eps.
tol	The tolerance. The smallest threshold is determined with an error of at most tol.

Details

The method uses binary search to find the best threshold. It applies threshold algorithm with function feasible; details see Rosenbaum (2017).

Often, we need a small and feasible threshold, and we prefer to estimate the threshold very precisely. Making tol smaller makes the number of closest pairs close to select_num.

You MUST install and load the optmatch package to use threshold.

Value

If the match is infeasible, a warning is issued. Otherwise, a list of results is returned.

A match may be infeasible if the caliper on p is too small, or ncontrol is too large, or if exact matching for exact is impossible.

epsilon	The smallest threshold, with an error of at most tol. This threshold is a little too large, at most tol too large, but because its error is on the high side, a match with this threshold ensures at least select_num matched pairs with distance not exceeding epsilon.
interval	An interval that contains the best threshold. The upper bound of the interval was returned as epsilon above.
interval.length	The length of interval. By definition, length.interval<=tol.

References

Rosenbaum, P.R. (2017) Imposing Minimax and Quantile Constraints on Optimal Matching in Observational Studies, Journal of Computational and Graphical Statistics, 26:1, 66-78, DOI: 10.1080/10618600.2016.1152971.

Examples

# To run this example, you must load the optmatch package.

data("nysr")
attach(nysr)
X<-cbind(family.income,family.structure,highest.education.parent.in.household,
female,race.black,race.hispanic,age.teenager,school.dropout)
detach(nysr)
threshold(z=nysr$intense,X=X,p=nysr$plogit,caliper=0.2,dat=nysr,select_num=10,tol=0.00001)

thickmatch documentation built on April 14, 2020, 5:30 p.m.