### Code Source: https://github.com/jbryer/TriMatch/blob/master/demo/tutoring.R
library(TriMatch)
## Loading required package: ggplot2
## Loading required package: scales
## Loading required package: reshape2
## Loading required package: ez
library(grid)
data(tutoring)
head(tutoring)
## treat Course Grade Gender Ethnicity Military ESL EdMother EdFather
## 3 Control ENG*201 4 FEMALE Other FALSE FALSE 3 6
## 4 Control ENG*201 4 FEMALE White FALSE FALSE 5 6
## 11 Control ENG*201 4 FEMALE White FALSE FALSE 1 1
## 12 Control ENG*201 4 FEMALE White FALSE FALSE 3 5
## 14 Control ENG*201 4 FEMALE White FALSE FALSE 2 2
## 16 Treat1 HSC*310 3 FEMALE White FALSE FALSE 3 3
## Age Employment Income Transfer GPA GradeCode Level ID
## 3 48 3 9 24 3.00 A Lower 377
## 4 49 3 9 25 2.72 A Lower 882
## 11 53 1 5 39 2.71 A Lower 292
## 12 52 3 5 48 4.00 A Lower 215
## 14 47 1 5 23 3.50 A Lower 252
## 16 53 3 9 63 3.55 B Upper 265
dim(tutoring)
## [1] 1142 17
table(tutoring$treat)
##
## Control Treat1 Treat2
## 918 134 90
summary(tutoring)
## treat Course Grade Gender Ethnicity
## Control:918 Length:1142 Min. :0.000 FEMALE:627 Black:211
## Treat1 :134 Class :character 1st Qu.:2.000 MALE :515 Other:193
## Treat2 : 90 Mode :character Median :4.000 White:738
## Mean :2.891
## 3rd Qu.:4.000
## Max. :4.000
## Military ESL EdMother EdFather
## Mode :logical Mode :logical Min. :1.000 Min. :1.000
## FALSE:783 FALSE:1049 1st Qu.:3.000 1st Qu.:3.000
## TRUE :359 TRUE :93 Median :3.000 Median :3.000
## Mean :3.785 Mean :3.684
## 3rd Qu.:5.000 3rd Qu.:5.000
## Max. :8.000 Max. :9.000
## Age Employment Income Transfer
## Min. :20.00 Min. :1.000 Min. :1.000 Min. : 3.00
## 1st Qu.:30.00 1st Qu.:3.000 1st Qu.:3.000 1st Qu.: 36.66
## Median :37.00 Median :3.000 Median :5.000 Median : 48.31
## Mean :36.92 Mean :2.667 Mean :5.059 Mean : 52.12
## 3rd Qu.:43.00 3rd Qu.:3.000 3rd Qu.:7.000 3rd Qu.: 65.00
## Max. :65.00 Max. :3.000 Max. :9.000 Max. :126.00
## GPA GradeCode Level ID
## Min. :0.000 Length:1142 Lower:988 Min. : 1.0
## 1st Qu.:2.890 Class :character Upper:154 1st Qu.: 286.2
## Median :3.215 Mode :character Median : 571.5
## Mean :3.166 Mean : 571.5
## 3rd Qu.:3.518 3rd Qu.: 856.8
## Max. :4.000 Max. :1142.0
names(tutoring)
## [1] "treat" "Course" "Grade" "Gender" "Ethnicity"
## [6] "Military" "ESL" "EdMother" "EdFather" "Age"
## [11] "Employment" "Income" "Transfer" "GPA" "GradeCode"
## [16] "Level" "ID"
table(tutoring$treat, useNA='ifany')
##
## Control Treat1 Treat2
## 918 134 90
table(tutoring$treat, tutoring$Course, useNA='ifany')
##
## ENG*101 ENG*201 HSC*310
## Control 349 518 51
## Treat1 22 36 76
## Treat2 31 32 27
formu <- ~ Gender + Ethnicity + Military + ESL + EdMother + EdFather + Age +
Employment + Income + Transfer + GPA
# tutoring$Treat1 <- !tutoring$treat == 'Control'
# lr1 <- glm(Treat1 ~ Gender + Ethnicity + Military + ESL + EdMother + EdFather + Age +
# Employment + Income + Transfer + GPA, data=tutoring, family=binomial)
# summary(lr1)
# lr2 <- stepAIC(lr1)
# summary(lr2)
# formu <- ~ Gender + Employment + Transfer
# multibalance.plot(tutoring.tpsa, cols=all.vars(formu))
# Estimate the propensity scores for the three models
tutoring.tpsa <- trips(tutoring, tutoring$treat, formu)
# Some useful information is saved as attributes.
names(attributes(tutoring.tpsa))
## [1] "names" "row.names" "class" "data" "nstrata"
## [6] "model1" "model2" "model3" "breaks1" "breaks2"
## [11] "breaks3" "groups"
# Prints a combined summary of the three logistic regression models
summary(tutoring.tpsa)
## Estimate Std. Error z value Pr(>|z|) m1 Estimate
## (Intercept) -1.23648 0.83153 -1.4870 1.37e-01 -2.65640
## GenderMALE -1.07738 0.24282 -4.4370 9.12e-06 *** -0.64908
## EthnicityOther 0.13627 0.33504 0.4067 6.84e-01 -0.52058
## EthnicityWhite 0.10327 0.26757 0.3860 7.00e-01 -0.32678
## MilitaryTRUE -0.02173 0.27115 -0.0801 9.36e-01 -0.31186
## ESLTRUE -0.22231 0.41734 -0.5327 5.94e-01 0.34207
## EdMother -0.02977 0.07361 -0.4045 6.86e-01 -0.09215
## EdFather -0.02219 0.06504 -0.3411 7.33e-01 0.07603
## Age 0.00137 0.01120 0.1222 9.03e-01 0.01901
## Employment -0.32900 0.13623 -2.4150 1.57e-02 * -0.29799
## Income 0.02081 0.04470 0.4655 6.42e-01 -0.08417
## Transfer 0.01699 0.00429 3.9635 7.38e-05 *** 0.00501
## GPA -0.11726 0.19484 -0.6018 5.47e-01 0.37795
## Std. Error z value Pr(>|z|) m2 Estimate Std. Error z value
## (Intercept) 1.00466 -2.644 0.00819 ** -1.51677 1.39589 -1.087
## GenderMALE 0.27930 -2.324 0.02013 * 0.50639 0.36026 1.406
## EthnicityOther 0.40023 -1.301 0.19336 -0.82650 0.52451 -1.576
## EthnicityWhite 0.29257 -1.117 0.26403 -0.45969 0.38109 -1.206
## MilitaryTRUE 0.33309 -0.936 0.34914 -0.50156 0.43316 -1.158
## ESLTRUE 0.41742 0.819 0.41252 0.99337 0.61273 1.621
## EdMother 0.08912 -1.034 0.30116 -0.04955 0.10803 -0.459
## EdFather 0.07629 0.997 0.31892 0.08704 0.09599 0.907
## Age 0.01286 1.477 0.13954 0.02009 0.01648 1.219
## Employment 0.16192 -1.840 0.06572 . 0.06055 0.20362 0.297
## Income 0.05522 -1.524 0.12742 -0.10214 0.06250 -1.634
## Transfer 0.00512 0.978 0.32804 -0.00763 0.00574 -1.331
## GPA 0.24244 1.559 0.11901 0.40313 0.29259 1.378
## Pr(>|z|) m3
## (Intercept) 0.277
## GenderMALE 0.160
## EthnicityOther 0.115
## EthnicityWhite 0.228
## MilitaryTRUE 0.247
## ESLTRUE 0.105
## EdMother 0.646
## EdFather 0.365
## Age 0.223
## Employment 0.766
## Income 0.102
## Transfer 0.183
## GPA 0.168
# Triangle plot of the propensity scores
plot(tutoring.tpsa, sample=c(200))
# In the three cases below we will use exact matching on the Course.
# Default maximumTreat
tutoring.matched <- trimatch(tutoring.tpsa, exact=tutoring[,c('Course')])
# Caliper matching
tutoring.matched.caliper <- trimatch(tutoring.tpsa, exact=tutoring[,c('Course')],
method=NULL)
# 2-to-1-to-1 matching
tutoring.matched.2to1 <- trimatch(tutoring.tpsa, exact=tutoring[,c('Course')],
method=OneToN, M1=2, M2=1)
# 3-to-2-to-1 matching
tutoring.matched.3to2 <- trimatch(tutoring.tpsa, exact=tutoring[,c('Course')],
method=OneToN, M1=3, M2=2)
# Examine unmatched cases.
summary(unmatched(tutoring.matched))
## 892 (78.1%) of 1142 total data points were not matched.
## Unmatched by treatment:
## Control Treat1 Treat2
## 834 (90.8%) 39 (29.1%) 19 (21.1%)
summary(unmatched(tutoring.matched.caliper))
## 638 (55.9%) of 1142 total data points were not matched.
## Unmatched by treatment:
## Control Treat1 Treat2
## 580 (63.2%) 39 (29.1%) 19 (21.1%)
summary(unmatched(tutoring.matched.2to1))
## 1000 (87.6%) of 1142 total data points were not matched.
## Unmatched by treatment:
## Control Treat1 Treat2
## 870 (94.8%) 97 (72.4%) 33 (36.7%)
summary(unmatched(tutoring.matched.3to2))
## 928 (81.3%) of 1142 total data points were not matched.
## Unmatched by treatment:
## Control Treat1 Treat2
## 831 (90.5%) 75 (56%) 22 (24.4%)
# Examine the differences in standardized propensity scores for each matched triplet.
# The caliper parameter allows us to see how many matched triplets we would loose
# if we reduced the caliper.
# TODO: Currently doesn't work
# distances.plot(tutoring.matched, caliper=.2)
# distances.plot(tutoring.matched.caliper, caliper=.2)
# We can overlay matched triplets on the triangle plot
plot(tutoring.matched, rows=c(1), line.alpha=1, draw.segments=TRUE)
##### Checking balance #########################################################
multibalance.plot(tutoring.tpsa) + ggtitle('Covariate Balance Plot')
# Continuous covariate
balance.plot(tutoring.matched, tutoring$Age, label='Age')
## Using propensity scores from model 3 for evaluating balance.
##
## Friedman rank sum test
##
## data: Covariate and Treatment and ID
## Friedman chi-squared = 11.274, df = 2, p-value = 0.003564
##
## Repeated measures ANOVA
##
## Effect DFn DFd F p p<.05 ges
## 2 Treatment 2 234 3.465795 0.03286147 * 0.01575012
# Discrete covariate
# balance.plot(tutoring.matched, tutoring$Ethnicity)
# Create a grid of figures.
bplots <- balance.plot(tutoring.matched, tutoring[,all.vars(formu)],
legend.position='none', x.axis.labels=c('C','T1','T1'), x.axis.angle=0)
bplots[['Military']] # We can plot one at at time.
summary(bplots) # Create a data frame with the statistical results
## Covariate Friedman Friedman.p Friedman.sig rmANOVA rmANOVA.p
## 1 Gender 14.6829268 0.0006481014 *** NA NA
## 2 Ethnicity 4.3058824 0.1161420606 NA NA
## 3 Military 14.1951220 0.0008271198 *** NA NA
## 4 ESL 4.1052632 0.1283965729 NA NA
## 5 EdMother 0.3315789 0.8472245785 0.1176035 8.891010e-01
## 6 EdFather 3.2722646 0.1947317486 2.0287005 1.338129e-01
## 7 Age 11.2739130 0.0035636980 ** 3.4657949 3.286147e-02
## 8 Employment 10.9559748 0.0041777293 ** 6.2756084 2.213700e-03
## 9 Income 18.7673861 0.0000840841 *** 10.9299870 2.897211e-05
## 10 Transfer 10.1115880 0.0063723052 ** 2.4261478 9.059687e-02
## 11 GPA 9.5240175 0.0085484206 ** 4.1399245 1.710535e-02
## rmANOVA.sig
## 1 <NA>
## 2 <NA>
## 3 <NA>
## 4 <NA>
## 5
## 6
## 7 *
## 8 **
## 9 ***
## 10 .
## 11 *
plot(bplots, cols=3, byrow=FALSE)
#print(bplots, cols=3, byrow=FALSE) # Will call summary and plot
##### Phase II #################################################################
matched.out <- merge(tutoring.matched, tutoring$Grade)
names(matched.out)
## [1] "Treat1" "Treat2" "Control" "D.m3" "D.m2"
## [6] "D.m1" "Dtotal" "Treat1.out" "Treat2.out" "Control.out"
head(matched.out)
## Treat1 Treat2 Control D.m3 D.m2 D.m1 Dtotal
## 1 368 39 331 0.007053754 0.001788577 1.039322e-02 0.01923555
## 2 158 279 365 0.003373585 0.009530680 1.071188e-02 0.02361614
## 3 899 209 100 0.001929173 0.013633300 9.183572e-03 0.02474604
## 4 692 596 1055 0.023785086 0.010292177 1.862058e-03 0.03593932
## 5 616 209 208 0.020203398 0.016562521 3.168865e-05 0.03679761
## 6 28 852 154 0.007501996 0.014214100 1.776640e-02 0.03948249
## Treat1.out Treat2.out Control.out
## 1 4 4 0
## 2 4 4 4
## 3 4 3 4
## 4 4 3 4
## 5 4 3 0
## 6 4 4 2
(s1 <- summary(tutoring.matched, tutoring$Grade))
## $PercentMatched
## Control Treat1 Treat2
## 0.09150327 0.70895522 0.78888889
##
## $friedman.test
##
## Friedman rank sum test
##
## data: Outcome and Treatment and ID
## Friedman chi-squared = 27.904, df = 2, p-value = 8.726e-07
##
##
## $rmanova
## $rmanova$ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 Treatment 2 234 23.84506 3.758176e-10 * 0.1146819
##
## $rmanova$`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 Treatment 0.7308876 1.268625e-08 *
##
## $rmanova$`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 Treatment 0.7879523 1.755235e-08 * 0.7968732 1.492693e-08
## p[HF]<.05
## 2 *
##
##
## $pairwise.wilcox.test
##
## Pairwise comparisons using Wilcoxon signed rank test
##
## data: out$Outcome and out$Treatment
##
## Treat1.out Treat2.out
## Treat2.out 0.031 -
## Control.out 0.001 9.6e-09
##
## P value adjustment method: bonferroni
##
## $t.tests
## Treatments t df p.value sig mean.diff
## 1 Treat1.out-Treat2.out -2.791302 117 6.132601e-03 ** -0.3220339
## 2 Treat1.out-Control.out 3.817862 117 2.168534e-04 *** 0.7033898
## 3 Treat2.out-Control.out 6.922623 117 2.539540e-10 *** 1.0254237
## ci.min ci.max
## 1 -0.5505191 -0.09354868
## 2 0.3385190 1.06826071
## 3 0.7320670 1.31878047
##
## attr(,"class")
## [1] "trimatch.summary" "list"
(s2 <- summary(tutoring.matched.caliper, tutoring$Grade))
## $PercentMatched
## Control Treat1 Treat2
## 0.3681917 0.7089552 0.7888889
##
## $friedman.test
##
## Friedman rank sum test
##
## data: Outcome and Treatment and ID
## Friedman chi-squared = 113, df = 2, p-value < 2.2e-16
##
##
## $rmanova
## $rmanova$ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 Treatment 2 2002 108.2106 2.374092e-45 * 0.06506132
##
## $rmanova$`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 Treatment 0.8232953 5.995288e-43 *
##
## $rmanova$`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 Treatment 0.8498309 5.513828e-39 * 0.851126 4.858834e-39
## p[HF]<.05
## 2 *
##
##
## $pairwise.wilcox.test
##
## Pairwise comparisons using Wilcoxon signed rank test
##
## data: out$Outcome and out$Treatment
##
## Treat1.out Treat2.out
## Treat2.out 1.1e-15 -
## Control.out 2.1e-09 < 2e-16
##
## P value adjustment method: bonferroni
##
## $t.tests
## Treatments t df p.value sig mean.diff
## 1 Treat1.out-Treat2.out -9.195197 1001 2.113881e-19 *** -0.3922156
## 2 Treat1.out-Control.out 6.232480 1001 6.755148e-10 *** 0.3872255
## 3 Treat2.out-Control.out 14.884958 1001 2.035852e-45 *** 0.7794411
## ci.min ci.max
## 1 -0.4759179 -0.3085133
## 2 0.2653051 0.5091460
## 3 0.6766846 0.8821976
##
## attr(,"class")
## [1] "trimatch.summary" "list"
(s3 <- summary(tutoring.matched.2to1, tutoring$Grade))
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot
## compute exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot
## compute exact p-value with zeroes
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot
## compute exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot
## compute exact p-value with zeroes
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot
## compute exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot
## compute exact p-value with zeroes
## $PercentMatched
## Control Treat1 Treat2
## 0.05228758 0.27611940 0.63333333
##
## $friedman.test
##
## Friedman rank sum test
##
## data: Outcome and Treatment and ID
## Friedman chi-squared = 18.955, df = 2, p-value = 7.654e-05
##
##
## $rmanova
## $rmanova$ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 Treatment 2 112 15.54945 1.097932e-06 * 0.1467116
##
## $rmanova$`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 Treatment 0.8085667 0.002898589 *
##
## $rmanova$`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 Treatment 0.8393252 6.02756e-06 * 0.8623044 4.722582e-06
## p[HF]<.05
## 2 *
##
##
## $pairwise.wilcox.test
##
## Pairwise comparisons using Wilcoxon signed rank test
##
## data: out$Outcome and out$Treatment
##
## Treat1.out Treat2.out
## Treat2.out 0.2977 -
## Control.out 0.0071 2.2e-05
##
## P value adjustment method: bonferroni
##
## $t.tests
## Treatments t df p.value sig mean.diff
## 1 Treat1.out-Treat2.out -1.730335 56 8.907832e-02 . -0.3157895
## 2 Treat1.out-Control.out 3.379801 56 1.326981e-03 ** 0.9122807
## 3 Treat2.out-Control.out 5.450673 56 1.167427e-06 *** 1.2280702
## ci.min ci.max
## 1 -0.6813848 0.04980581
## 2 0.3715631 1.45299832
## 3 0.7767277 1.67941268
##
## attr(,"class")
## [1] "trimatch.summary" "list"
(s4 <- summary(tutoring.matched.3to2, tutoring$Grade))
## $PercentMatched
## Control Treat1 Treat2
## 0.09477124 0.44029851 0.75555556
##
## $friedman.test
##
## Friedman rank sum test
##
## data: Outcome and Treatment and ID
## Friedman chi-squared = 32.271, df = 2, p-value = 9.828e-08
##
##
## $rmanova
## $rmanova$ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 Treatment 2 224 25.03567 1.538341e-10 * 0.1176893
##
## $rmanova$`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 Treatment 0.7564572 1.872981e-07 *
##
## $rmanova$`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 Treatment 0.8041541 6.33888e-09 * 0.8140958 5.246814e-09
## p[HF]<.05
## 2 *
##
##
## $pairwise.wilcox.test
##
## Pairwise comparisons using Wilcoxon signed rank test
##
## data: out$Outcome and out$Treatment
##
## Treat1.out Treat2.out
## Treat2.out 0.0043 -
## Control.out 0.0019 4e-09
##
## P value adjustment method: bonferroni
##
## $t.tests
## Treatments t df p.value sig mean.diff
## 1 Treat1.out-Treat2.out -3.311306 112 1.250340e-03 ** -0.4070796
## 2 Treat1.out-Control.out 3.643848 112 4.086158e-04 *** 0.6902655
## 3 Treat2.out-Control.out 7.275262 112 5.046039e-11 *** 1.0973451
## ci.min ci.max
## 1 -0.6506622 -0.1634971
## 2 0.3149281 1.0656029
## 3 0.7984901 1.3962002
##
## attr(,"class")
## [1] "trimatch.summary" "list"
# Loess plot for the optimal matching method
loess3.plot(tutoring.matched, tutoring$Grade, ylab='Grade')
## `geom_smooth()` using method = 'loess'
# Draw lines connecting each matched triplet
loess3.plot(tutoring.matched, tutoring$Grade, ylab='Grade',
points.alpha=.5, plot.connections=TRUE)
## `geom_smooth()` using method = 'loess'
# Loess plot for the caliper matching method
loess3.plot(tutoring.matched.caliper, tutoring$Grade, ylab='Grade',
points.alpha=.1, method='loess')
# Loess plot for the 2-to-1 matching method
loess3.plot(tutoring.matched.2to1, tutoring$Grade, ylab='Grade', span=.9)
## `geom_smooth()` using method = 'loess'
# Loess plot for the 3-to-2 matching method
loess3.plot(tutoring.matched.3to2, tutoring$Grade, ylab='Grade', span=.9)
## `geom_smooth()` using method = 'loess'
boxdiff.plot(tutoring.matched, tutoring$Grade,
ordering=c('Treat2','Treat1','Control')) +
ggtitle('Boxplot of Differences: Optimal Matching')
boxdiff.plot(tutoring.matched.caliper, tutoring$Grade,
ordering=c('Treat2','Treat1','Control')) +
ggtitle('Boxplot of Differences: Caliper Matching')
boxdiff.plot(tutoring.matched.2to1, tutoring$Grade,
ordering=c('Treat2','Treat1','Control')) +
ggtitle('Boxplot of Differences: 2-to-1-to-n Matching')
boxdiff.plot(tutoring.matched.3to2, tutoring$Grade,
ordering=c('Treat2','Treat1','Control')) +
ggtitle('Boxplot of Differences: 3-to-2-to-n Matching')
print(print('Optimal'=s1, 'Caliper'=s2, '2-to-1'=s3, '3-to-2'=s4), row.names=FALSE)
## Method Friedman.chi2 Friedman.p rmANOVA.F rmANOVA.p
## Optimal 27.90354 8.726175e-07 *** 23.84506 3.758176e-10 ***
## Caliper 112.99646 2.904890e-25 *** 108.21057 2.374092e-45 ***
## 2-to-1 18.95541 7.653924e-05 *** 15.54945 1.097932e-06 ***
## 3-to-2 32.27083 9.828281e-08 *** 25.03567 1.538341e-10 ***
##### Sensitivity Analysis #####################################################
library(rbounds)
## Loading required package: Matching
## Loading required package: MASS
## ##
## ## Matching (Version 4.9-2, Build Date: 2015-12-25)
## ## See http://sekhon.berkeley.edu/matching for additional documentation.
## ## Please cite software as:
## ## Jasjeet S. Sekhon. 2011. ``Multivariate and Propensity Score Matching
## ## Software with Automated Balance Optimization: The Matching package for R.''
## ## Journal of Statistical Software, 42(7): 1-52.
## ##
psens(matched.out$Treat1.out, matched.out$Control.out, Gamma=2, GammaInc=0.1)
##
## Rosenbaum Sensitivity Test for Wilcoxon Signed Rank P-Value
##
## Unconfounded estimate .... 2e-04
##
## Gamma Lower bound Upper bound
## 1.0 2e-04 0.0002
## 1.1 0e+00 0.0006
## 1.2 0e+00 0.0018
## 1.3 0e+00 0.0043
## 1.4 0e+00 0.0090
## 1.5 0e+00 0.0168
## 1.6 0e+00 0.0287
## 1.7 0e+00 0.0453
## 1.8 0e+00 0.0672
## 1.9 0e+00 0.0944
## 2.0 0e+00 0.1269
##
## Note: Gamma is Odds of Differential Assignment To
## Treatment Due to Unobserved Factors
##
psens(matched.out$Treat2.out, matched.out$Control.out, Gamma=2, GammaInc=0.1)
##
## Rosenbaum Sensitivity Test for Wilcoxon Signed Rank P-Value
##
## Unconfounded estimate .... 0
##
## Gamma Lower bound Upper bound
## 1.0 0 0e+00
## 1.1 0 0e+00
## 1.2 0 0e+00
## 1.3 0 0e+00
## 1.4 0 0e+00
## 1.5 0 0e+00
## 1.6 0 0e+00
## 1.7 0 0e+00
## 1.8 0 1e-04
## 1.9 0 1e-04
## 2.0 0 2e-04
##
## Note: Gamma is Odds of Differential Assignment To
## Treatment Due to Unobserved Factors
##
psens(matched.out$Treat1.out, matched.out$Treat2.out, Gamma=2, GammaInc=0.1)
##
## Rosenbaum Sensitivity Test for Wilcoxon Signed Rank P-Value
##
## Unconfounded estimate .... 0.9949
##
## Gamma Lower bound Upper bound
## 1.0 0.9949 0.9949
## 1.1 0.9871 0.9982
## 1.2 0.9729 0.9994
## 1.3 0.9505 0.9998
## 1.4 0.9188 0.9999
## 1.5 0.8777 1.0000
## 1.6 0.8280 1.0000
## 1.7 0.7713 1.0000
## 1.8 0.7096 1.0000
## 1.9 0.6451 1.0000
## 2.0 0.5798 1.0000
##
## Note: Gamma is Odds of Differential Assignment To
## Treatment Due to Unobserved Factors
##