# Example of ATT estimation from CEM output An example of ATT estimation from CEM output ```r att(obj, formula, data, model="linear", extrapolate=FALSE, ntree=2000) ## S3 method for class 'cem.att' plot(x, obj, data, vars=NULL, plot=TRUE, ecolors, ...) ## S3 method for class 'cem.att' summary(object, ...) ``` ## Arguments - `obj`: a `cem.match` or `cem.match.list` object - `formula`: a model formula. See Details. - `data`: a single data.frame or a list of data.frame's in case of `cem.match.list` - `model`: one model. See Details. - `extrapolate`: extrapolate the CEM restriced estimate to the whole data. Default = `FALSE`. - `ntree`: number of trees to generate in random forest model. Default = `2000`. - `x`: the output from the `att` function - `vars`: a vector of variable names to be used in the parallel plots. By default all variables involved in data matching are used. - `object`: an object of class `cem.att` function - `plot`: if `TRUE` the plot is produced, otherwise only calculations are made. - `ecolors`: a vector of three colors respectively for positive, zero and negative treatment effect. Default `c("blue","black","red")`. - `...`: passed to the plot function or to `printCoefmat` for the method summary ## Details Argument `model` can be `lm, linear` for linear regression model; `logit` for the the logistic model; `lme, linear-RE` for the linear model with random effects. Also `rf, forest` for the randomforest algorithm. If the outcome is `y` and the treatment variable is `T`, then a `formula` like `y ~ T` will produce the simplest estimate the ATT: with lm, it is just the coefficient on `T`, which is the same as the difference in means, weighted by CEM stratum size. Users 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. When `extrapolate` = `TRUE`, the estimate model is extrapolated to the whole set of data. There is a `print` method for the output of `att`. Specifying the option `TRUE` in a `print` command gives complete output from the estimated model when availalble. ## Returns A matrix of estimates with their standard error, or a list in the case of `cem.match.list`. For `plot.att` a list of strata estimated treatment effect and group ("positive", "negative", "zero") and individual treatment and effect and group. The individual treatment effect and group is given by the treatment effect of the strata. Similarly for the group ("positive", "negative", "zero"). Also, colors associated to estimated treatment effects are returned for easy subsequent plotting. ## References Iacus, King, Porro (2011) tools:::Rd_expr_doi("10.1198/jasa.2011.tm09599") Iacus, King, Porro (2012) tools:::Rd_expr_doi("10.1093/pan/mpr013") Iacus, King, Porro (2019) tools:::Rd_expr_doi("10.1017/pan.2018.29") ## Author(s) Stefano Iacus, Gary King, and Giuseppe Porro ## Examples ```r data(LL) # cem match: automatic bin choice mat <- cem(treatment="treated",data=LL, drop="re78", keep.all=TRUE) mat mat$k2k # ATT estimate homo1 <- att(mat, re78~treated, data=LL) rand1 <- att(mat, re78~treated, data=LL, model="linear-RE") rf1 <- att(mat, re78~treated, data=LL, model="rf") homo2 <- att(mat, re78~treated, data=LL, extra=TRUE) rand2 <- att(mat, re78~treated, data=LL, model="linear-RE", extra=TRUE) rf2 <- att(mat, re78~treated, data=LL, model="rf", extra=TRUE) homo1 summary(homo1) rand1 rf1 homo2 rand2 rf2 plot( homo1, mat, LL, vars=c("age","education","re74","re75")) plot( rand1, mat, LL, vars=c("age","education","re74","re75")) plot( rf1, mat, LL, vars=c("age","education","re74","re75")) plot( homo2, mat, LL, vars=c("age","education","re74","re75")) plot( rand2, mat, LL, vars=c("age","education","re74","re75")) plot( rf2, mat, LL, vars=c("age","education","re74","re75")) # reduce the match into k2k using euclidean distance within cem strata mat2 <- k2k(mat, LL, "euclidean", 1) mat2 mat2$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 percent of the rows of LL data # randomly in one colum per row set.seed(123) LL1 <- LL idx <- sample(1:n, .3*n) for(i in idx){ LL1[i,sample(2:k,1)] <- NA } imputed <- amelia(LL1) imputed <- imputed$imputations[1:5] mat <- cem("treated", datalist=imputed, data=LL1, drop="re78") print(mat) att(mat, re78 ~ treated, data=imputed) } ```

att function