mfrd_est  R Documentation 
mfrd_est
implements the frontier approach for multivariate regression discontinuity estimation in Wong, Steiner and Cook (2013).
It is based on the MFRDD code in Stata from Wong, Steiner, and Cook (2013).
mfrd_est( y, x1, x2, c1, c2, t.design = NULL, local = 0.15, front.bw = NA, m = 10, k = 5, kernel = "triangular", ngrid = 250, margin = 0.03, boot = NULL, cluster = NULL, stop.on.error = TRUE )
y 
A numeric object containing outcome variable. 
x1 
A numeric object containing the first assignment variable. 
x2 
A numeric object containing the second assignment variable. 
c1 
A numeric value containing the cutpoint at which assignment to the treatment is determined for 
c2 
A numeric value containing the cutpoint at which assignment to the treatment is determined for 
t.design 
A character vector of length 2 specifying the treatment option according to design.
The first entry is for 
local 
A nonnegative numeric value specifying the range of neighboring points around the cutoff on the standardized scale, for each assignment variable. The default is 0.15. 
front.bw 
A nonnegative numeric vector of length 3 specifying the bandwidths at which to estimate the RD for each
of three effects models (complete model, heterogeneous treatment model, and treatment only model)
detailed in Wong, Steiner, and Cook (2013).
If 
m 
A nonnegative integer specifying the number of uniformlyatrandom samples to draw as search candidates for 
k 
A nonnegative integer specifying the number of folds for crossvalidation to determine 
kernel 
A string indicating which kernel to use. Options are 
ngrid 
A nonnegative integer specifying the number of nonzero grid points on each assignment variable, which is also the number of zero grid points on each assignment variable. The default is 250. The value used in Wong, Steiner and Cook (2013) is 2500, which may cause long computational time. 
margin 
A nonnegative numeric value specifying the range of grid points beyond the minimum and maximum of sample points on each assignment variable. This grid is used to impute potential outcomes along the frontier, as in Wong, Steiner, and Cook (2013). The default is 0.03. 
boot 
An optional nonnegative integer specifying the number of bootstrap samples to obtain standard error of estimates. 
cluster 
An optional vector of length n specifying clusters within which the errors are assumed to be correlated. This will result in reporting cluster robust SEs. It is suggested that data with a discrete running variable be clustered by each unique value of the running variable (Lee and Card, 2008). 
stop.on.error 
A logical value indicating whether to remove bootstraps which cause error in the 
mfrd_est
returns an object of class "mfrd
".
The functions summary
and plot
are used to obtain and print a summary and
plot of the estimated regression discontinuity. The object of class mfrd
is a list
containing the following components:
w 
Numeric vector specifying the weight of frontier 1 and frontier 2, respectively. 
est 
Numeric matrix of the estimate of the discontinuity in the outcome under a complete model (no prefix), heterogeneous treatment (ht) effects model, and treatment (t) only model, for the parametric case and for each corresponding bandwidth. Estimates with suffix "ev1" and "ev2" correspond to expected values for each frontier, under a given model. Estimates with suffix "ate" correspond to average treatment effects across both frontiers, under a given model. 
d 
Numeric matrix of the effect size (Cohen's d) for estimate. 
se 
Numeric matrix of the standard error for each corresponding bandwidth and .... 
m_s 
A list containing estimates for the complete model, under parametric
and nonparametric (optimal, half, and double bandwidth) cases. A list of
coefficient estimates, residuals, effects, weights (in the nonparametric case),

m_h 
A list containing estimates for the heterogeneous treatments model, under parametric
and nonparametric (optimal, half, and double bandwidth) cases. A list of
coefficient estimates, residuals, effects, weights (in the nonparametric case),

m_t 
A list containing estimates for the treatment only model, under parametric
and nonparametric (optimal, half, and double bandwidth) cases. A list of
coefficient estimates, residuals, effects, weights (in the nonparametric case),

dat_h 
A list containing four data frames, one for each case: parametric or nonparametric (optimal, half, and double bandwidth). Each data frame contains functions and densities for each frontier and treatment model. 
dat 
A data frame containing the outcome ( 
obs 
List of the number of observations used in each model. 
impute 
A logical value indicating whether multiple imputation is used or not. 
call 
The matched call. 
front.bw 
Numeric vector of each bandwidth used to estimate the density at the frontier for the three effects models (complete model, heterogeneous treatment model, and treatment only model) detailed in Wong, Steiner, and Cook (2013). 
Wong, V., Steiner, P, and Cook, T. (2013). Analyzing regression discontinuity designs with multiple assignment variables: A comparative study of four estimation methods. Journal of Educational and Behavioral Statistics, 38(2), 107141. doi: 10.3102/1076998611432172.
Lee, D. and Card, D. (2008). A Regression discontinuity inference with specification error. Journal of Econometrics, 142(2), 655674. doi: 10.1016/j.jeconom.2007.05.003.
set.seed(12345) x1 < runif(1000, 1, 1) x2 < runif(1000, 1, 1) cov < rnorm(1000) y < 3 + 2 * (x1 >= 0) + 3 * cov + 10 * (x2 >= 0) + rnorm(1000) mfrd_est(y = y, x1 = x1, x2 = x2, c1 = 0, c2 = 0, t.design = c("geq", "geq"))
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