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.
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)A vector whose ith coordinate is 1 for a treated unit and is 0 for a control.
A matrix with length(z) rows giving the covariates. X should be of full column rank.
A vector of with length(z)=length(p) giving the variable used to define the caliper. For instance, p might be the propensity score.
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.
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.
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.
If not NULL, then a vector of length(z)=length(p) giving variable that need to be exactly matched.
If not NULL, then a vector of length length(z) giving variable that need to be exactly matched.
A vector of with length(z)=length(fine) giving the nominal levels that are to be nearly-finely balanced.
A numeric penalty imposed for each violation of fine balance.
The penalty for a mismatch on nearexact.
If rank=TRUE, a rank-based Mahalanobis distance will be calculated. Otherwise (with default value FALSE), a traditional Mahalanobis distance will be computed.
A positive number giving the required number of matched pairs with distance not exceeding eps.
The tolerance. The smallest threshold is determined with an error of at most tol.
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.
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.
An interval that contains the best threshold. The upper bound of the interval was returned as epsilon above.
The length of interval. By definition, length.interval<=tol.
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.
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.
# NOT RUN {
# To run this example, you must load the optmatch package.
# }
# NOT RUN {
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)
# }
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