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Last data update: 2014.03.03

R: Estimating the AMTE, the ATCE and the AMTIE

INT	R Documentation

Estimating the AMTE, the ATCE and the AMTIE

Description

Estimating the average marginal treatment effect (AMTE), the average treatment combination effect (ATCE) and the average marginal treatment interaction effect (AMTIE) under the assumption of independently randomized factorial treatments. Researchers need to change the baseline condition by relevel the target.data.

Usage

INT(object, target.data, column, dist = "target", base, 
    sort = TRUE, compare = FALSE, order = 2)

Arguments

`object`	An output object from `FindIt`.
`target.data`	If `dist= "target"`, this data is used to compute the AMTEs, ATCEs and AMTIEs. This data should represent the target population in terms of the treatment distribution and samples. The first column contains outcome variables and the other columns should be factorial treatments of interest.
`column`	Researchers can explore the AMTIEs within any factor interactions by specifying the names of factors through this argument.
`dist`	If `dist="target"`, `INT` computes the AMTEs, ATCEs and AMTIEs for the target population specified by `target.data`. If `dist="sample"`, it computes them for the data used to fit the model. If `dist="unique"`, it computes them for the unique samples in the data used to fit the model.
`base`	An optional argument that specifies the baseline condition. This argument can be used only when `column` is used, and the order of `base` should follow the order of `column`.
`sort`	If `sort=TRUE`, the AMTE, the ATCE and the AMTIE are sorted in descending order.
`compare`	If `compare=TRUE`, `INT` computes the range of all factor interactions of the order specified with `order`. Researchers can identify the most important factor interaction for the specified order.
`order`	`INT` computes the ATCEs and AMTIEs of this order. Can be 2 or 3.

Details

INT estimates the AMTEs, ATCEs and AMTIEs under the assumption of independently randomized factorial treatments.

Value

`Range of AMTIE`	The range of the estimated AMTIEs
`AMTIE`	Estimated AMTIEs for treatment combinations
`ATCE`	Estimated ATCEs and AMTIEs for treatment combinations
`Sum of AMTEs`	Sum of the estimated AMTEs of each factor and AMTIEs for treatment combinations

Author(s)

Naoki Egami, Marc Ratkovic and Kosuke Imai.

References

Imai, Kosuke and Marc Ratkovic. 2013. “Estimating Treatment Effect Heterogeneity in Randomized Program Evaluation.” Annals of Applied Statistics, Vol.7, No.1(March), pp. 443-470. http://imai.princeton.edu/research/files/svm.pdf

Egami, Naoki and Kosuke Imai. 2015. “Causal Interaction in High-Dimension.” Working paper. http://imai.princeton.edu/research/files/int.pdf

Examples

################################################### 
## Conjoint Analysis: Causal Interaction.
################################################### 
data(Immigration)

## Not run: 
## The SVM classifier with a lasso constraint is estimated.
## The model includes all three-way and two-way interactions as 
## well as main effects of five factorial treatments.

## Run to search for lambdas.
F.conjoint<- FindIt(model.treat= outcome ~
                    Education+Gender+Origin+Experience+Plans,
                    nway=3,
                    data = Immigration,
                    type="binary",
                    treat.type="multiple")

## Make the full factorial design matrix as the target population. 
full <- full.FindIt(F.conjoint)

## Compute the predicted potential outcomes for the target population.
Unifdata <- predict(F.conjoint,newdata=full,sort=FALSE)$data

## End(Not run)
## load pre-computed F.conjoint and Unifdata
data(F.conjoint)
data(Unifdata)

## Compute AMTEs, ATCEs, and AMTIEs

## Range of each factor interaction.
## The range of the AMTEs for all factors
compare1 <- INT(F.conjoint,target.data=Unifdata,compare=TRUE,order=1)
compare1

## The range of the two-way AMTIEs for all two-way factor interactions
compare2 <- INT(F.conjoint,target.data=Unifdata,compare=TRUE,order=2)
compare2

## Not run: 
## The range of the three-way AMTIEs for all three-way factor interactions
compare3 <- INT(F.conjoint,target.data=Unifdata,compare=TRUE,order=3)
compare3

## End(Not run)

## Compute AMTIEs within factor interactions.
## Origin x Experience
out.OP <- INT(F.conjoint,target.data=Unifdata,
              column=c("Origin","Experience"),
              base=c("India","No.job"), order=2)
out.OP

## Not run: 
## Education x Gender x Origin
out.EGO <- INT(F.conjoint,target.data=Unifdata,
               column=c("Education","Gender","Origin"),
               base=c("No.formal","female","India"), order=3)
out.EGO

## End(Not run)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(FindIt)
Loading required package: glmnet
Loading required package: Matrix
Loading required package: foreach
Loaded glmnet 2.0-5

Loading required package: lars
Loaded lars 1.2

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FindIt/INT.Rd_%03d_medium.png", width=480, height=480)
> ### Name: INT
> ### Title: Estimating the AMTE, the ATCE and the AMTIE
> ### Aliases: INT
> 
> ### ** Examples
> 
> ################################################### 
> ## Conjoint Analysis: Causal Interaction.
> ################################################### 
> data(Immigration)
> 
> ## Not run: 
> ##D ## The SVM classifier with a lasso constraint is estimated.
> ##D ## The model includes all three-way and two-way interactions as 
> ##D ## well as main effects of five factorial treatments.
> ##D 
> ##D ## Run to search for lambdas.
> ##D F.conjoint<- FindIt(model.treat= outcome ~
> ##D                     Education+Gender+Origin+Experience+Plans,
> ##D                     nway=3,
> ##D                     data = Immigration,
> ##D                     type="binary",
> ##D                     treat.type="multiple")
> ##D 
> ##D ## Make the full factorial design matrix as the target population. 
> ##D full <- full.FindIt(F.conjoint)
> ##D 
> ##D ## Compute the predicted potential outcomes for the target population.
> ##D Unifdata <- predict(F.conjoint,newdata=full,sort=FALSE)$data
> ## End(Not run)
> ## load pre-computed F.conjoint and Unifdata
> data(F.conjoint)
> data(Unifdata)
> 
> ## Compute AMTEs, ATCEs, and AMTIEs
> 
> ## Range of each factor interaction.
> ## The range of the AMTEs for all factors
> compare1 <- INT(F.conjoint,target.data=Unifdata,compare=TRUE,order=1)
[1] "Using Data representing the target population."
[1] "Range of Marginal Effects"
> compare1
  Education      Gender      Origin  Experience       Plans 
0.197383880 0.007739259 0.126250464 0.087042921 0.267419190 
> 
> ## The range of the two-way AMTIEs for all two-way factor interactions
> compare2 <- INT(F.conjoint,target.data=Unifdata,compare=TRUE,order=2)
[1] "Using Data representing the target population."
> compare2
           V1         V2  range.TIE
8      Origin Experience 0.09497208
3   Education Experience 0.08462559
9      Origin      Plans 0.07603530
2   Education     Origin 0.06145049
10 Experience      Plans 0.05552839
4   Education      Plans 0.04373174
1   Education     Gender 0.04204575
7      Gender      Plans 0.03679968
5      Gender     Origin 0.03343086
6      Gender Experience 0.01627208
> 
> ## Not run: 
> ##D ## The range of the three-way AMTIEs for all three-way factor interactions
> ##D compare3 <- INT(F.conjoint,target.data=Unifdata,compare=TRUE,order=3)
> ##D compare3
> ## End(Not run)
> 
> ## Compute AMTIEs within factor interactions.
> ## Origin x Experience
> out.OP <- INT(F.conjoint,target.data=Unifdata,
+               column=c("Origin","Experience"),
+               base=c("India","No.job"), order=2)
[1] "Using Data representing the target population."
> out.OP
$`Range of AMTIE`
[1] 0.09497208

$AMTIE
         AMTIE      Origin    Experience
24  0.05781929 Philippines    Three.Five
39  0.02278772       China       One.Two
27  0.01900762      Mexico    Three.Five
5   0.01166398     Somalia        No.job
15  0.01130097     Somalia Morethan.five
33  0.00783490       Sudan       One.Two
3   0.00337015       Sudan        No.job
32  0.00242682        Iraq       One.Two
13  0.00192642       Sudan Morethan.five
25  0.00187452     Somalia    Three.Five
36  0.00095525      France       One.Two
38  0.00095525      Poland       One.Two
40  0.00095525     Germany       One.Two
2   0.00043286        Iraq        No.job
1   0.00000000       India        No.job
11 -0.00036302       India Morethan.five
6  -0.00103870      France        No.job
8  -0.00103870      Poland        No.job
10 -0.00103870     Germany        No.job
9  -0.00116432       China        No.job
16 -0.00140171      France Morethan.five
18 -0.00140171      Poland Morethan.five
20 -0.00140171     Germany Morethan.five
19 -0.00152733       China Morethan.five
31 -0.00216084       India       One.Two
12 -0.00581640        Iraq Morethan.five
37 -0.00790280      Mexico       One.Two
22 -0.00935660        Iraq    Three.Five
21 -0.00978947       India    Three.Five
17 -0.01025977      Mexico Morethan.five
26 -0.01082816      France    Three.Five
28 -0.01082816      Poland    Three.Five
30 -0.01082816     Germany    Three.Five
7  -0.01315837      Mexico        No.job
34 -0.01948207 Philippines       One.Two
14 -0.02183903 Philippines Morethan.five
23 -0.02544479       Sudan    Three.Five
4  -0.02881151 Philippines        No.job
29 -0.03240939       China    Three.Five
35 -0.03715279     Somalia       One.Two

$ATCE
           ATCE       AMTIE      Origin    Experience
24  0.154402938  0.05781929 Philippines    Three.Five
20  0.121031247 -0.00140171     Germany Morethan.five
18  0.118807677 -0.00140171      Poland Morethan.five
30  0.100724439 -0.01082816     Germany    Three.Five
27  0.099890810  0.01900762      Mexico    Three.Five
28  0.098500870 -0.01082816      Poland    Three.Five
40  0.087542873  0.00095525     Germany       One.Two
11  0.086679906 -0.00036302       India Morethan.five
14  0.085624970 -0.02183903 Philippines Morethan.five
38  0.085319304  0.00095525      Poland       One.Two
16  0.085159887 -0.00140171      France Morethan.five
19  0.082613227 -0.00152733       China Morethan.five
17  0.081503781 -0.01025977      Mexico Morethan.five
13  0.079817504  0.00192642       Sudan Morethan.five
39  0.071082942  0.02278772       China       One.Two
21  0.066373098 -0.00978947       India    Three.Five
26  0.064853079 -0.01082816      France    Three.Five
34  0.052136597 -0.01948207 Philippines       One.Two
36  0.051671514  0.00095525      France       One.Two
33  0.049880642  0.00783490       Sudan       One.Two
31  0.049036743 -0.00216084       India       One.Two
37  0.048015407 -0.00790280      Mexico       One.Two
15  0.046922401  0.01130097     Somalia Morethan.five
23  0.041565940 -0.02544479       Sudan    Three.Five
29  0.040850817 -0.03240939       China    Three.Five
10  0.034351341 -0.00103870     Germany        No.job
8   0.032127772 -0.00103870      Poland        No.job
25  0.026615593  0.00187452     Somalia    Three.Five
1   0.000000000  0.00000000       India        No.job
6  -0.001520019 -0.00103870      France        No.job
9  -0.004066679 -0.00116432       China        No.job
3  -0.005781686  0.00337015       Sudan        No.job
4  -0.008390429 -0.02881151 Philippines        No.job
7  -0.008437747 -0.01315837      Mexico        No.job
12 -0.009633901 -0.00581640        Iraq Morethan.five
22 -0.024054464 -0.00935660        Iraq    Three.Five
32 -0.037236030  0.00242682        Iraq       One.Two
35 -0.037376699 -0.03715279     Somalia       One.Two
5  -0.039757505  0.01166398     Somalia        No.job
2  -0.090427562  0.00043286        Iraq        No.job

$`Sum of AMTEs`
    Sum of AMTEs       AMTIE      Origin    Experience
20  0.1224329595 -0.00140171     Germany Morethan.five
18  0.1202093902 -0.00140171      Poland Morethan.five
30  0.1115526016 -0.01082816     Germany    Three.Five
28  0.1093290323 -0.01082816      Poland    Three.Five
14  0.1074640034 -0.02183903 Philippines Morethan.five
24  0.0965836454  0.05781929 Philippines    Three.Five
17  0.0917635473 -0.01025977      Mexico Morethan.five
11  0.0870429213 -0.00036302       India Morethan.five
40  0.0865876190  0.00095525     Germany       One.Two
16  0.0865615998 -0.00140171      France Morethan.five
38  0.0843640497  0.00095525      Poland       One.Two
19  0.0841405612 -0.00152733       China Morethan.five
27  0.0808831893  0.01900762      Mexico    Three.Five
13  0.0778910846  0.00192642       Sudan Morethan.five
21  0.0761625634 -0.00978947       India    Three.Five
26  0.0756812418 -0.01082816      France    Three.Five
29  0.0732602032 -0.03240939       China    Three.Five
34  0.0716186628 -0.01948207 Philippines       One.Two
23  0.0670107266 -0.02544479       Sudan    Three.Five
37  0.0559182067 -0.00790280      Mexico       One.Two
31  0.0511975808 -0.00216084       India       One.Two
36  0.0507162592  0.00095525      France       One.Two
39  0.0482952206  0.02278772       China       One.Two
33  0.0420457440  0.00783490       Sudan       One.Two
15  0.0356214320  0.01130097     Somalia Morethan.five
10  0.0353900382 -0.00103870     Germany        No.job
8   0.0331664689 -0.00103870      Poland        No.job
25  0.0247410741  0.00187452     Somalia    Three.Five
4   0.0204210820 -0.02881151 Philippines        No.job
7   0.0047206259 -0.01315837      Mexico        No.job
1   0.0000000000  0.00000000       India        No.job
35 -0.0002239085 -0.03715279     Somalia       One.Two
6  -0.0004813215 -0.00103870      France        No.job
9  -0.0029023601 -0.00116432       China        No.job
12 -0.0038175047 -0.00581640        Iraq Morethan.five
3  -0.0091518367  0.00337015       Sudan        No.job
22 -0.0146978627 -0.00935660        Iraq    Three.Five
32 -0.0396628453  0.00242682        Iraq       One.Two
5  -0.0514214893  0.01166398     Somalia        No.job
2  -0.0908604261  0.00043286        Iraq        No.job

> 
> ## Not run: 
> ##D ## Education x Gender x Origin
> ##D out.EGO <- INT(F.conjoint,target.data=Unifdata,
> ##D                column=c("Education","Gender","Origin"),
> ##D                base=c("No.formal","female","India"), order=3)
> ##D out.EGO
> ## End(Not run)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>