## Phase I# Note that the dependent variable is not included in the formula. The TriMatch# functions will replace the dependent variable depending on which pair is# being modeled.tutoring.formu<-~Gender+Ethnicity+Military+ESL+EdMother+EdFather+Age+Employment+Income+Transfer+GPA# trips will estimate the propensity scores for each pairing of groupstutoring.tpsa<-trips(tutoring, tutoring$treat, tutoring.formu)plot(tutoring.tpsa, sample=c(200))
# trimatch finds matched triplets.tutoring.matched<-trimatch(tutoring.tpsa)# Partial exact matchingtutoring.matched2<-trimatch(tutoring.tpsa, exact=tutoring$Level)# Plotting the results of trimatch is a subset of the triangle plot with only# points that were matched. There is also an additional parameter, rows, that# will overlay matched triplets.plot(tutoring.matched, rows=1, line.alpha=1, draw.segments=TRUE)
## Examine the unmatched studentsunmatched<-unmatched(tutoring.matched)summary(unmatched)
## 819 (71.7%) of 1142 total data points were not matched.
## Unmatched by treatment:
## Control Treat1 Treat2
## 795 (86.6%) 17 (12.7%) 7 (7.78%)
##
## Friedman rank sum test
##
## data: Covariate and Treatment and ID
## Friedman chi-squared = 0.4, df = 2, p-value = 0.8187
# Create a grid of figures.bplots<-balance.plot(tutoring.matched, tutoring[,all.vars(tutoring.formu)], legend.position='none', x.axis.labels=c('C','T1','T1'), x.axis.angle=0)bplots[['Military']]# We can plot one at at time.
summary(bplots)# Create a data frame with the statistical results
## Covariate Friedman Friedman.p Friedman.sig rmANOVA rmANOVA.p
## 1 Gender 2.16666667 0.33846543 NA NA
## 2 Ethnicity 0.05678233 0.97200807 NA NA
## 3 Military 0.40000000 0.81873075 NA NA
## 4 ESL 4.78571429 0.09136826 . NA NA
## 5 EdMother 1.55974843 0.45846368 0.76509335 0.4662146
## 6 EdFather 0.02794411 0.98612510 0.06102055 0.9408158
## 7 Age 4.14982578 0.12556736 1.70723419 0.1831598
## 8 Employment 2.04048583 0.36050736 1.27194067 0.2818249
## 9 Income 0.59582543 0.74236614 0.39251642 0.6757086
## 10 Transfer 3.08717949 0.21361291 0.55080160 0.5770812
## 11 GPA 1.37542662 0.50272433 0.49589373 0.6095348
## rmANOVA.sig
## 1 <NA>
## 2 <NA>
## 3 <NA>
## 4 <NA>
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## Phase II# The summary function performs a number of statistical tests including Friedman# rank sum test, repeated measures ANOVA, and if one or both of those tests have# p values less than 0.5 (the default, but configurable), then a pairwise Wilcox# test and three paired t-tests will also be performed.(sout<-summary(tutoring.matched, tutoring$Grade))
## $PercentMatched
## Control Treat1 Treat2
## 0.1339869 0.8731343 0.9222222
##
## $friedman.test
##
## Friedman rank sum test
##
## data: Outcome and Treatment and ID
## Friedman chi-squared = 17.404, df = 2, p-value = 0.0001663
##
##
## $rmanova
## $rmanova$ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 Treatment 2 294 16.66293 1.396209e-07 * 0.06818487
##
## $rmanova$`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 Treatment 0.8668353 2.946934e-05 *
##
## $rmanova$`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 Treatment 0.8824842 6.035469e-07 * 0.8923995 5.333417e-07 *
##
##
## $pairwise.wilcox.test
##
## Pairwise comparisons using Wilcoxon signed rank test with continuity correction
##
## data: out$Outcome and out$Treatment
##
## Treat1.out Treat2.out
## Treat2.out 0.0046 -
## Control.out 0.0165 1.9e-06
##
## P value adjustment method: bonferroni
##
## $t.tests
## Treatments t df p.value sig mean.diff ci.min
## 1 Treat1.out-Treat2.out -3.095689 147 2.351743e-03 ** -0.3378378 -0.5535076
## 2 Treat1.out-Control.out 2.939953 147 3.813865e-03 ** 0.4459459 0.1461816
## 3 Treat2.out-Control.out 5.443253 147 2.140672e-07 *** 0.7837838 0.4992224
## ci.max
## 1 -0.1221681
## 2 0.7457103
## 3 1.0683452
##
## attr(,"class")
## [1] "trimatch.summary" "list"
# The Loess plot is imperfect with three sets of propensity scores. There is a# model parameter to specify which model to use. Once we a model is selected# we have propensity scores for two of the three groups. We impute a propensity# score on that model's scale for the third group as the midpoint between# the other two propensity scores that unit was matched to.loess3.plot(tutoring.matched, tutoring$Grade, se=FALSE, method='loess')
# Turn on 95% confidence interval (see also the level parameter)loess3.plot(tutoring.matched, tutoring$Grade, se=TRUE, method='loess')
# We can also pass other parameters to the loess function.loess3.plot(tutoring.matched, tutoring$Grade, se=TRUE, method='loess', span=1)
# This is a busy plot, but since all the lines are practically vertical, the# distance between each pair of propensity scores is minimal.loess3.plot(tutoring.matched, tutoring$Grade, se=FALSE, method='loess', plot.connections=TRUE)
# The merge function will add the outcome to the matched triplet data frame.# This is useful for other approaches to analyzing the matched triplets.tmatch.out<-merge(tutoring.matched, tutoring$Grade)head(tmatch.out)
