24:null 25:["$","title",null,{"children":"Stat Notes | Propensity Score R Package MatchIt Introduction | Zhihao Yao | Observable"}] 2a:T9ae,--- ## Planning > - Selecting the type of effect to be estimated > - Selecting a target population > - Selecting covariates to balance > **Check Initial Imbalance** > The code below can be used to check the initial imbalance of the data that matching is attempting to eliminate: ```r m.out0 <- matchit(treat ~ age + educ + race + married + nodegree + re74 + re75, data = lalonde, method = NULL, distance = "glm") ``` > Parameters: > - `formula`: treatment to the covariates used in estimating the propensity score and for which balance is to be assessed > - `method`: method of matching to be performed (will show more details later). `'NULL'` let us assess balance prior to matching > - `distance`: method for estimating the propensity score (`glm` refers to logistic regression) ```r summary(m.out0) ## ## Call: ## matchit(formula = treat ~ age + educ + race + married + nodegree + ## re74 + re75, data = lalonde, method = NULL, distance = "glm") ## ## Summary of Balance for All Data: ## Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean ## distance 0.5774 0.1822 1.7941 0.9211 0.3774 ## age 25.8162 28.0303 -0.3094 0.4400 0.0813 ## educ 10.3459 10.2354 0.0550 0.4959 0.0347 ## raceblack 0.8432 0.2028 1.7615 . 0.6404 ## racehispan 0.0595 0.1422 -0.3498 . 0.0827 ## racewhite 0.0973 0.6550 -1.8819 . 0.5577 ## married 0.1892 0.5128 -0.8263 . 0.3236 ## nodegree 0.7081 0.5967 0.2450 . 0.1114 ## re74 2095.5737 5619.2365 -0.7211 0.5181 0.2248 ## re75 1532.0553 2466.4844 -0.2903 0.9563 0.1342 ## eCDF Max ## distance 0.6444 ## age 0.1577 ## educ 0.1114 ## raceblack 0.6404 ## racehispan 0.0827 ## racewhite 0.5577 ## married 0.3236 ## nodegree 0.1114 ## re74 0.4470 ## re75 0.2876 ## ## ## Sample Sizes: ## Control Treated ## All 429 185 ## Matched 429 185 ## Unmatched 0 0 ## Discarded 0 0 ``` Values of standardized mean differences and eCDF statistics close to zero and values of variance ratios close to one indicate good balance.2b:T6b33,{ const nearest = md`
> ### Nearest Neighbor Matching (method = "nearest") > method = "nearest" performs greedy nearest neighbor matching. A distance is computed between each treated unit and each control unit, and, one by one, each treated unit is assigned a control unit as a match. The matching is "greedy" in the sense that there is no action taken to optimize an overall criterion; each match is selected without considering the other matches that may occur subsequently.


m.out1 <- matchit(treat ~ age + educ + race + married + 
                   nodegree + re74 + re75, data = lalonde,
                 method = "nearest", distance = "glm")
m.out1

## A matchit object
##  - method: 1:1 nearest neighbor matching without replacement
##  - distance: Propensity score
##              - estimated with logistic regression
##  - number of obs.: 614 (original), 370 (matched)
##  - target estimand: ATT
##  - covariates: age, educ, race, married, nodegree, re74, re75

summary(m.out1)

## 
## Call:
## matchit(formula = treat ~ age + educ + race + married + nodegree + 
##     re74 + re75, data = lalonde, method = "nearest", distance = "glm")
## 
## Summary of Balance for All Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## distance          0.5774        0.1822          1.7941     0.9211    0.3774
## age              25.8162       28.0303         -0.3094     0.4400    0.0813
## educ             10.3459       10.2354          0.0550     0.4959    0.0347
## raceblack         0.8432        0.2028          1.7615          .    0.6404
## racehispan        0.0595        0.1422         -0.3498          .    0.0827
## racewhite         0.0973        0.6550         -1.8819          .    0.5577
## married           0.1892        0.5128         -0.8263          .    0.3236
## nodegree          0.7081        0.5967          0.2450          .    0.1114
## re74           2095.5737     5619.2365         -0.7211     0.5181    0.2248
## re75           1532.0553     2466.4844         -0.2903     0.9563    0.1342
##            eCDF Max
## distance     0.6444
## age          0.1577
## educ         0.1114
## raceblack    0.6404
## racehispan   0.0827
## racewhite    0.5577
## married      0.3236
## nodegree     0.1114
## re74         0.4470
## re75         0.2876
## 
## 
## Summary of Balance for Matched Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## distance          0.5774        0.3629          0.9739     0.7566    0.1321
## age              25.8162       25.3027          0.0718     0.4568    0.0847
## educ             10.3459       10.6054         -0.1290     0.5721    0.0239
## raceblack         0.8432        0.4703          1.0259          .    0.3730
## racehispan        0.0595        0.2162         -0.6629          .    0.1568
## racewhite         0.0973        0.3135         -0.7296          .    0.2162
## married           0.1892        0.2108         -0.0552          .    0.0216
## nodegree          0.7081        0.6378          0.1546          .    0.0703
## re74           2095.5737     2342.1076         -0.0505     1.3289    0.0469
## re75           1532.0553     1614.7451         -0.0257     1.4956    0.0452
##            eCDF Max Std. Pair Dist.
## distance     0.4216          0.9740
## age          0.2541          1.3938
## educ         0.0757          1.2474
## raceblack    0.3730          1.0259
## racehispan   0.1568          1.0743
## racewhite    0.2162          0.8390
## married      0.0216          0.8281
## nodegree     0.0703          1.0106
## re74         0.2757          0.7965
## re75         0.2054          0.7381
## 
## Sample Sizes:
##           Control Treated
## All           429     185
## Matched       185     185
## Unmatched     244       0
## Discarded       0       0

` const optimal = md`
> ### Optimal Pair Matching (method = "optimal") > method = "optimal" performs optimal pair matching. The matching is optimal in the sense that that sum of the absolute pairwise distances in the matched sample is as small as possible. The method functionally relies on optmatch::pairmatch().


# 1:1 optimal PS matching with exact matching on race
m.out1 <- matchit(treat ~ age + educ + race + married + 
                   nodegree + re74 + re75, data = lalonde,
                 method = "optimal", exact = ~race)
m.out1

## A matchit object
##  - method: 1:1 optimal pair matching
##  - distance: Propensity score
##              - estimated with logistic regression
##  - number of obs.: 614 (original), 232 (matched)
##  - target estimand: ATT
##  - covariates: age, educ, race, married, nodegree, re74, re75

summary(m.out1)
## 
## Call:
## matchit(formula = treat ~ age + educ + race + married + nodegree + 
##     re74 + re75, data = lalonde, method = "optimal", exact = ~race)
## 
## Summary of Balance for All Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## distance          0.5774        0.1822          1.7941     0.9211    0.3774
## age              25.8162       28.0303         -0.3094     0.4400    0.0813
## educ             10.3459       10.2354          0.0550     0.4959    0.0347
## raceblack         0.8432        0.2028          1.7615          .    0.6404
## racehispan        0.0595        0.1422         -0.3498          .    0.0827
## racewhite         0.0973        0.6550         -1.8819          .    0.5577
## married           0.1892        0.5128         -0.8263          .    0.3236
## nodegree          0.7081        0.5967          0.2450          .    0.1114
## re74           2095.5737     5619.2365         -0.7211     0.5181    0.2248
## re75           1532.0553     2466.4844         -0.2903     0.9563    0.1342
##            eCDF Max
## distance     0.6444
## age          0.1577
## educ         0.1114
## raceblack    0.6404
## racehispan   0.0827
## racewhite    0.5577
## married      0.3236
## nodegree     0.1114
## re74         0.4470
## re75         0.2876
## 
## 
## Summary of Balance for Matched Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## distance          0.4972        0.4901          0.0325     1.0030    0.0057
## age              25.9914       26.1293         -0.0193     0.4688    0.0776
## educ             10.1552       10.2241         -0.0343     0.6206    0.0227
## raceblack         0.7500        0.7500          0.0000          .    0.0000
## racehispan        0.0948        0.0948          0.0000          .    0.0000
## racewhite         0.1552        0.1552          0.0000          .    0.0000
## married           0.2500        0.2759         -0.0660          .    0.0259
## nodegree          0.6724        0.6552          0.0379          .    0.0172
## re74           2869.0758     2951.5004         -0.0169     1.4249    0.0496
## re75           1800.6676     1785.1522          0.0048     1.6652    0.0372
##            eCDF Max Std. Pair Dist.
## distance     0.0776          0.0438
## age          0.2241          1.3036
## educ         0.0517          1.3206
## raceblack    0.0000          0.0000
## racehispan   0.0000          0.0000
## racewhite    0.0000          0.0000
## married      0.0259          0.5943
## nodegree     0.0172          1.0239
## re74         0.2586          0.8065
## re75         0.1207          0.8471
## 
## Sample Sizes:
##           Control Treated
## All           429     185
## Matched       116     116
## Unmatched     313      69
## Discarded       0       0

` const full = md`
> ### Optimal Full Matching (method = "full") > method = "full" performs optimal full matching, which is a form of subclassification wherein all units, both treatment and control (i.e., the "full" sample), are assigned to a subclass and receive at least one match. The matching is optimal in the sense that that sum of the absolute distances between the treated and control units in each subclass is as small as possible. The method relies on and is a wrapper for optmatch::fullmatch().


m.out1 <- matchit(treat ~ age + educ + race + nodegree +
                    married + re74 + re75, data = lalonde,
                  method = "full")
m.out1

## A matchit object
##  - method: Optimal full matching
##  - distance: Propensity score
##              - estimated with logistic regression
##  - number of obs.: 614 (original), 614 (matched)
##  - target estimand: ATT
##  - covariates: age, educ, race, nodegree, married, re74, re75

summary(m.out1)
## 
## Call:
## matchit(formula = treat ~ age + educ + race + nodegree + married + 
##     re74 + re75, data = lalonde, method = "full")
## 
## Summary of Balance for All Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## distance          0.5774        0.1822          1.7941     0.9211    0.3774
## age              25.8162       28.0303         -0.3094     0.4400    0.0813
## educ             10.3459       10.2354          0.0550     0.4959    0.0347
## raceblack         0.8432        0.2028          1.7615          .    0.6404
## racehispan        0.0595        0.1422         -0.3498          .    0.0827
## racewhite         0.0973        0.6550         -1.8819          .    0.5577
## nodegree          0.7081        0.5967          0.2450          .    0.1114
## married           0.1892        0.5128         -0.8263          .    0.3236
## re74           2095.5737     5619.2365         -0.7211     0.5181    0.2248
## re75           1532.0553     2466.4844         -0.2903     0.9563    0.1342
##            eCDF Max
## distance     0.6444
## age          0.1577
## educ         0.1114
## raceblack    0.6404
## racehispan   0.0827
## racewhite    0.5577
## nodegree     0.1114
## married      0.3236
## re74         0.4470
## re75         0.2876
## 
## 
## Summary of Balance for Matched Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## distance          0.5774        0.5761          0.0061     0.9917    0.0041
## age              25.8162       24.7372          0.1508     0.4859    0.0827
## educ             10.3459       10.2846          0.0305     0.5696    0.0224
## raceblack         0.8432        0.8347          0.0236          .    0.0086
## racehispan        0.0595        0.0611         -0.0070          .    0.0017
## racewhite         0.0973        0.1042         -0.0234          .    0.0069
## nodegree          0.7081        0.7068          0.0030          .    0.0014
## married           0.1892        0.1371          0.1329          .    0.0520
## re74           2095.5737     2144.8386         -0.0101     1.3198    0.0399
## re75           1532.0553     1598.8210         -0.0207     1.8985    0.0701
##            eCDF Max Std. Pair Dist.
## distance     0.0486          0.0192
## age          0.3212          1.2869
## educ         0.0617          1.2522
## raceblack    0.0086          0.0324
## racehispan   0.0017          0.5555
## racewhite    0.0069          0.4168
## nodegree     0.0014          1.0135
## married      0.0520          0.4806
## re74         0.2447          0.8626
## re75         0.2481          0.8179
## 
## Sample Sizes:
##               Control Treated
## All            429.       185
## Matched (ESS)   52.96     185
## Matched        429.       185
## Unmatched        0.         0
## Discarded        0.         0

` const genetic = md`
> ### Genetic Matching (method = "genetic") > method = "genetic" performs genetic matching. Genetic matching is a form of nearest neighbor matching where distances are computed as the generalized Mahalanobis distance, which is a generalization of the Mahalanobis distance with a scaling factor for each covariate that represents the importance of that covariate to the distance. A genetic algorithm is used to select the scaling factors. The scaling factors are chosen as those which maximize a criterion related to covariate balance, which can be chosen, but which by default is the smallest p-value in covariate balance tests among the covariates.


# 1:1 genetic matching with PS as a covariate
m.out1 <- matchit(treat ~ age + educ + race + nodegree +
                    married + re74 + re75, data = lalonde,
                  method = "genetic",
                  pop.size = 10) #use much larger pop.size
m.out1

## A matchit object
##  - method: 1:1 genetic matching without replacement
##  - distance: Propensity score
##              - estimated with logistic regression
##  - number of obs.: 614 (original), 370 (matched)
##  - target estimand: ATT
##  - covariates: age, educ, race, nodegree, married, re74, re75

summary(m.out1)
## 
## Call:
## matchit(formula = treat ~ age + educ + race + nodegree + married + 
##     re74 + re75, data = lalonde, method = "genetic", pop.size = 10)
## 
## Summary of Balance for All Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## distance          0.5774        0.1822          1.7941     0.9211    0.3774
## age              25.8162       28.0303         -0.3094     0.4400    0.0813
## educ             10.3459       10.2354          0.0550     0.4959    0.0347
## raceblack         0.8432        0.2028          1.7615          .    0.6404
## racehispan        0.0595        0.1422         -0.3498          .    0.0827
## racewhite         0.0973        0.6550         -1.8819          .    0.5577
## nodegree          0.7081        0.5967          0.2450          .    0.1114
## married           0.1892        0.5128         -0.8263          .    0.3236
## re74           2095.5737     5619.2365         -0.7211     0.5181    0.2248
## re75           1532.0553     2466.4844         -0.2903     0.9563    0.1342
##            eCDF Max
## distance     0.6444
## age          0.1577
## educ         0.1114
## raceblack    0.6404
## racehispan   0.0827
## racewhite    0.5577
## nodegree     0.1114
## married      0.3236
## re74         0.4470
## re75         0.2876
## 
## 
## Summary of Balance for Matched Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## distance          0.5774        0.3540          1.0143     0.7047    0.1626
## age              25.8162       25.6000          0.0302     0.5525    0.0597
## educ             10.3459       10.2054          0.0699     0.4569    0.0381
## raceblack         0.8432        0.4703          1.0259          .    0.3730
## racehispan        0.0595        0.2703         -0.8914          .    0.2108
## racewhite         0.0973        0.2595         -0.5472          .    0.1622
## nodegree          0.7081        0.6378          0.1546          .    0.0703
## married           0.1892        0.2811         -0.2346          .    0.0919
## re74           2095.5737     3236.7618         -0.2335     0.8456    0.0930
## re75           1532.0553     1807.9451         -0.0857     1.1168    0.0477
##            eCDF Max Std. Pair Dist.
## distance     0.4216          1.0368
## age          0.1784          0.7404
## educ         0.0919          0.8925
## raceblack    0.3730          1.0259
## racehispan   0.2108          1.1657
## racewhite    0.1622          0.5472
## nodegree     0.0703          0.1546
## married      0.0919          0.2346
## re74         0.3297          0.4172
## re75         0.1838          0.3585
## 
## Sample Sizes:
##           Control Treated
## All           429     185
## Matched       185     185
## Unmatched     244       0
## Discarded       0       0

` const exact = md`
> ### Exact Matching (method = "exact") > method = "exact" performs exact matching. With exact matching, a complete cross of the covariates is used to form subclasses defined by each combination of the covariate levels. Any subclass that doesn't contain both treated and control units is discarded, leaving only subclasses containing treatment and control units that are exactly equal on the included covariates. The benefits of exact matching are that confounding due to the covariates included is completely eliminated, regardless of the functional form of the treatment or outcome models. The problem is that typically many units will be discarded, sometimes dramatically reducing precision and changing the target population of inference. To use exact matching in combination with another matching method (i.e., to exact match on some covariates and some other form of matching on others), use the exact argument with that method.


# 1:1 genetic matching with PS as a covariate
m.out1 <- matchit(treat ~ age + race + married + educ, data = lalonde,
                  method = "exact")
m.out1

## A matchit object
##  - method: Exact matching
##  - number of obs.: 614 (original), 113 (matched)
##  - target estimand: ATT
##  - covariates: age, race, married, educ

summary(m.out1)
## 
## Call:
## matchit(formula = treat ~ age + race + married + educ, data = lalonde, 
##     method = "exact")
## 
## Summary of Balance for All Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## age              25.8162       28.0303         -0.3094     0.4400    0.0813
## raceblack         0.8432        0.2028          1.7615          .    0.6404
## racehispan        0.0595        0.1422         -0.3498          .    0.0827
## racewhite         0.0973        0.6550         -1.8819          .    0.5577
## married           0.1892        0.5128         -0.8263          .    0.3236
## educ             10.3459       10.2354          0.0550     0.4959    0.0347
##            eCDF Max
## age          0.1577
## raceblack    0.6404
## racehispan   0.0827
## racewhite    0.5577
## married      0.3236
## educ         0.1114
## 
## 
## Summary of Balance for Matched Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## age              19.9815       19.9815               0     0.9936         0
## raceblack         0.7778        0.7778               0          .         0
## racehispan        0.0370        0.0370               0          .         0
## racewhite         0.1852        0.1852               0          .         0
## married           0.0370        0.0370               0          .         0
## educ             10.3333       10.3333               0     0.9936         0
##            eCDF Max Std. Pair Dist.
## age               0               0
## raceblack         0               0
## racehispan        0               0
## racewhite         0               0
## married           0               0
## educ              0               0
## 
## Sample Sizes:
##               Control Treated
## All            429.       185
## Matched (ESS)   40.36      54
## Matched         59.        54
## Unmatched      370.       131
## Discarded        0.         0

` const cem =md`
> ### Coarsened Exact Matching (method = "cem") > method = "cem" performs coarsened exact matching. With coarsened exact matching, covariates are coarsened into bins, and a complete cross of the coarsened covariates is used to form subclasses defined by each combination of the coarsened covariate levels. Any subclass that doesn't contain both treated and control units is discarded, leaving only subclasses containing treatment and control units that are exactly equal on the coarsened covariates. The coarsening process can be controlled by an algorithm or by manually specifying cutpoints and groupings. The benefits of coarsened exact matching are that the tradeoff between exact matching and approximate balancing can be managed to prevent discarding too many units, which can otherwise occur with exact matching.


# Coarsened exact matching on age, race, married, and educ with educ
# coarsened into 5 bins and race coarsened into 2 categories,
# grouping "white" and "hispan" together
m.out1 <- matchit(treat ~ age + race + married + educ, data = lalonde,
                  method = "cem", cutpoints = list(educ = 5),
                  grouping = list(race = list(c("white", "hispan"),
                                              c("black"))))

m.out1

## A matchit object
##  - method: Coarsened exact matching
##  - number of obs.: 614 (original), 393 (matched)
##  - target estimand: ATT
##  - covariates: age, race, married, educ

summary(m.out1)
## 
## Call:
## matchit(formula = treat ~ age + race + married + educ, data = lalonde, 
##     method = "cem", cutpoints = list(educ = 5), grouping = list(race = list(c("white", 
##         "hispan"), c("black"))))
## 
## Summary of Balance for All Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## age              25.8162       28.0303         -0.3094     0.4400    0.0813
## raceblack         0.8432        0.2028          1.7615          .    0.6404
## racehispan        0.0595        0.1422         -0.3498          .    0.0827
## racewhite         0.0973        0.6550         -1.8819          .    0.5577
## married           0.1892        0.5128         -0.8263          .    0.3236
## educ             10.3459       10.2354          0.0550     0.4959    0.0347
##            eCDF Max
## age          0.1577
## raceblack    0.6404
## racehispan   0.0827
## racewhite    0.5577
## married      0.3236
## educ         0.1114
## 
## 
## Summary of Balance for Matched Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## age              24.1007       23.7091          0.0547     0.8882    0.0140
## raceblack         0.8188        0.8188          0.0000          .    0.0000
## racehispan        0.0671        0.0360          0.1317          .    0.0312
## racewhite         0.1141        0.1452         -0.1051          .    0.0312
## married           0.1745        0.1745         -0.0000          .    0.0000
## educ             10.5369       10.8649         -0.1631     0.7974    0.0177
##            eCDF Max Std. Pair Dist.
## age          0.0897          0.1555
## raceblack    0.0000          0.0000
## racehispan   0.0312          0.4829
## racewhite    0.0312          0.3853
## married      0.0000          0.0000
## educ         0.1865          0.3962
## 
## Sample Sizes:
##               Control Treated
## All            429.       185
## Matched (ESS)   52.84     149
## Matched        244.       149
## Unmatched      185.        36
## Discarded        0.         0

` const subclass = md`
> ### Subclassification (method = "subclass") > method = "subclass" performs subclassification on the distance measure (i.e., propensity score). Treatment and control units are placed into subclasses based on quantiles of the propensity score in the treated group, in the control group, or overall, depending on the desired estimand. Weights are computed based on the proportion of treated units in each subclass. Subclassification implemented here does not rely on any other package.


# PS subclassification for the ATT with 7 subclasses
s.out1 <- matchit(treat ~ age + educ + race + nodegree +
                    married + re74 + re75, data = lalonde,
                  method = "subclass", subclass = 7)

m.out1

## A matchit object
##  - method: Coarsened exact matching
##  - number of obs.: 614 (original), 393 (matched)
##  - target estimand: ATT
##  - covariates: age, race, married, educ

summary(m.out1)
## 
## Call:
## matchit(formula = treat ~ age + race + married + educ, data = lalonde, 
##     method = "cem", cutpoints = list(educ = 5), grouping = list(race = list(c("white", 
##         "hispan"), c("black"))))
## 
## Summary of Balance for All Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## age              25.8162       28.0303         -0.3094     0.4400    0.0813
## raceblack         0.8432        0.2028          1.7615          .    0.6404
## racehispan        0.0595        0.1422         -0.3498          .    0.0827
## racewhite         0.0973        0.6550         -1.8819          .    0.5577
## married           0.1892        0.5128         -0.8263          .    0.3236
## educ             10.3459       10.2354          0.0550     0.4959    0.0347
##            eCDF Max
## age          0.1577
## raceblack    0.6404
## racehispan   0.0827
## racewhite    0.5577
## married      0.3236
## educ         0.1114
## 
## 
## Summary of Balance for Matched Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
## age              24.1007       23.7091          0.0547     0.8882    0.0140
## raceblack         0.8188        0.8188          0.0000          .    0.0000
## racehispan        0.0671        0.0360          0.1317          .    0.0312
## racewhite         0.1141        0.1452         -0.1051          .    0.0312
## married           0.1745        0.1745         -0.0000          .    0.0000
## educ             10.5369       10.8649         -0.1631     0.7974    0.0177
##            eCDF Max Std. Pair Dist.
## age          0.0897          0.1555
## raceblack    0.0000          0.0000
## racehispan   0.0312          0.4829
## racewhite    0.0312          0.3853
## married      0.0000          0.0000
## educ         0.1865          0.3962
## 
## Sample Sizes:
##               Control Treated
## All            429.       185
## Matched (ESS)   52.84     149
## Matched        244.       149
## Unmatched      185.        36
## Discarded        0.         0

` if(methods.name === 'nearest') { return nearest }else if(methods.name === 'optimal') { return optimal }else if(methods.name === 'full') { return full }else if(methods.name === 'genetic') { return genetic }else if(methods.name === 'exact') { return exact }else if(methods.name === 'cem') { return cem }else if(methods.name === 'subclass') { return subclass } }2c:Tb07,--- ## Assessing the Quality of Matches > `MatchIt` offers a few tools for the assessment of covariate balance after matching. These include graphical and statistical methods. More detail on the interpretation of the included plots and statistics can be found in vignette("assessing-balance"). > > To assess the quality of the resulting matches numerically, we can use the `summary()` function on m.out1 as before. Here we set `un = FALSE` to suppress display of the balance before matching for brevity and because we already saw it. (Leaving it as `TRUE`, its default, would display balance both before and after matching.)


# Checking balance after NN matching
summary(m.out1, un = FALSE)

## 
## Call:
## matchit(formula = treat ~ age + educ + race + married + nodegree + 
##     re74 + re75, data = lalonde, method = "nearest", distance = "glm")
## 
## Summary of Balance for Matched Data:
##            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean eCDF Max Std. Pair Dist.
## distance          0.5774        0.3629          0.9739     0.7566    0.1321   0.4216          0.9740
## age              25.8162       25.3027          0.0718     0.4568    0.0847   0.2541          1.3938
## educ             10.3459       10.6054         -0.1290     0.5721    0.0239   0.0757          1.2474
## raceblack         0.8432        0.4703          1.0259          .    0.3730   0.3730          1.0259
## racehispan        0.0595        0.2162         -0.6629          .    0.1568   0.1568          1.0743
## racewhite         0.0973        0.3135         -0.7296          .    0.2162   0.2162          0.8390
## married           0.1892        0.2108         -0.0552          .    0.0216   0.0216          0.8281
## nodegree          0.7081        0.6378          0.1546          .    0.0703   0.0703          1.0106
## re74           2095.5737     2342.1076         -0.0505     1.3289    0.0469   0.2757          0.7965
## re75           1532.0553     1614.7451         -0.0257     1.4956    0.0452   0.2054          0.7381
## 
## Sample Sizes:
##           Control Treated
## All           429     185
## Matched       185     185
## Unmatched     244       0
## Discarded       0       0

> The matching procedure left 244 control units unmatched. Ideally, unmatched units would be those far from the treated units and would require greater extrapolation were they to have been retained. We can visualize the distribution of propensity scores of those who were matched using `plot()` with `type = "jitter"`:


plot(m.out1, type = "jitter", interactive = FALSE)

2d:T1518,--- ## Estimating the Treatment Effect > After 1:1 matching without replacement (i.e., the first matching specification above), we can run a simple regression of the outcome on the treatment in the matched sample (i.e., including the matching weights). With continuous outcomes, it is often a good idea to also include the covariates used in the matching in the effect estimation, as doing so can provide additional robustness to slight imbalances remaining after the matching and can improve precision. We’ll extract the matched dataset from the `matchit` object using `match.data()`. This dataset only contains the matched units and adds columns for `distance`, `weights`, and `subclass`.


m.data1 <- match.data(m.out1)
head(m.data1)

##      treat age educ   race married nodegree re74 re75       re78  distance weights subclass
## NSW1     1  37   11  black       1        1    0    0  9930.0460 0.6387699       1        1
## NSW2     1  22    9 hispan       0        1    0    0  3595.8940 0.2246342       1       98
## NSW3     1  30   12  black       0        0    0    0 24909.4500 0.6782439       1      109
## NSW4     1  27   11  black       0        1    0    0  7506.1460 0.7763241       1      120
## NSW5     1  33    8  black       0        1    0    0   289.7899 0.7016387       1      131
## NSW6     1  22    9  black       0        1    0    0  4056.4940 0.6990699       1      142

>The treatment effect in this dataset can be estimated using the standard regression functions in R, like `lm()` or `glm()`, being sure to include the matching weights (stored in the weights variable of the `match.data()` output) in the estimation. Cluster-robust standard error is recommended for most analyses, with pair membership as the clustering variable; the `lmtest` and `sandwich` packages together make this straightforward.


library("lmtest") #coeftest
library("sandwich") #vcovCL

fit1 <- lm(re78 ~ treat + age + educ + race + married + nodegree + 
             re74 + re75, data = m.data1, weights = weights)

coeftest(fit1, vcov. = vcovCL, cluster = ~subclass)

## 
## t test of coefficients:
## 
##                Estimate  Std. Error t value Pr(>|t|)   
## (Intercept) -2.5816e+03  3.3209e+03 -0.7774 0.437439   
## treat        1.3449e+03  7.3084e+02  1.8403 0.066552 . 
## age          7.8035e+00  4.4148e+01  0.1768 0.859797   
## educ         6.0220e+02  2.1007e+02  2.8667 0.004391 **
## racehispan   1.5335e+03  1.0248e+03  1.4964 0.135417   
## racewhite    4.6943e+02  8.9854e+02  0.5224 0.601687   
## married     -1.5825e+02  9.3354e+02 -0.1695 0.865482   
## nodegree     9.2328e+02  1.1496e+03  0.8032 0.422412   
## re74         2.6362e-02  1.6646e-01  0.1584 0.874257   
## re75         2.2068e-01  1.6771e-01  1.3158 0.189069   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

> Given the results of these two estimates, The result from the second analysis (using full matching) looks better because better balance was achieved on all the variables, making the effect estimate less sensitive to the form of the outcome model. > > Since different matching methods require different treatments, the table below shows the instructions for each method. It is important to ensure the right methods are used with the matching specification used in order for the estimated effects and standard errors to be valid. More details can be found vignette("estimating-effects").

Section	Matching Method
After Pair Matching Without Replacement	Nearest neighbor matching without replacement
-	Optimal matching
-	Genetic matching without replacement
-	Coarsened exact matching with `k2k = TRUE`
After Pair Matching With Replacement	Nearest neighbor matching with replacement
-	Genetic matching with replacement
After Full Matching	Full matching
	Cardinality and template matching
After Stratum Matching	Propensity score subclassification
-	Exact matching
-	Coarsened exact matching with `k2k = FALSE` (the default)

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Stat Notes | Propensity Score R Package `MatchIt` Introduction

","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":72,"value":"---\n> According to the `MatchIt` website, a matching analysis involves four primary steps: \n**

Planning
Matching
Assessing the quality of matches
Estimating the treatment effect and its uncertainty

**","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":80,"value":"> First, we load `MatchIt` and bring in the `lalonde` dataset.\n\n ```r\n library(\"MatchIt\")\n data(\"lalonde\")\n \n head(lalonde)\n ```\n
\n\n| | treat | age | educ | race | married | nodegree | re74 | re75 | re78 |\n|:----:|:-----:|:---:|:----:|:------:|:-------:|:--------:|:----:|:----:|:--------:|\n| NSW1 | 1 | 37 | 11 | black | 1 | 1 | 0 | 0 | 9930.046 |\n| NSW2 | 1 | 22 | 9 | hispan | 0 | 1 | 0 | 0 | 3595.894 |\n| NSW3 | 1 | 30 | 12 | black | 0 | 0 | 0 | 0 | 24909.45 |\n| NSW4 | 1 | 27 | 11 | black | 0 | 1 | 0 | 0 | 7506.146 |\n| NSW5 | 1 | 33 | 8 | black | 0 | 1 | 0 | 0 | 289.7899 |\n\n
","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":97,"value":"> This dataset has 614 observations (185 treated, 429 control). There are 9 variables measured for each individual.\n\n> - \"treat\" is the treatment assignment (1=treated, 0=control).\n\n> - \"age\" is age in years.\n\n> - \"educ\" is education in number of years of schooling.\n\n> - \"race\" is the race/ethnicity, (Black, Hispanic, or White). \n\n> - \"married\" is an indicator for married (1=married, 0=not married).\n\n> - \"nodegree\" is an indicator for whether the individual has a high school degree (1=no degree, 0=degree).\n\n> - \"re74\" is income in 1974, in U.S. dollars.\n\n> - \"re75\" is income in 1975, in U.S. dollars.\n\n> - \"re78\" is income in 1978, in U.S. dollars.\n\n> \"treat\" is the treatment variable, \"re78\" is the outcome, and the others are pre-treatment covariates.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":108,"value":"$2a","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":121,"value":"---\n## Matching\n\n> There are several different classes and methods of matching by using parameter `method`:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":125,"value":"viewof methods = Inputs.select(data, {label: \"\", format: x => x.fullName, value: data.find(t => t.name === \"nearest\")})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":140,"value":"$2b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":183,"value":"$2c","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":194,"value":"FileAttachment(\"image.png\").image()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":199,"value":"

\nplot(m.out1, type = \"qq\", interactive = FALSE,\n     which.xs = c(\"age\", \"married\", \"re75\"))\n

","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":201,"value":"image1 = FileAttachment(\"image@1.png\").image()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":208,"value":"$2d","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":259,"value":"---\n\n## Reference\n\n> * `MatchIt` website\n> * Propensity score matching with R: conventional methods and new features\n> * R Tutorial 8: Propensity Score Matching","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":14,"value":"## Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":129,"value":"data = [\n {name: \"nearest\", fullName: \"Nearest Neighbor Matching\"},\n {name: \"optimal\", fullName: \"Optimal Pair Matching\"},\n {name: \"full\", fullName: \"Optimal Full Matching\"},\n {name: \"genetic\", fullName: \"Genetic Matching\"},\n {name: \"exact\", fullName: \"Exact Matching\"},\n {name: \"cem\", fullName: \"Coarsened Exact Matching\"},\n {name: \"subclass\", fullName: \"Subclassification\"},\n ]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":88,"value":"highlightRender = (language, src) => {\n let pre = document.createElement('pre');\n pre.innerHTML = `\n ${src}\n `;\n highlight.highlightBlock(pre);\n return pre;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":86,"value":"hljsCSS = html`\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":83,"value":"highlight = require('https://cdn.jsdelivr.net/gh/highlightjs/cdn-release@9.18.5/build/highlight.min.js')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":229,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"}],"files":"$W2e","stdlib":"1","titling":"auto"}} 29:"$28:body"