ismw_est {causaldrf}

The inverse second moment weighting (ismw) estimator

Description

This method estimates the ADRF by using weighting matrices instead of scalars. The weight matrices require conditional expectations of the treatment and higher order conditional expectations. It uses outputs from the t_mod function.

Usage

ismw_est(Y,
         treat,
         data,
         e_treat_1,
         e_treat_2,
         e_treat_3,
         e_treat_4,
         degree )

Arguments

Y

is the the name of the outcome variable contained in data.

treat

is the name of the treatment variable contained in data.

data

is a dataframe containing Y, treat, and X.

e_treat_1

a vector, representing the conditional expectation of treat from t_mod.

e_treat_2

a vector, representing the conditional expectation of treat^2 from t_mod.

e_treat_3

a vector, representing the conditional expectation of treat^3 from t_mod.

e_treat_4

a vector, representing the conditional expectation of treat^4 from t_mod.

degree

is 1 for linear and 2 for quadratic outcome model.

Details

This function estimates the ADRF requires estimated moments and uses the outputs of the t_mod function as inputs. For more details, see Schafer and Galagate (2015).

Value

ismw_est returns an object of class "causaldrf_simple", a list that contains the following components:

param

the estimated parameters.

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.

See Also

iptw_est, ismw_est, reg_est, aipwee_est, wtrg_est, etc. for other estimates.

t_mod, overlap_fun to prepare the data for use in the different estimates.

Examples

## Example from Schafer (2015).

example_data <- sim_data

t_mod_list <- t_mod(treat = T,
                treat_formula = T ~ B.1 + B.2 + B.3 + B.4 + B.5 + B.6 + B.7 + B.8,
                data = example_data,
                treat_mod = "Normal")

cond_exp_data <- t_mod_list$T_data

full_data <- cbind(example_data, cond_exp_data)

ismw_list <- ismw_est(Y = Y,
                      treat = T,
                      data = full_data,
                      e_treat_1 = full_data$est_treat,
                      e_treat_2 = full_data$est_treat_sq,
                      e_treat_3 = full_data$est_treat_cube,
                      e_treat_4 = full_data$est_treat_quartic,
                      degree = 1)

sample_index <- sample(1:1000, 100)

plot(example_data$T[sample_index],
      example_data$Y[sample_index],
      xlab = "T",
      ylab = "Y",
      main = "ismw estimate")

abline(ismw_list$param[1],
ismw_list$param[2],
        lty=2,
        lwd = 2,
        col = "blue")

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

rm(example_data, t_mod_list, cond_exp_data, full_data, ismw_list, sample_index)