optmatch (version 0.9-3)

fullmatch: Optimal full matching

Description

Given two groups, such as a treatment and a control group, and a method of creating a treatment-by-control discrepancy matrix indicating desirability and permissibility of potential matches (or optionally an already created such discrepancy matrix), create optimal full matches of members of the groups. Optionally, incorporate restrictions on matched sets' ratios of treatment to control units.

Usage

fullmatch(x, min.controls = 0, max.controls = Inf,
    omit.fraction = NULL, mean.controls = NULL,
    tol = 0.001, data = NULL, ...)
  full(x, min.controls = 0, max.controls = Inf,
    omit.fraction = NULL, mean.controls = NULL,
    tol = 0.001, data = NULL, ...)

Arguments

x

Any valid input to match_on. fullmatch will use x and any optional arguments to generate a distance before performing the matching.

If x is a numeric vector, there must also be passed a vector

min.controls

The minimum ratio of controls to treatments that is to be permitted within a matched set: should be non-negative and finite. If min.controls is not a whole number, the reciprocal of a whole number, or zero, then it is rounded d

max.controls

The maximum ratio of controls to treatments that is to be permitted within a matched set: should be positive and numeric. If max.controls is not a whole number, the reciprocal of a whole number, or Inf, then it is rounded

omit.fraction

Optionally, specify what fraction of controls or treated subjects are to be rejected. If omit.fraction is a positive fraction less than one, then fullmatch leaves up to that fraction of the control reservoir unmatched.

mean.controls

Optionally, specify the average number of controls per treatment to be matched. Must be no less than than min.controls and no greater than the either max.controls or the ratio of total number of controls versus total numb

tol

Because of internal rounding, fullmatch may solve a slightly different matching problem than the one specified, in which the match generated by fullmatch may not coincide with an optimal solution of the specified problem.

data

Optional data.frame or vector to use to get order of the final matching factor. If a data.frame, the rownames are used. If a vector, the names are first tried, otherwise the contents

...

Additional arguments, including within, which may be passed to match_on.

Value

• A optmatch object (factor) indicating matched groups.

Details

If passing an already created discrepancy matrix, finite entries indicate permissible matches, with smaller discrepancies indicating more desirable matches. The matrix must have row and column names.

If it is desirable to create the discrepancies matrix beforehand (for example, if planning on running several different matching schemes), consider using match_on to generate the distances. This generic function has several useful methods for handling propensity score models, computing Mahalanobis distances (and other arbitrary distances), and using user supplied functions. These distances can also be combined with those generated by exactMatch and caliper to create very nuanced matching specifications.

The value of tol can have a substantial effect on computation time; with smaller values, computation takes longer. Not every tolerance can be met, and how small a tolerance is too small varies with the machine and with the details of the problem. If fullmatch can't guarantee that the tolerance is as small as the given value of argument tol, then matching proceeds but a warning is issued.

By default, fullmatch will attempt, if the given constraints are infeasible, to find a feasible problem using the same constraints. This will almost surely involve using a more restrictive omit.fraction or mean.controls. (This will never automatically omit treatment units.) Note that this does not guarantee that the returned match has the least possible number of omitted subjects, it only gives a match that is feasible within the given constraints. It may often be possible to loosen the omit.fraction or mean.controls constraint and still find a feasible match. The auto recovery is controlled by options("fullmatch_try_recovery").

If the program detects a large problem as been requested that may exceed the computational power of the user's computer, a warning is issued. If you wish to disable this warning, set options("optmatch_warn_on_big_problem" = FALSE).

References

Hansen, B.B. and Klopfer, S.O. (2006), Optimal full matching and related designs via network flows, Journal of Computational and Graphical Statistics, 15, 609--627.

Hansen, B.B. (2004), Full Matching in an Observational Study of Coaching for the SAT, Journal of the American Statistical Association, 99, 609--618.

Rosenbaum, P. (1991), A Characterization of Optimal Designs for Observational Studies, Journal of the Royal Statistical Society, Series B, 53, 597--610.

Examples

data(nuclearplants)
### Full matching on a Mahalanobis distance.
( fm1 <- fullmatch(pr ~ t1 + t2, data = nuclearplants) )
summary(fm1)

### Full matching with restrictions.
( fm2 <- fullmatch(pr ~ t1 + t2, min.controls = .5, max.controls = 4, data = nuclearplants) )
summary(fm2)

### Full matching to half of available controls.
( fm3 <- fullmatch(pr ~ t1 + t2, omit.fraction = .5, data = nuclearplants) )
summary(fm3)

### Full matching attempts recovery when the initial restrictions are infeasible.
### Limiting max.controls = 1 allows use of only 10 of 22 controls.
( fm4 <- fullmatch(pr ~ t1 + t2, max.controls = 1, data=nuclearplants) )
summary(fm4)
### To recover restrictions
optmatch_restrictions(fm4)

### Full matching within a propensity score caliper.
ppty <- glm(pr ~ . - (pr + cost), family = binomial(), data = nuclearplants)
### Note that units without counterparts within the caliper are automatically dropped.
### For more complicated models, create a distance matrix and pass it to fullmatch.
mhd <- match_on(pr ~ t1 + t2, data = nuclearplants) + caliper(match_on(ppty))
( fm5 <- fullmatch(mhd, data = nuclearplants) )
summary(fm5)

### Propensity balance assessment. Requires RItools package.
if (require(RItools)) summary(fm5,ppty)

### The order of the names in the match factor is the same
### as the nuclearplants data.frame since we used the data argument
### when calling fullmatch. The order would be unspecified otherwise.
cbind(nuclearplants, matches = fm5)