cem (version 1.0.44)

att: Example of ATT estimation from CEM output

Description

An example of ATT estimation from CEM output

Usage

att(obj, formula, data, model="lm", family="binomial")

Arguments

obj

a cem.atch or multicem object

data

a single data.frame or a list of data.frame's in case of multicem

formula

formula type specification of model. See Details.

model

either lm or glm. See Details.

family

used if model is glm, otherwise ignored.

Value

• A matrix of estimates with their standard error, or a list in the case of multicem.

Details

Argument data must be a single data frame or a list of (mulitply imputed) data frames.

Argument model can be lm or glm if the outcome variable in the ATT estimation is, e.g., a binary outcome. If the outcome is y and the treatment variable is T, then a formula like y ~ T is enough to estimate the ATT: it is just the coefficient of T. User can add covariates to span any remaining imbalance after the match, such as y ~ T + age + sex, to adjust for variables age and sex.

In the case of multiply imputed datasets, the model is applied to each single matched data and the ATT and is the standard error estimated using the standard formulas for combining results of multiply imputed data.

References

Stefano Iacus, Gary King, Giuseppe Porro, ``Matching for Casual Inference Without Balance Checking,'' http://gking.harvard.edu/files/abs/cem-abs.shtml

Examples

data(LL)

# cem match: automatic bin choice
mat <- cem(treatment="treated",data=LL, drop="re78")
mat
mat$k2k

# ATT estimate
att(mat, re78~treated,  data=LL)


# reduce the match into k2k using euclidean distance within cem strata
mat2 <- k2k(mat, LL, "euclidean", 1)
mat2
mat2$k2k

# ATT estimate after k2k
att(mat2, re78~treated, data=LL)

# example with missing data
# using multiply imputated data
# we use Amelia for multiple imputation
if(require(Amelia)){
 data(LL)
 n <- dim(LL)[1]
 k <- dim(LL)[2]

# we generate missing values in 30% of the rows of LL data
# randomly in one colum per row
 LL1 <- LL
 idx <- sample(1:n, .3*n)
 invisible(sapply(idx, function(x) LL1[x,sample(2:k,1)] <<- NA))


 imputed <- amelia(LL1)[1:5] 

 mat <- cem("treated", datalist=imputed, data=LL1, drop="re78")

 print(mat)
  
 att(mat, re78 ~ treated, data=imputed)
}