FindIt: 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.

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

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.

Details

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

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.fas.harvard.edu/research/files/svm.pdf

Egami, Naoki and Kosuke Imai. 2019. Causal Interaction in Factorial Experiments: Application to Conjoint Analysis, Journal of the American Statistical Association. http://imai.fas.harvard.edu/research/files/int.pdf

Examples

Run this code

# NOT RUN {

################################################### 
## 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") 
# }
# 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)
# }
# 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)
# }
# NOT RUN {
# }

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