CMatch {CMatching} | R Documentation |

This function implements multivariate and propensity score matching in clusters defined by the `Group`

variable. It returns an object of class ”`CMatch`

” which can be be summarized and used as input of the `CMatchBalance`

function to examine how much the procedure resulted in improved covariate balance.

CMatch(type, Y = NULL, Tr, X, Group = NULL, estimand = "ATT", M = 1, exact = NULL, caliper = 0.25, weights = NULL, replace = TRUE, ties = TRUE, ...)

`type` |
The type of matching desired. "within" for a pure within-cluster matching and "pwithin" for matching preferentially within. The preferential approach first searches for matchable units within the same cluster. If no match was found the algorithm searches in other clusters. |

`Y` |
A vector containing the outcome of interest. |

`Tr` |
A vector indicating the treated and control units. |

`X` |
A matrix of covariates we wish to match on. This matrix should contain all confounders or the propensity score or a combination of both. |

`Group` |
A vector describing the clustering structure (typically the cluster ID). This can be any numeric vector of the same length of |

`estimand` |
The causal estimand desired, one of "ATE", "ATT" and "ATC", which stand for Average Treatment Effect, Average Treatment effect on the Treated and on the Controls, respectively. Default is "ATT". |

`M` |
The number of matches which are sought for each unit. Default is 1 ("one-to-one matching"). |

`exact` |
An indicator for whether exact matching on the variables contained in |

`caliper` |
A maximum allowed distance for matching units. Units for which no match was found within caliper distance are discarded. Default is 0.25. The caliper is interpreted in standard deviation units of the |

`weights` |
A vector of specific observation weights. |

`replace` |
Matching can be with or without replacement depending on whether matches can be re-used or not. Default is TRUE. |

`ties` |
An indicator for dealing with multiple matches. If more than M matches are found for each unit the additional matches are a) wholly retained with equal weights if ties=TRUE; b) a random one is chosen if ties=FALSE. Default is TRUE. |

`...` |
Additional arguments to be passed to the |

This function is meant to be a natural extension of the `Match`

function to clustered data. It retains the main arguments of `Match`

but it has additional output showing matching results cluster by cluster.
It differs from wrapper `Matchby`

in package `Matching`

in the way standard errors are calculated and because the caliper is in standard deviation units of the covariates on the overall dataset (so the caliper is the same for all clusters). Moreover, observation weights are available.

`index.control` |
The index of control observations in the matched dataset. |

`index.treated` |
The index of control observations in the matched dataset. |

`index.dropped` |
The index of dropped observations due to the exact or caliper option. Note that these observations are treated if estimand is "ATT", controls if "ATC". |

`est` |
The causal estimate. This is provided only if |

`se` |
A model-based standard error for the causal estimand. This is a cluster robust estimator of the standard error for the linear model: |

`mdata` |
A list containing the matched datasets produced by |

`orig.treated.nobs.by.group` |
The original number of treated observations by group in the dataset. |

`orig.control.nobs.by.group` |
The original number of control observations by group in the dataset. |

`orig.dropped.nobs.by.group` |
The number of dropped observations by group after within cluster matching. |

`orig.nobs` |
The original number of observations in the dataset. |

`orig.wnobs` |
The original number of weighted observations in the dataset. |

`orig.treated.nobs` |
The original number of treated observations in the dataset. |

`orig.control.nobs` |
The original number of control observations in the dataset. |

`wnobs` |
the number of weighted observations in the matched dataset. |

`caliper` |
The caliper used. |

`intcaliper` |
The internal caliper used. |

`exact` |
The value of the exact argument. |

`ndrops.matches` |
The number of matches dropped either because of the caliper or exact option (or because of forcing the match within-clusters). |

`estimand` |
The estimand required. |

The function returns an object of class `CMatch`

. The `CMatchBalance`

function can be used to examine the covariate balance before and after matching (see the examples below).

Massimo Cannas <massimo.cannas@unica.it>

Sekhon, Jasjeet S. 2011. Multivariate and Propensity Score Matching Software with Automated Balance Optimization. *Journal of Statistical Software 42(7): 1-52.* http://www.jstatsoft.org/v42/i07/

Arpino, B., and Cannas, M. (2016) Propensity score matching with clustered data. An application to the estimation of the impact of caesarean section on the Apgar score. *Statistics in Medicine, 35: 2074–2091*. doi: 10.1002/sim.6880.

See also `Match`

, ` MatchBalance`

data(schools) # Kreft and De Leeuw, Introducing Multilevel Modeling, Sage (1988). # The data set is the subsample of NELS-88 data consisting of 10 handpicked schools # from the 1003 schools in the full data set. # Suppose that the effect of homeworks on math score is unconfounded conditional on X # and unobserved school features (we assume this only for illustrative purpouse). # Let us consider the following variables: X<-schools$ses # or X<-as.matrix(schools[,c("ses","white","public")]) Y<-schools$math Tr<-ifelse(schools$homework>1,1,0) Group<-schools$schid # When Group is missing or there is only one Group CMatch returns # the output of the Match function with a warning. # Let us assume that the effect of homeworks (Tr) on math score (Y) # is unconfounded conditional on X and other unobserved school features. # Several strategies to handle unobserved group characteristics # are described in Arpino & Cannas, 2016 (see References). # Multivariate Matching on covariates in X # default parameters: one-to-one matching on X with replacement with a caliper of 0.25 ### Matching within schools mw<-CMatch(type="within",Y=Y, Tr=Tr, X=X, Group=Group, caliper=0.1) # compare balance before and after matching bmw <- CMatchBalance(Tr~X,data=schools,match.out=mw) # calculate proportion of matched observations (mw$orig.treated.nobs-mw$ndrops)/mw$orig.treated.nobs # check number of drops by school mw$orig.dropped.nobs.by.group # examine output mw # complete list of results summary(mw) # basic statistics ### Match preferentially within school # i.e. first match within schools # then (try to) match remaining units between schools mpw <- CMatch(type="pwithin",Y=schools$math, Tr=Tr, X=schools$ses, Group=schools$schid, caliper=0.1) # examine covariate balance bmpw<- CMatchBalance(Tr~ses,data=schools,match.out=mpw) # equivalent to MatchBalance(...) with mpw coerced to class "Match" # proportion of matched observations (mpw$orig.treated.nobs-mpw$ndrops) / mpw$orig.treated.nobs # check drops by school mpw$orig.dropped.nobs.by.group.after.pref.within # proportion of matched observations after match-within only (mpw$orig.treated.nobs-sum(mpw$orig.dropped.nobs.by.group.after.within)) / mpw$orig.treated.nobs # see complete output mpw # or use summary method for main results summary(mpw) #### Propensity score matching # estimate the ps model mod <- glm(Tr~ses+parented+public+sex+race+urban, family=binomial(link="logit"),data=schools) eps <- fitted(mod) # eg 1: within school propensity score matching psmw <- CMatch(type="within",Y=schools$math, Tr=Tr, X=eps, Group=schools$schid, caliper=0.1) # equivalent to direct call at MatchW(Y=schools$math, Tr=Tr, X=eps, # Group=schools$schid, caliper=0.1) # eg 2: preferential within school propensity score matching psmw <- CMatch(type="pwithin",Y=schools$math, Tr=Tr, X=eps, Group=schools$schid, caliper=0.1) # Other strategies for controlling unobserved cluster covariates # via different specifications of propensity score (see Arpino and Mealli): # eg 3: propensity score matching using ps estimated from a logit model with dummies for hospitals mod <- glm(Tr ~ ses + parented + public + sex + race + urban +schid - 1,family=binomial(link="logit"),data=schools) eps <- fitted(mod) dpsm <- CMatch(type="within",Y=schools$math, Tr=Tr, X=eps, Group=NULL, caliper=0.1) # this is equivalent to run Match with X=eps # eg4: propensity score matching using ps estimated from multilevel logit model # (random intercept at the hospital level) require(lme4) mod<-glmer(Tr ~ ses + parented + public + sex + race + urban + (1 | schid), family=binomial(link="logit"), data=schools) eps <- fitted(mod) mpsm<-CMatch(type="within",Y=schools$math, Tr=Tr, X=eps, Group=NULL, caliper=0.1) # this is equivalent to run Match with X=eps

[Package *CMatching* version 2.3.0 Index]