iw_est {causaldrf} R Documentation

## The inverse weighting estimator (nonparametric method)

### Description

This is a nonparametric method that estimates the ADRF by using a local linear regression of Y on treat with weighted kernel function. For details, see Flores et. al. (2012).

### Usage

iw_est(Y,
treat,
treat_formula,
data,
grid_val,
bandw,
treat_mod,
...)


### Arguments

 Y is the the name of the outcome variable contained in data. treat is the name of the treatment variable contained in data. treat_formula an object of class "formula" (or one that can be coerced to that class) that regresses treat on a linear combination of X: a symbolic description of the model to be fitted. data is a dataframe containing Y, treat, and X. grid_val contains the treatment values to be evaluated. bandw is the bandwidth. Default is 1. treat_mod a description of the error distribution to be used in the model for treatment. Options include: "Normal" for normal model, "LogNormal" for lognormal model, "Sqrt" for square-root transformation to a normal treatment, "Poisson" for Poisson model, "NegBinom" for negative binomial model, "Gamma" for gamma model. link_function is either "log", "inverse", or "identity" for the "Gamma" treat_mod. ... additional arguments to be passed to the treatment regression function.

### Details

(D_{0}(t) S_{2}(t) - D_{1}(t) S_{1}(t)) / (S_{0}(t) S_{2}(t) - S_{1}^{2}(t))

where

D_{j}(t) = \sum_{i = 1}^{N} \tilde{K}_{h, X} (T_i - t) (T_i - t)^j Y_i

and S_{j}(t) = \sum_{i = 1}^{N} \tilde{K}_{h, X} (T_i - t) (T_i - t)^j \tilde{K}_{h, X}(t) = K_{h}(t) / \hat{R}_i(t) which is a local linear regression. More details are given in Flores (2012).

### Value

iw_est returns an object of class "causaldrf", a list that contains the following components:

 param parameter estimates for a iw fit. t_mod the result of the treatment model fit. call the matched call.

### References

Schafer, J.L., Galagate, D.L. (2015). Causal inference with a continuous treatment and outcome: alternative estimators for parametric dose-response models. Manuscript in preparation.

Flores, Carlos A., et al. "Estimating the effects of length of exposure to instruction in a training program: the case of job corps." Review of Economics and Statistics 94.1 (2012): 153-171.

nw_est, iw_est, hi_est, gam_est, add_spl_est, bart_est, etc. for other estimates.

### Examples

## Example from Schafer (2015).

example_data <- sim_data

iw_list <- iw_est(Y = Y,
treat = T,
treat_formula = T ~ B.1 + B.2 + B.3 + B.4 + B.5 + B.6 + B.7 + B.8,
data = example_data,
grid_val = seq(8, 16, by = 1),
bandw = bw.SJ(example_data$T), treat_mod = "Normal") sample_index <- sample(1:1000, 100) plot(example_data$T[sample_index],
example_data$Y[sample_index], xlab = "T", ylab = "Y", main = "iw estimate") lines(seq(8, 16, by = 1), iw_list$param,
lty = 2,
lwd = 2,
col = "blue")

legend('bottomright',
"iw estimate",
lty=2,
lwd = 2,
col = "blue",
bty='Y',
cex=1)

rm(example_data, iw_list, sample_index)

## Example from Imai & van Dyk (2004).

data("nmes_data")
# look at only people with medical expenditures greater than 0
nmes_nonzero <- nmes_data[which(nmes_data$TOTALEXP > 0), ] iw_list <- iw_est(Y = TOTALEXP, treat = packyears, treat_formula = packyears ~ LASTAGE + I(LASTAGE^2) + AGESMOKE + I(AGESMOKE^2) + MALE + RACE3 + beltuse + educate + marital + SREGION + POVSTALB, data = nmes_nonzero, grid_val = seq(5, 100, by = 5), bandw = bw.SJ(nmes_nonzero$packyears),
treat_mod = "LogNormal")

set.seed(307)
sample_index <- sample(1:nrow(nmes_nonzero), 1000)

plot(nmes_nonzero$packyears[sample_index], nmes_nonzero$TOTALEXP[sample_index],
xlab = "packyears",
ylab = "TOTALEXP",
main = "iw estimate",
ylim = c(0, 10000),
xlim = c(0, 100))

lines(seq(5, 100, by = 5),
iw_list\$param,
lty = 2,
lwd = 2,
col = "blue")

legend('topright',
"iw estimate",
lty=2,
lwd = 2,
col = "blue",
bty='Y',
cex = 1)
abline(0, 0)


[Package causaldrf version 0.4.2 Index]