This method estimates the linear or quadratic parameters of the ADRF by estimating a leastsquares fit on the basis functions which are composed of combinations of the covariates, propensity spline basis, and treatment values.
1 2 3 4 5 6 7 8 9 10 11 12 13 14  prop_spline_est(Y,
treat,
covar_formula = ~ 1,
covar_lin_formula = ~ 1,
covar_sq_formula = ~ 1,
data,
e_treat_1 = NULL,
degree = 1,
wt = NULL,
method = "same",
spline_df = NULL,
spline_const = 1,
spline_linear = 1,
spline_quad = 1)

Y 
is the the name of the outcome variable contained in 
treat 
is the name of the treatment variable contained in

covar_formula 
is the formula to describe the covariates needed
to estimate the constant term:

covar_lin_formula 
is the formula to describe the covariates needed
to estimate the linear term, t:

covar_sq_formula 
is the formula to describe the covariates needed
to estimate the quadratic term, t^2:

data 
is a dataframe containing 
e_treat_1 
a vector, representing the conditional expectation of

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 with no spline terms. If method = "different", then different sets of covariates can be used to estimate the constant, linear, and/or quadratic term. To use spline terms, it is necessary to set method = "different". covar_lin_formula and covar_sq_formula must be specified if method = "different". 
spline_df 
degrees of freedom. The default, spline_df = NULL, corresponds to no knots. 
spline_const 
is the number of spline terms to include when estimating the constant term. 
spline_linear 
is the number of spline terms to include when estimating the linear term. 
spline_quad 
is the number of spline terms to include when estimating the quadratic term. 
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 and spline basis functions derived from the propensity function component.
prop_spline_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. 
Schafer, J.L., Galagate, D.L. (2015). Causal inference with a continuous treatment and outcome: alternative estimators for parametric doseresponse models. Manuscript in preparation.
Little, Roderick and An, Hyonggin (2004). ROBUST LIKELIHOODBASED ANALYSIS OF MULTIVARIATE DATA WITH MISSING VALUES. Statistica Sinica. 14: 949–968.
Schafer, Joseph L, Kang, Joseph (2008). Average causal effects from nonrandomized studies: a practical guide and simulated example. Psychological methods, 13.4, 279.
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 47 48 49 50  ## 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$T_data
full_data < cbind(example_data, cond_exp_data)
prop_spline_list < prop_spline_est(Y = Y,
treat = T,
covar_formula = ~ B.1 + B.2 + B.3 + B.4 + B.5 + B.6 + B.7 + B.8,
covar_lin_formula = ~ 1,
covar_sq_formula = ~ 1,
data = example_data,
e_treat_1 = full_data$est_treat,
degree = 1,
wt = NULL,
method = "different",
spline_df = 5,
spline_const = 4,
spline_linear = 4,
spline_quad = 4)
sample_index < sample(1:1000, 100)
plot(example_data$T[sample_index],
example_data$Y[sample_index],
xlab = "T",
ylab = "Y",
main = "propensity spline estimate")
abline(prop_spline_list$param[1],
prop_spline_list$param[2],
lty = 2,
col = "blue",
lwd = 2)
legend('bottomright',
"propensity spline estimate",
lty = 2,
bty = 'Y',
cex = 1,
col = "blue",
lwd = 2)
rm(example_data, prop_spline_list, sample_index)

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