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Last data update: 2014.03.03

R: FindIt for Estimating Heterogeneous Treatment Effects

FindIt

R Documentation

FindIt for Estimating Heterogeneous Treatment Effects

Description

FindIt returns a model with the most predictive treatment-treatment interactions or treatment-covariate interactions.

Usage

FindIt(model.treat, model.main, model.int,data = NULL,
       type = "binary", treat.type = "multiple", nway,	
       search.lambdas = TRUE, lambdas = NULL,
       make.twoway = TRUE, make.allway = TRUE,	
       wts = 1, scale.c = 1, scale.int = 1, fit.glmnet = TRUE, 
       make.reference = TRUE,reference.main = NULL,threshold = 0.999999)

Arguments

`model.treat`	A formula that specifies outcome and treatment variables.
`model.main`	An optional formula that specifies pre-treatment covariates to be adjusted.
`model.int`	A formula specifying pre-treatment covariates to be interacted with treatment assignments when `treat.type="single"`.
`data`	An optional data frame, list or environment (or object coercible by 'as.data.frame' to a data frame) containing the variables in the model. If not found in 'data', the variables are taken from 'environment(formula)', typically the environment from which 'FindIt' is called.
`type`	"binary" for a binary outcome variable, which needs to be `integer` class; "continuous" for a continuous outcome variable.
`treat.type`	"single" for interactions between a single treatment variable, which needs to be `integer` class, and multiple pre-treatment covariates specified with `model.int`; "multiple" is used when treatment-treatment interactions are of interest and `treat` is a matrix of multiple treatments.
`nway`	An argument passed to `makeallway` when `treat.type="multiple"`. `FindIt` generates treatment-treatment interactions up to the order specified with this argument. In general, it is recommended to use the number of factorial treatments. The current version covers up to four way interactions.
`search.lambdas`	Whether to search for the tuning parameters for the LASSO constraints. If `FALSE`, `lambdas` must be supplied.
`lambdas`	Tuning parameters to be given to `FindIt`; only used if `search.lambdas=FALSE`.
`make.twoway`	If `make.twoway=TRUE`, all possible two-way interactions for the pre-treatment covariates specified in `model.main` and `model.int` are generated within `FindIt`. The default is set to be `TRUE`.
`make.allway`	If `make.allway=TRUE`, all possible treatment-treatment interactions for multiple treatments are generated when `treat.type="multiple"`. Interactions of the order up to the value of `nway` is computed.
`wts`	An optional set of scaling weights. The default is 1.
`scale.c`	A set of weights for recaling the pre-treatment covariates; only used if `make.twoway=FALSE`. `maketwoway` is useful for generating these.
`scale.int`	A set of weights for recaling the covariates to be interacted with treatment variables ; only used if `make.twoway=FALSE`. `maketwoway` is useful for generating these.
`fit.glmnet`	Whether to fit using the coordinate descent method in glmnet (TRUE) or the regularization path method of LARS (FALSE).
`make.reference`	Whether to make a reference matrix to check which columns are dropped when `makeallway=TRUE`.
`reference.main`	If `make.allway=FALSE` and researchers generate a matrix of all possible interactions between factorial treatments, `reference` from `makeallway` function is better to be passed to `FindIt` through this argument.
`threshold`	An argument passed to `makeallway` when `treat.type="multiple"`. Threshold to drop correlated columns when `makeallway` is used.

Details

Implements the alternating line search algorithm for estimating the tuning parameters, as described in Imai and Ratkovic (2013).

Value

`coefs`	A named vector of scaled coefficients
`coefs.orig`	A vector of coefficients on the original scale, if scale.c and scale.t was used
`fit`	Fitted values on an SVM scale
`names.out`	Names of the coefficients
`y`	A vector of observed outcomes
`X.c`	A matrix of pre-treatment covariates to be adjusted
`X.t`	A matrix of treatments and treatment-treatment interactions, or treatment-covariate interactions
`GCV`	GCV statistic at the minimum
`ATE`	When `treat.type="single"`, the estimated ATE. When `treat.type="multiple"`, the estimated treatment effect of each unique treatment combination
`lambdas`	Tuning parameters used for the fit
`reference`	When `treat.type="multiple"`, after making all interaction terms, columns with no variation or columns perfectly correlated with one of other columns are automatically dropped. `reference` shows which columns are kept and dropped.

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


################################################### 
## Example 1: Treatment-Covariate Interaction
################################################### 
data(LaLonde)

## The model includes a treatment variable, 
## nine covariates to be interacted with the treatment variable,
## and the same nine covariates to be adjusted.

## Not run: 

## Run to find the LASSO parameters
F1  <-FindIt(model.treat= outcome ~ treat,
             model.main= ~ age+educ+black+hisp+white+
             marr+nodegr+log.re75+u75,
             model.int= ~ age+educ+black+hisp+white+
             marr+nodegr+log.re75+u75,
             data = LaLonde,  
             type="binary",
             treat.type="single") 

## End(Not run)

## Fit with uncovered lambda parameters.
F1  <-FindIt(model.treat= outcome ~ treat,
             model.main= ~ age+educ+black+hisp+white+
             marr+nodegr+log.re75+u75,
             model.int= ~ age+educ+black+hisp+white+
             marr+nodegr+log.re75+u75,
             data = LaLonde, 
             type="binary",
             treat.type="single",
             search.lambdas=FALSE,
             lambdas = c(-3.8760,-4.0025) )

summary(F1)

## Returns all the estimated treatment effects. 
pred1 <- predict(F1)
## Top10
head(pred1$data, n=10)
## Bottom 10
tail(pred1$data ,n=10)

## Visualize all the estimated treatment effects.
## Not run: 
plot(pred1)

## End(Not run)

################################################### 
## Example 2: Treatment-Treatment Interaction
################################################### 

## Not run: 
data(GerberGreen)

## The model includes four factorial treatments and 
## all two, three, four-way interactions between them.
## Four pre-treatment covariates are adjusted.

## Run to search for lambdas.
F2<- FindIt(model.treat= voted98 ~ persngrp+phnscrpt+mailings+appeal,
             nway=4,
             model.main= ~ age+majorpty+vote96.1+vote96.0,
             data = GerberGreen,
             type="binary",
             treat.type="multiple")

## Fit, given selected lambdas.
F2<- FindIt(model.treat= voted98 ~ persngrp+phnscrpt+mailings+appeal,
             nway=4,
             model.main= ~ age+majorpty+vote96.1+vote96.0,
             data = GerberGreen,
             type="binary",
             treat.type="multiple",
             search.lambdas=FALSE,
             lambdas=c(-15.000,-6.237))

## Returns coefficient estimates.
summary(F2)

## Returns predicted values for unique treatment combinations.
pred2 <- predict(F2,unique=TRUE)
## Top 10
head(pred2$data, n=10)
## Bottom 10
tail(pred2$data, n=10)

## Visualize predicted values for each treatment combination.
plot(pred2)

## End(Not run)

################################################### 
## Example 3: 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/FindIt.Rd_%03d_medium.png", width=480, height=480)
> ### Name: FindIt
> ### Title: FindIt for Estimating Heterogeneous Treatment Effects
> ### Aliases: FindIt summary.FindIt
> 
> ### ** Examples
> 
> 
> ################################################### 
> ## Example 1: Treatment-Covariate Interaction
> ################################################### 
> data(LaLonde)
> 
> ## The model includes a treatment variable, 
> ## nine covariates to be interacted with the treatment variable,
> ## and the same nine covariates to be adjusted.
> 
> ## Not run: 
> ##D 
> ##D ## Run to find the LASSO parameters
> ##D F1  <-FindIt(model.treat= outcome ~ treat,
> ##D              model.main= ~ age+educ+black+hisp+white+
> ##D              marr+nodegr+log.re75+u75,
> ##D              model.int= ~ age+educ+black+hisp+white+
> ##D              marr+nodegr+log.re75+u75,
> ##D              data = LaLonde,  
> ##D              type="binary",
> ##D              treat.type="single") 
> ## End(Not run)
> 
> ## Fit with uncovered lambda parameters.
> F1  <-FindIt(model.treat= outcome ~ treat,
+              model.main= ~ age+educ+black+hisp+white+
+              marr+nodegr+log.re75+u75,
+              model.int= ~ age+educ+black+hisp+white+
+              marr+nodegr+log.re75+u75,
+              data = LaLonde, 
+              type="binary",
+              treat.type="single",
+              search.lambdas=FALSE,
+              lambdas = c(-3.8760,-4.0025) )
> 
> summary(F1)

Call:
 Treatment Model: outcome ~ treat
 Main Model : ~age + educ + black + hisp + white + marr + nodegr + log.re75 + 
    u75
 Interaction Covariates: ~age + educ + black + hisp + white + marr + nodegr + log.re75 + 
    u75
 Treatment type: [1] "single"
 Outcome type: [1] "binary"

ATE:
[1] 0.07903784

Coefficients:
            Intercept                black1                white1 
                0.164                 -0.11               0.00577 
                  age              log.re75             hisp1:age 
              -0.0111               -0.0369               -0.0127 
       white1:nodegr1             marr1:age          nodegr1:u751 
              -0.0557               0.00294              -0.00997 
          nodegr1:age          nodegr1:educ              u751:age 
             -0.00505              -0.00667               0.00351 
                age.2            log.re75.2                 treat 
              0.00058               -0.0102                0.0692 
          treat:marr1 treat:black1:log.re75  treat:hisp1:log.re75 
               0.0495               0.00629               -0.0418 
 treat:white1:nodegr1      treat:marr1:educ    treat:nodegr1:u751 
                0.181                0.0108               -0.0848 
       treat:u751:age       treat:u751:educ           treat:age.2 
                0.018                0.0403             -0.000232 
         treat:educ.2 
              0.00828 

---------
Model Fit Statistics:
GCV:
  Null:  0.986  Model:  625.985 
Percent Misclassified:
   Null:  0.43   Model:  0.32 
   Percent Improvement, vs. NULL:  26.75 % 
Percent Outside Margin:
  1.108 %, n = 8 
> 
> ## Returns all the estimated treatment effects. 
> pred1 <- predict(F1)
> ## Top10
> head(pred1$data, n=10)
    Treatment.effect outcome treatment age educ black hisp white marr nodegr
25         0.4828246       0         0  31    4     0    0     1    0      1
719        0.4657111       1         1  31    4     1    0     0    0      1
263        0.4350411       0         0  33    5     0    1     0    0      1
503        0.3979228       1         1  28   15     1    0     0    0      0
255        0.3850236       1         0  30   14     1    0     0    1      0
434        0.3708778       1         1  22   16     1    0     0    0      0
168        0.3679018       1         0  32   12     0    1     0    1      0
174        0.3674185       0         0  50   10     0    1     0    0      1
53         0.3619136       1         0  28   11     0    1     0    1      1
186        0.3605496       1         0  34   13     1    0     0    1      0
    log.re75 u75
25  9.278092   0
719 8.299286   0
263 0.000000   1
503 0.000000   1
255 0.000000   1
434 0.000000   1
168 0.000000   1
174 0.000000   1
53  0.000000   1
186 0.000000   1
> ## Bottom 10
> tail(pred1$data ,n=10)
    Treatment.effect outcome treatment age educ black hisp white marr nodegr
235       -0.1391499       1         0  29   12     0    0     1    0      0
266       -0.1392401       1         0  50    8     1    0     0    1      1
107       -0.1445337       1         0  29    9     0    1     0    0      1
554       -0.1492456       0         1  29   10     0    1     0    0      1
264       -0.1565843       0         0  31   12     0    0     1    0      0
548       -0.1576406       0         1  31   12     0    0     1    0      0
595       -0.1880842       0         1  34   11     0    1     0    0      1
302       -0.1945496       0         0  36   11     0    1     0    0      1
245       -0.2029329       0         0  27   12     0    1     0    0      0
268       -0.2140965       0         0  36   12     0    1     0    0      0
     log.re75 u75
235  9.409273   0
266  8.636042   0
107  9.698982   0
554  9.088286   0
264  6.206576   0
548  7.867489   0
595  8.442685   0
302  8.026497   0
245 10.098273   0
268  9.350189   0
> 
> ## Visualize all the estimated treatment effects.
> ## Not run: 
> ##D plot(pred1)
> ## End(Not run)
> 
> ################################################### 
> ## Example 2: Treatment-Treatment Interaction
> ################################################### 
> 
> ## Not run: 
> ##D data(GerberGreen)
> ##D 
> ##D ## The model includes four factorial treatments and 
> ##D ## all two, three, four-way interactions between them.
> ##D ## Four pre-treatment covariates are adjusted.
> ##D 
> ##D ## Run to search for lambdas.
> ##D F2<- FindIt(model.treat= voted98 ~ persngrp+phnscrpt+mailings+appeal,
> ##D              nway=4,
> ##D              model.main= ~ age+majorpty+vote96.1+vote96.0,
> ##D              data = GerberGreen,
> ##D              type="binary",
> ##D              treat.type="multiple")
> ##D 
> ##D ## Fit, given selected lambdas.
> ##D F2<- FindIt(model.treat= voted98 ~ persngrp+phnscrpt+mailings+appeal,
> ##D              nway=4,
> ##D              model.main= ~ age+majorpty+vote96.1+vote96.0,
> ##D              data = GerberGreen,
> ##D              type="binary",
> ##D              treat.type="multiple",
> ##D              search.lambdas=FALSE,
> ##D              lambdas=c(-15.000,-6.237))
> ##D 
> ##D ## Returns coefficient estimates.
> ##D summary(F2)
> ##D 
> ##D ## Returns predicted values for unique treatment combinations.
> ##D pred2 <- predict(F2,unique=TRUE)
> ##D ## Top 10
> ##D head(pred2$data, n=10)
> ##D ## Bottom 10
> ##D tail(pred2$data, n=10)
> ##D 
> ##D ## Visualize predicted values for each treatment combination.
> ##D plot(pred2)
> ## End(Not run)
> 
> ################################################### 
> ## Example 3: Conjoint Analysis. Causal Interaction.
> ################################################### 
> data(Immigration)
> 
> ## Not run: 
> ##D 
> ##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 
>