FindIt (version 1.0)

CausalANOVA: Estimating the AMEs and AMIEs with the CausalANOVA.

Description

CausalANOVA estimates coefficients of the specified ANOVA with regularization. By taking differences in coefficients, the function recovers the AMEs and AMIEs.

Usage

CausalANOVA(formula,data,cost,pair.id=NULL,nway=2,diff=TRUE,
	    select.prob=FALSE,boot=100,block.id=NULL,seed=1234,
	    eps=1e-5,fac.level=NULL,ord.fac=NULL,verbose=TRUE)

Arguments

formula

a formula that specifies outcome and treatment variables.

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 'CausalANOVA' is called.

cost

a cost parameter ranging from 0 to 1. 1 corresponds to no regularization. It is recommended to choose the value using cross validation with cv.GashANOVA.

pair.id

unique identifiers for each pair of comparison. This option is used when dif=TRUE.

nway

"2" when the two way causal interactions are of interest and "3" when the three-way and two-way causal interactions are of interest. Default is 2.

diff

a logical indicating whether the outcome is the choice between a pair. If diff=TRUE, pair.id should specify a pair of comparison.

select.prob

a logical indicating whether selection probabilities are computed. We recommend to use this option when the model is finalized.

boot

the number of bootstrap replicates.

block.id

unique identifies for blocks that the function uses for block bootstrap.

seed

seed for bootstrap.

eps

a tolerance parameter in the internal optimization algorithm.

fac.level

optional. A vector containing the number of levels in each factor. The order of fac.level should match to the order of columns in the data. For example, when the first and second columns of the design matrix is "Education" and "Race", the first and second element of fac.level should be the number of levels in "Education" and "Race", respectively.

ord.fac

optional. logical vectors indicating whether each factor has ordered (TRUE) or unordered (FALSE) levels. When levels are ordered, the function uses the order given by function levels(). If levels are ordered, the function places penalties on the differences between adjacent levels. If levels are unordered, the function places penalties on the differences based on every pairwise comparison.

verbose

whether it prints the value of a cost parameter used.

Value

intercept

an intercept of the estimated ANOVA model.If diff=TRUE, this should be close to 0.5.

coefs

a named vector of coefficients of the estimated ANOVA model.

formula

the formula used in the function.

cost

the cost parameter used in the function.

...

arguments passed to the function or arguments only for the internal use.

Details

Suggested workflow.

1. Specify the order of levels within each factor using levels(). Since the function places penalties on the differences between adjacent levels when levels are ordered, it is crucial to specify the order of levels within each factor carefully.

2. Run cv.CausalANOVA. Select the cost parameter minimizing the cross-validation error. Or choose largest value of cost such that error is within 1 standard error of the minimum. plot.cv.CausalANOVA can be used to investigate how cross-validation errors vary depending on cost parameters.

3. Run CausalANOVA. Run the main model with the chosen cost parameter and see summary by summary.CausalANOVA. If researchers want to compute selection probabilities, set select.prob=TRUE. Given it is computationally intensive, we recommend to compute selection probabilities when the model is finalized. The selection probability for the range of the AME (AMIE) is one minus the proportion of bootstrap replicates in which all coefficients for the corresponding factor (factor interaction) are estimated to be zero. The selection probability of the AME (AMIE) is the proportion of bootstrap replicates in which the sign of the effect is the same as the point estimate.

4. Investigate two-way interactions. Run plot.CausalANOVA and visualize the AMIEs by choosing two factors of interest. Run AMIE to examine decomposition of the average combination effect into the AMIE and AMEs.

References

Post, J. B. and Bondell, H. D. 2013. ``Factor selection and structural identification in the interaction anova model.'' Biometrics 69, 1, 70--79.

Egami, Naoki and Kosuke Imai. 2016+. ``Causal Interaction in Factorial Experiments: Application to Conjoint Analysis.'' Working paper. http://imai.princeton.edu/research/files/int.pdf

See Also

cv.CausalANOVA,AMIE

Examples

# NOT RUN {
data(Carlson)
## Specify the order of each factor
Carlson$newRecordF<- factor(Carlson$newRecordF,ordered=TRUE,
                         levels=c("YesLC", "YesDis","YesMP",
                             "noLC","noDis","noMP","noBusi"))
Carlson$promise <- factor(Carlson$promise,ordered=TRUE,levels=c("jobs","clinic","education"))
Carlson$coeth_voting <- factor(Carlson$coeth_voting,ordered=FALSE,levels=c("0","1"))
Carlson$relevantdegree <- factor(Carlson$relevantdegree,ordered=FALSE,levels=c("0","1"))

## Run cv.CausalANOVA
# }
# NOT RUN {
cv.fit <- cv.CausalANOVA(won ~ newRecordF + promise + coeth_voting + relevantdegree,
                         data=Carlson,
                         pair.id=Carlson$contestresp,diff=TRUE, nway=2)

cv.fit
plot(cv.fit)
# }
# NOT RUN {
fit <- CausalANOVA(won ~ newRecordF + promise + coeth_voting + relevantdegree,
                    data=Carlson,
                    pair.id=Carlson$contestresp,diff=TRUE, nway=2,cost=0.15)
## Or when we need selection probabilities.
# }
# NOT RUN {
fit <- CausalANOVA(won ~ newRecordF + promise + coeth_voting + relevantdegree,
                    data=Carlson,
                    pair.id=Carlson$contestresp,diff=TRUE,nway=2,cost=0.15,
                    select.prob=TRUE,boot=500,block.id=Carlson$respcodeS)
# }
# NOT RUN {
summary(fit)

# }
# NOT RUN {
## plot 
plot(fit,fac.name=c("newRecordF","coeth_voting"))
# }
# NOT RUN {
## compute AMIEs
amie1 <- AMIE(fit,fac.name=c("promise","newRecordF"),
              level.name=c("jobs","noLC"),
              base.name=c("jobs","YesLC"))

amie2 <- AMIE(fit,fac.name=c("newRecordF","coeth_voting"),
              level.name=c("noBus","1"),
              base.name=c("noMP","0"))

# }