This method uses weight matrices to estimate parameters for an ADRF with quadratic or linear fits.

1 2 3 4 5 6 7 8 9 |

`Y` |
is the output |

`treat` |
is the treatment variable |

`covar_formula` |
is the formula for the covariates model of the form: ~ X.1 + .... |

`data` |
will contain all the data: X, treat, and Y |

`e_treat_1` |
is estimated treatment |

`e_treat_2` |
is estimated treatment squared |

`e_treat_3` |
is estimated treatment cubed |

`e_treat_4` |
is estimated treatment to the fourth |

`degree` |
is 1 for linear fit and 2 for quadratic fit |

This function estimates the ADRF by the method described in Schafer and Galagate (2015) which uses weight matrices to adjust for possible bias.

`wtrg_est`

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

`param` |
the estimated parameters. |

`call` |
the matched call. |

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*.

`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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | ```
## 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$T_data
full_data <- cbind(example_data, cond_exp_data)
wtrg_list <- wtrg_est(Y = Y,
treat = T,
covar_formula = ~ B.1 + B.2 + B.3 + B.4 + B.5 + B.6 + B.7 + B.8,
data = example_data,
e_treat_1 = full_data$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$Y[sample_index],
xlab = "T",
ylab = "Y",
main = "weighted regression estimate")
abline(wtrg_list$param[1],
wtrg_list$param[2],
lty = 2,
lwd = 2,
col = "blue")
legend('bottomright',
"weighted regression estimate",
lty = 2,
lwd = 2,
col = "blue",
bty='Y',
cex=1)
rm(example_data, t_mod_list, cond_exp_data, full_data, wtrg_list, sample_index)
``` |

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