The regression prediction estimator

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Description

This method estimates the linear or quadratic parameters of the ADRF by estimating a least-squares fit on the basis functions which are composed of combinations of the covariates and treatment values.

Usage

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reg_est(Y,
        treat,
        covar_formula,
        covar_lin_formula = NULL,
        covar_sq_formula = NULL,
        data,
        degree,
        wt = NULL,
        method = "same")

Arguments

Y

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

treat

is the name of the treatment variable contained in data.

covar_formula

is the formula to describe the covariates needed to estimate the constant term: ~ X.1 + ..... Can include higher order terms or interactions. i.e. ~ X.1 + I(X.1^2) + X.1 * X.2 + ..... Don't forget the tilde before listing the covariates.

covar_lin_formula

is the formula to describe the covariates needed to estimate the linear term, t: ~ X.1 + ..... Can include higher order terms or interactions. i.e. ~ X.1 + I(X.1^2) + X.1 * X.2 + ..... Don't forget the tilde before listing the covariates.

covar_sq_formula

is the formula to describe the covariates needed to estimate the quadratic term, t^2: ~ X.1 + ..... Can include higher order terms or interactions. i.e. ~ X.1 + I(X.1^2) + X.1 * X.2 + ..... Don't forget the tilde before listing the covariates.

data

is a dataframe containing Y, treat, and X.

degree

is 1 for linear and 2 for quadratic outcome model.

wt

is weight used in lsfit for outcome regression. Default is wt = NULL.

method

is "same" if the same set of covariates are used to estimate the constant, linear, and/or quadratic term. If method = "different", then different sets of covariates can be used to estimate the constant, linear, and/or quadratic term. covar_lin_formula and covar_sq_formula must be specified if method = "different".

Details

This function estimates the ADRF by the method described in Schafer and Galagate (2015) that fits an outcome model using a function of the covariates.

Value

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

param

the estimated parameters.

out_mod

the result of the outcome model fit using lsfit.

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.

Schafer, Joseph L, Kang, Joseph (2008). Average causal effects from nonrandomized studies: a practical guide and simulated example. Psychological methods, 13.4, 279.

See Also

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

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

Examples

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## Example from Schafer (2015).

example_data <- sim_data

reg_list <- reg_est(Y = Y,
                    treat = T,
                    covar_formula = ~ B.1 + B.2 + B.3 + B.4 + B.5 + B.6 + B.7 + B.8,
                    covar_lin_formula = ~ 1,
                    covar_sq_formula = ~ 1,
                    data = example_data,
                    degree = 1,
                    wt = NULL,
                    method = "same")

sample_index <- sample(1:1000, 100)

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

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

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

rm(example_data, reg_list, sample_index)