,
Bastiaan Quast [aut, cre] | Title: | Toolbox for Regression Discontinuity Design ('RDD') |
|---|---|
| Description: | Set of functions for Regression Discontinuity Design ('RDD'), for data visualisation, estimation and testing. |
| Authors: | Matthieu Stigler [aut] ,
Bastiaan Quast [aut, cre] |
| Maintainer: | Bastiaan Quast <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 2.0.0 |
| Built: | 2024-11-20 04:21:43 UTC |
| Source: | https://github.com/bquast/rddtools |
Convert a rdd object to lm
as.lm(x)as.lm(x)
x |
An object to convert to lm |
An object of class lm
as.npreg which converts rdd_reg objects into npreg from package np.
data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) reg_para <- rdd_reg_lm(rdd_object=house_rdd) reg_para_lm <- as.lm(reg_para) reg_para_lm plot(reg_para_lm, which=4)data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) reg_para <- rdd_reg_lm(rdd_object=house_rdd) reg_para_lm <- as.lm(reg_para) reg_para_lm plot(reg_para_lm, which=4)
npreg objectConvert an rdd_object to a non-parametric regression npreg from package np
as.npregbw(x, ...) as.npreg(x, ...)as.npregbw(x, ...) as.npreg(x, ...)
x |
Object of class |
... |
This function converts an rdd_reg object into an npreg object from package np
Note that the output won't be the same, since npreg does not offer a triangular kernel, but a Gaussian or Epanechinkov one.
Another reason why estimates might differ slightly is that npreg implements a multivariate kernel, while rdd_reg
proceeds as if the kernel was univariate. A simple solution to make the multivariate kernel similar to the univariate one
is to set the bandwidth for x and Dx to a large number, so that they converge towards a constant, and one obtains back the univariate kernel.
An object of class npreg or npregbw
as.lm which converts rdd_reg objects into lm.
# Estimate ususal rdd_reg: data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) reg_nonpara <- rdd_reg_np(rdd_object=house_rdd) ## Convert to npreg: reg_nonpara_np <- as.npreg(reg_nonpara) reg_nonpara_np rdd_coef(reg_nonpara_np, allCo=TRUE, allInfo=TRUE) ## Compare with result obtained with a Gaussian kernel: bw_lm <- dnorm(house_rdd$x, sd=rddtools:::getBW(reg_nonpara)) reg_nonpara_gaus <- rdd_reg_lm(rdd_object=house_rdd, w=bw_lm) all.equal(rdd_coef(reg_nonpara_gaus),rdd_coef(reg_nonpara_np))# Estimate ususal rdd_reg: data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) reg_nonpara <- rdd_reg_np(rdd_object=house_rdd) ## Convert to npreg: reg_nonpara_np <- as.npreg(reg_nonpara) reg_nonpara_np rdd_coef(reg_nonpara_np, allCo=TRUE, allInfo=TRUE) ## Compare with result obtained with a Gaussian kernel: bw_lm <- dnorm(house_rdd$x, sd=rddtools:::getBW(reg_nonpara)) reg_nonpara_gaus <- rdd_reg_lm(rdd_object=house_rdd, w=bw_lm) all.equal(rdd_coef(reg_nonpara_gaus),rdd_coef(reg_nonpara_np))
Correct standard-errors to account for clustered data, doing either a degrees of freedom correction or using a heteroskedasticidty-cluster robust covariance matrix possibly on the range specified by bandwidth
clusterInf(object, clusterVar, vcov. = NULL, type = c("df-adj", "HC"), ...)clusterInf(object, clusterVar, vcov. = NULL, type = c("df-adj", "HC"), ...)
object |
Object of class lm, from which rdd_reg also inherits. |
clusterVar |
The variable containing the cluster attributions. |
vcov. |
Specific covariance function to pass to coeftest. See help of sandwich |
type |
The type of cluster correction to use: either the degrees of freedom, or a HC matrix. |
... |
Further arguments passed to coeftest |
The output of the coeftest function, which is itself of class coeftest
Wooldridge (2003) Cluster-sample methods in applied econometrics. AmericanEconomic Review, 93, p. 133-138
vcovCluster, which implements the cluster-robust covariance matrix estimator used by cluserInf
data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) reg_para <- rdd_reg_lm(rdd_object=house_rdd) # here we just generate randomly a cluster variable: nlet <- sort(c(outer(letters, letters, paste, sep=''))) clusRandom <- sample(nlet[1:60], size=nrow(house_rdd), replace=TRUE) # now do post-inference: clusterInf(reg_para, clusterVar=clusRandom) clusterInf(reg_para, clusterVar=clusRandom, type='HC')data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) reg_para <- rdd_reg_lm(rdd_object=house_rdd) # here we just generate randomly a cluster variable: nlet <- sort(c(outer(letters, letters, paste, sep=''))) clusRandom <- sample(nlet[1:60], size=nrow(house_rdd), replace=TRUE) # now do post-inference: clusterInf(reg_para, clusterVar=clusRandom) clusterInf(reg_para, clusterVar=clusRandom, type='HC')
Tests equality of distribution with a Kolmogorov-Smirnov for each covariates, between the two full groups or around the discontinuity threshold
covarTest_dis( object, bw, exact = NULL, p.adjust = c("none", "holm", "BH", "BY", "hochberg", "hommel", "bonferroni") ) ## S3 method for class 'rdd_data' covarTest_dis( object, bw = NULL, exact = FALSE, p.adjust = c("none", "holm", "BH", "BY", "hochberg", "hommel", "bonferroni") ) ## S3 method for class 'rdd_reg' covarTest_dis( object, bw = NULL, exact = FALSE, p.adjust = c("none", "holm", "BH", "BY", "hochberg", "hommel", "bonferroni") )covarTest_dis( object, bw, exact = NULL, p.adjust = c("none", "holm", "BH", "BY", "hochberg", "hommel", "bonferroni") ) ## S3 method for class 'rdd_data' covarTest_dis( object, bw = NULL, exact = FALSE, p.adjust = c("none", "holm", "BH", "BY", "hochberg", "hommel", "bonferroni") ) ## S3 method for class 'rdd_reg' covarTest_dis( object, bw = NULL, exact = FALSE, p.adjust = c("none", "holm", "BH", "BY", "hochberg", "hommel", "bonferroni") )
object |
object of class rdd_data |
bw |
a bandwidth |
exact |
Argument of the |
p.adjust |
Whether to adjust the p-values for multiple testing. Uses the |
A data frame with, for each covariate, the K-S statistic and its p-value.
Matthieu Stigler <[email protected]>
covarTest_mean for the t-test of equality of means
data(house) ## Add randomly generated covariates set.seed(123) n_Lee <- nrow(house) Z <- data.frame(z1 = rnorm(n_Lee, sd=2), z2 = rnorm(n_Lee, mean = ifelse(house<0, 5, 8)), z3 = sample(letters, size = n_Lee, replace = TRUE)) house_rdd_Z <- rdd_data(y = house$y, x = house$x, covar = Z, cutpoint = 0) ## Kolmogorov-Smirnov test of equality in distribution: covarTest_dis(house_rdd_Z, bw=0.3) ## Can also use function covarTest_dis() for a t-test for equality of means around cutoff: covarTest_mean(house_rdd_Z, bw=0.3) ## covarTest_dis works also on regression outputs (bw will be taken from the model) reg_nonpara <- rdd_reg_np(rdd_object=house_rdd_Z) covarTest_dis(reg_nonpara)data(house) ## Add randomly generated covariates set.seed(123) n_Lee <- nrow(house) Z <- data.frame(z1 = rnorm(n_Lee, sd=2), z2 = rnorm(n_Lee, mean = ifelse(house<0, 5, 8)), z3 = sample(letters, size = n_Lee, replace = TRUE)) house_rdd_Z <- rdd_data(y = house$y, x = house$x, covar = Z, cutpoint = 0) ## Kolmogorov-Smirnov test of equality in distribution: covarTest_dis(house_rdd_Z, bw=0.3) ## Can also use function covarTest_dis() for a t-test for equality of means around cutoff: covarTest_mean(house_rdd_Z, bw=0.3) ## covarTest_dis works also on regression outputs (bw will be taken from the model) reg_nonpara <- rdd_reg_np(rdd_object=house_rdd_Z) covarTest_dis(reg_nonpara)
Tests equality of means by a t-test for each covariate, between the two full groups or around the discontinuity threshold
covarTest_mean( object, bw = NULL, paired = FALSE, var.equal = FALSE, p.adjust = c("none", "holm", "BH", "BY", "hochberg", "hommel", "bonferroni") ) ## S3 method for class 'rdd_data' covarTest_mean( object, bw = NULL, paired = FALSE, var.equal = FALSE, p.adjust = c("none", "holm", "BH", "BY", "hochberg", "hommel", "bonferroni") ) ## S3 method for class 'rdd_reg' covarTest_mean( object, bw = NULL, paired = FALSE, var.equal = FALSE, p.adjust = c("none", "holm", "BH", "BY", "hochberg", "hommel", "bonferroni") )covarTest_mean( object, bw = NULL, paired = FALSE, var.equal = FALSE, p.adjust = c("none", "holm", "BH", "BY", "hochberg", "hommel", "bonferroni") ) ## S3 method for class 'rdd_data' covarTest_mean( object, bw = NULL, paired = FALSE, var.equal = FALSE, p.adjust = c("none", "holm", "BH", "BY", "hochberg", "hommel", "bonferroni") ) ## S3 method for class 'rdd_reg' covarTest_mean( object, bw = NULL, paired = FALSE, var.equal = FALSE, p.adjust = c("none", "holm", "BH", "BY", "hochberg", "hommel", "bonferroni") )
object |
object of class rdd_data |
bw |
a bandwidth |
paired |
Argument of the |
var.equal |
Argument of the |
p.adjust |
Whether to adjust the p-values for multiple testing. Uses the |
A data frame with, for each covariate, the mean on each size, the difference, t-stat and ts p-value.
Matthieu Stigler <[email protected]>
covarTest_dis for the Kolmogorov-Smirnov test of equality of distribution
data(house) ## Add randomly generated covariates set.seed(123) n_Lee <- nrow(house) Z <- data.frame(z1 = rnorm(n_Lee, sd=2), z2 = rnorm(n_Lee, mean = ifelse(house<0, 5, 8)), z3 = sample(letters, size = n_Lee, replace = TRUE)) house_rdd_Z <- rdd_data(y = house$y, x = house$x, covar = Z, cutpoint = 0) ## test for equality of means around cutoff: covarTest_mean(house_rdd_Z, bw=0.3) ## Can also use function covarTest_dis() for Kolmogorov-Smirnov test: covarTest_dis(house_rdd_Z, bw=0.3) ## covarTest_mean works also on regression outputs (bw will be taken from the model) reg_nonpara <- rdd_reg_np(rdd_object=house_rdd_Z) covarTest_mean(reg_nonpara)data(house) ## Add randomly generated covariates set.seed(123) n_Lee <- nrow(house) Z <- data.frame(z1 = rnorm(n_Lee, sd=2), z2 = rnorm(n_Lee, mean = ifelse(house<0, 5, 8)), z3 = sample(letters, size = n_Lee, replace = TRUE)) house_rdd_Z <- rdd_data(y = house$y, x = house$x, covar = Z, cutpoint = 0) ## test for equality of means around cutoff: covarTest_mean(house_rdd_Z, bw=0.3) ## Can also use function covarTest_dis() for Kolmogorov-Smirnov test: covarTest_dis(house_rdd_Z, bw=0.3) ## covarTest_mean works also on regression outputs (bw will be taken from the model) reg_nonpara <- rdd_reg_np(rdd_object=house_rdd_Z) covarTest_mean(reg_nonpara)
Calls the DCdensity test from package rdd on a rdd_object.
dens_test(rdd_object, bin = NULL, bw = NULL, plot = TRUE, ...)dens_test(rdd_object, bin = NULL, bw = NULL, plot = TRUE, ...)
rdd_object |
object of class rdd_data |
bin |
Argument of the |
bw |
Argument of the |
plot |
Whether to return a plot. Logical, default ot TRUE. |
... |
Further arguments passed to |
data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) dens_test(house_rdd)data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) dens_test(house_rdd)
Generate the simulations reported in Imbens and Kalyanaraman (2012)
gen_mc_ik( n = 200, version = 1, sd = 0.1295, output = c("data.frame", "rdd_data"), size )gen_mc_ik( n = 200, version = 1, sd = 0.1295, output = c("data.frame", "rdd_data"), size )
n |
The size of sampel to generate |
version |
The MC version of Imbens and Kalnayaraman (between 1 and 4). |
sd |
The standard deviation of the error term. |
output |
Whether to return a data-frame, or already a rdd_data |
size |
The size of the effect, this depends on the specific version, defaults are as in ik: 0.04, NULL, 0.1, 0.1 |
An data frame with x and y variables.
mc1_dat <- gen_mc_ik() MC1_rdd <- rdd_data(y=mc1_dat$y, x=mc1_dat$x, cutpoint=0) ## Use np regression: reg_nonpara <- rdd_reg_np(rdd_object=MC1_rdd) reg_nonpara # Represent the curves: plotCu <- function(version=1, xlim=c(-0.1,0.1)){ res <- gen_mc_ik(sd=0.0000001, n=1000, version=version) res <- res[order(res$x),] ylim <- range(subset(res, x>=min(xlim) & x<=max(xlim), 'y')) plot(res, type='l', xlim=xlim, ylim=ylim, main=paste('DGP', version)) abline(v=0) xCut <- res[which(res$x==min(res$x[res$x>=0]))+c(0,-1),] points(xCut, col=2) } layout(matrix(1:4,2, byrow=TRUE)) plotCu(version=1) plotCu(version=2) plotCu(version=3) plotCu(version=4) layout(matrix(1))mc1_dat <- gen_mc_ik() MC1_rdd <- rdd_data(y=mc1_dat$y, x=mc1_dat$x, cutpoint=0) ## Use np regression: reg_nonpara <- rdd_reg_np(rdd_object=MC1_rdd) reg_nonpara # Represent the curves: plotCu <- function(version=1, xlim=c(-0.1,0.1)){ res <- gen_mc_ik(sd=0.0000001, n=1000, version=version) res <- res[order(res$x),] ylim <- range(subset(res, x>=min(xlim) & x<=max(xlim), 'y')) plot(res, type='l', xlim=xlim, ylim=ylim, main=paste('DGP', version)) abline(v=0) xCut <- res[which(res$x==min(res$x[res$x>=0]))+c(0,-1),] points(xCut, col=2) } layout(matrix(1:4,2, byrow=TRUE)) plotCu(version=1) plotCu(version=2) plotCu(version=3) plotCu(version=4) layout(matrix(1))
Randomized experiments from non-random selection in U.S. House elections
Dataset described used in Imbens and Kalyamaran (2012), and probably the same dataset used in Lee (2008),
A data frame with 6558 observations and two variables:
Vote at election t-1
Vote at election t
Guido Imbens webpage: https://scholar.harvard.edu/imbens/scholar_software/regression-discontinuity
Imbens, Guido and Karthik Kalyanaraman. (2012) 'Optimal Bandwidth Choice for the regression discontinuity estimator,' Review of Economic Studies (2012) 79, 933-959
Lee, D. (2008) Randomized experiments from non-random selection in U.S. House elections, Journal of Econometrics, 142, 675-697
data(house) rdd_house <- rdd_data(x=x, y=y, data=house, cutpoint=0) summary(rdd_house) plot(rdd_house)data(house) rdd_house <- rdd_data(x=x, y=y, data=house, cutpoint=0) summary(rdd_house) plot(rdd_house)
Data from the Initiative Nationale du Development Humaine, collected as the part of the SNSF project "Development Aid and Social Dynamics"
A data frame with two variables with 720 observations each
Arcand, Rieger, and Nguyen (2015) 'Development Aid and Social Dyanmics Data Set'
# load the data data(indh) # construct rdd_data frame rdd_dat_indh <- rdd_data(y=choice_pg, x=poverty, data=indh, cutpoint=30) # inspect data frame summary(rdd_dat_indh) # perform non-parametric regression ( reg_np_indh <- rdd_reg_np(rdd_dat_indh) )# load the data data(indh) # construct rdd_data frame rdd_dat_indh <- rdd_data(y=choice_pg, x=poverty, data=indh, cutpoint=30) # inspect data frame summary(rdd_dat_indh) # perform non-parametric regression ( reg_np_indh <- rdd_reg_np(rdd_dat_indh) )
Binned plot of the forcing and outcome variable
## S3 method for class 'rdd_data' plot( x, h = NULL, nbins = NULL, xlim = range(object$x, na.rm = TRUE), cex = 0.7, nplot = 1, device = c("base", "ggplot"), ... )## S3 method for class 'rdd_data' plot( x, h = NULL, nbins = NULL, xlim = range(object$x, na.rm = TRUE), cex = 0.7, nplot = 1, device = c("base", "ggplot"), ... )
x |
Object of class rdd_data |
h |
The binwidth parameter (note this differs from the bandwidth parameter!) |
nbins |
Alternative to h, the total number of bins in the plot. |
xlim |
The range of the x data |
cex |
Size of the points, see |
nplot |
Number of plot to draw |
device |
Type of device used. Currently not used. |
... |
Further arguments passed to the |
Produces a simple binned plot averaging values within each interval. The length of the intervals
is specified with the argument h, specifying the whole binwidth (contrary to the usual bandwidth
argument, that gives half of the length of the kernel window.
When no bandwidth is given, the bandwidth of Ruppert et al is used, see rdd_bw_rsw.
A plot
Matthieu Stigler <[email protected]>
data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) plot(house_rdd) ## Specify manually the bandwidth: plot(house_rdd, h=0.2) ## Show three plots with different bandwidth: plot(house_rdd, h=c(0.2,0.3,0.4), nplot=3) ## Specify instead of the bandwidth, the final number of bins: plot(house_rdd, nbins=22) ## If the specified number of bins is odd, the larger number is given to side with largest range plot(house_rdd, nbins=21)data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) plot(house_rdd) ## Specify manually the bandwidth: plot(house_rdd, h=0.2) ## Show three plots with different bandwidth: plot(house_rdd, h=c(0.2,0.3,0.4), nplot=3) ## Specify instead of the bandwidth, the final number of bins: plot(house_rdd, nbins=22) ## If the specified number of bins is odd, the larger number is given to side with largest range plot(house_rdd, nbins=21)
Do a 'scatterplot bin smoothing'
plotBin( x, y, h = NULL, nbins = NULL, cutpoint = 0, plot = TRUE, type = c("value", "number"), xlim = range(x, na.rm = TRUE), cex = 0.9, main = NULL, xlab, ylab, ... )plotBin( x, y, h = NULL, nbins = NULL, cutpoint = 0, plot = TRUE, type = c("value", "number"), xlim = range(x, na.rm = TRUE), cex = 0.9, main = NULL, xlab, ylab, ... )
x |
Forcing variable |
y |
Output |
h |
the bandwidth (defaults to |
nbins |
number of Bins |
cutpoint |
Cutpoint |
plot |
Logical. Whether to plot or only returned silently |
type |
Whether returns the y averages, or the x frequencies |
xlim, cex, main, xlab, ylab
|
Usual parameters passed to plot(), see |
... |
further arguments passed to plot. |
Returns silently values
McCrary, Justin.
Draw a plot of placebo tests, estimating the impact on fake cutpoints
plotPlacebo(object, device = c("ggplot", "base"), ...) ## S3 method for class 'rdd_reg' plotPlacebo( object, device = c("ggplot", "base"), from = 0.25, to = 0.75, by = 0.1, level = 0.95, same_bw = FALSE, vcov. = NULL, plot = TRUE, output = c("data", "ggplot"), ... ) plotPlaceboDens(object, device = c("ggplot", "base"), ...) ## S3 method for class 'rdd_reg' plotPlaceboDens( object, device = c("ggplot", "base"), from = 0.25, to = 0.75, by = 0.1, level = 0.95, same_bw = FALSE, vcov. = NULL, ... ) computePlacebo( object, from = 0.25, to = 0.75, by = 0.1, level = 0.95, same_bw = FALSE, vcov. = NULL )plotPlacebo(object, device = c("ggplot", "base"), ...) ## S3 method for class 'rdd_reg' plotPlacebo( object, device = c("ggplot", "base"), from = 0.25, to = 0.75, by = 0.1, level = 0.95, same_bw = FALSE, vcov. = NULL, plot = TRUE, output = c("data", "ggplot"), ... ) plotPlaceboDens(object, device = c("ggplot", "base"), ...) ## S3 method for class 'rdd_reg' plotPlaceboDens( object, device = c("ggplot", "base"), from = 0.25, to = 0.75, by = 0.1, level = 0.95, same_bw = FALSE, vcov. = NULL, ... ) computePlacebo( object, from = 0.25, to = 0.75, by = 0.1, level = 0.95, same_bw = FALSE, vcov. = NULL )
object |
the output of an RDD regression |
device |
Whether to draw a base or a ggplot graph. |
from |
Starting point of the fake cutpoints sequence. Refers ot the quantile of each side of the true cutpoint |
to |
Ending point of the fake cutpoints sequence. Refers ot the quantile of each side of the true cutpoint |
by |
Increments of the from-to sequence |
level |
Level of the confidence interval shown |
same_bw |
Whether to re-estimate the bandwidth at each point |
vcov. |
Specific covariance function to pass to coeftest. See help of package |
plot |
Whether to actually plot the data. |
output |
Whether to return (invisibly) the data frame containing the bandwidths and corresponding estimates, or the ggplot object |
... |
Further arguments passed to specific methods. |
A data frame containing the cutpoints, their corresponding estimates and confidence intervals.
Matthieu Stigler <[email protected]>
data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) reg_nonpara <- rdd_reg_np(rdd_object=house_rdd) plotPlacebo(reg_nonpara) # Use with another vcov function; cluster case reg_nonpara_lminf <- rdd_reg_np(rdd_object=house_rdd, inference='lm') # need to be a function applied to updated object! vc <- function(x) vcovCluster(x, clusterVar=model.frame(x)$x) plotPlacebo(reg_nonpara_lminf, vcov. = vc)data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) reg_nonpara <- rdd_reg_np(rdd_object=house_rdd) plotPlacebo(reg_nonpara) # Use with another vcov function; cluster case reg_nonpara_lminf <- rdd_reg_np(rdd_object=house_rdd, inference='lm') # need to be a function applied to updated object! vc <- function(x) vcovCluster(x, clusterVar=model.frame(x)$x) plotPlacebo(reg_nonpara_lminf, vcov. = vc)
Draw a plot showing the LATE estimates depending on multiple bandwidths
plotSensi( rdd_regobject, from, to, by = 0.01, level = 0.95, output = c("data", "ggplot"), plot = TRUE, ... ) ## S3 method for class 'rdd_reg_np' plotSensi( rdd_regobject, from, to, by = 0.05, level = 0.95, output = c("data", "ggplot"), plot = TRUE, device = c("ggplot", "base"), vcov. = NULL, ... ) ## S3 method for class 'rdd_reg_lm' plotSensi( rdd_regobject, from, to, by = 0.05, level = 0.95, output = c("data", "ggplot"), plot = TRUE, order, type = c("colour", "facet"), ... )plotSensi( rdd_regobject, from, to, by = 0.01, level = 0.95, output = c("data", "ggplot"), plot = TRUE, ... ) ## S3 method for class 'rdd_reg_np' plotSensi( rdd_regobject, from, to, by = 0.05, level = 0.95, output = c("data", "ggplot"), plot = TRUE, device = c("ggplot", "base"), vcov. = NULL, ... ) ## S3 method for class 'rdd_reg_lm' plotSensi( rdd_regobject, from, to, by = 0.05, level = 0.95, output = c("data", "ggplot"), plot = TRUE, order, type = c("colour", "facet"), ... )
rdd_regobject |
object of a RDD regression, from either |
from |
First bandwidth point. Default value is max(1e-3, bw-0.1) |
to |
Last bandwidth point. Default value is bw+0.1 |
by |
Increments in the |
level |
Level of the confidence interval |
output |
Whether to return (invisibly) the data frame containing the bandwidths and corresponding estimates, or the ggplot object |
plot |
Whether to actually plot the data. |
device |
Whether to draw a base or a ggplot graph. |
vcov. |
Specific covariance function to pass to coeftest. See help of package |
order |
For parametric models (from |
type |
For parametric models (from |
... |
Further arguments passed to specific methods |
A data frame containing the bandwidths and corresponding estimates and confidence intervals.
Matthieu Stigler <[email protected]>
data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) #Non-parametric estimate bw_ik <- rdd_bw_ik(house_rdd) reg_nonpara <- rdd_reg_np(rdd_object=house_rdd, bw=bw_ik) plotSensi(reg_nonpara) plotSensi(reg_nonpara, device='base') #Parametric estimate: reg_para_ik <- rdd_reg_lm(rdd_object=house_rdd, order=4, bw=bw_ik) plotSensi(reg_para_ik) plotSensi(reg_para_ik, type='facet')data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) #Non-parametric estimate bw_ik <- rdd_bw_ik(house_rdd) reg_nonpara <- rdd_reg_np(rdd_object=house_rdd, bw=bw_ik) plotSensi(reg_nonpara) plotSensi(reg_nonpara, device='base') #Parametric estimate: reg_para_ik <- rdd_reg_lm(rdd_object=house_rdd, order=4, bw=bw_ik) plotSensi(reg_para_ik) plotSensi(reg_para_ik, type='facet')
Simple wrapper of the Calonico-Cattaneo-Titiunik (2014) bandwidth selection procedures
for RDD estimators rdbwselect.
rdd_bw_cct_estim( rdd_object, method = c("mserd", "msetwo", "msesum", "msecomb1", "msecomb2", "cerrd", "certwo", "cersum", "cercomb1"), kernel = c("Triangular", "Uniform", "Epanechnikov"), ... )rdd_bw_cct_estim( rdd_object, method = c("mserd", "msetwo", "msesum", "msecomb1", "msecomb2", "cerrd", "certwo", "cersum", "cercomb1"), kernel = c("Triangular", "Uniform", "Epanechnikov"), ... )
rdd_object |
of class rdd_data created by |
method |
The type of method used. See |
kernel |
The type of kernel used: either |
... |
further arguments passed to |
See documentation of rdbwselect
Original code written by Calonico, Cattaneo, Farrell and Titiuni, see rdbwselect
Calonico, S., M. D. Cattaneo, and R. Titiunik. 2014a. Robust Nonparametric Confidence Intervals for Regression-Discontinuity Designs. Econometrica 82(6): 2295-2326. https://www.tandfonline.com/doi/abs/10.1080/01621459.2015.1017578.
rdd_bw_ik Local RDD bandwidth selector using the plug-in method of Imbens and Kalyanaraman (2012)
data(house) rd<- rdd_data(x=house$x, y=house$y, cutpoint=0) rdd_bw_cct_estim(rd)data(house) rd<- rdd_data(x=house$x, y=house$y, cutpoint=0) rdd_bw_cct_estim(rd)
Simple wrapper of the Calonico-Cattaneo-Titiunik (2015) bandwidth selection procedures
for RDD visualisation rdplot.
rdd_bw_cct_plot( rdd_object, method = c("esmv", "es", "espr", "esmvpr", "qs", "qspr", "qsmv", "qsmvpr"), ... )rdd_bw_cct_plot( rdd_object, method = c("esmv", "es", "espr", "esmvpr", "qs", "qspr", "qsmv", "qsmvpr"), ... )
rdd_object |
of class rdd_data created by |
method |
The type of method used. See |
... |
further arguments passed to |
See documentation of rdplot
Original code written by Calonico, Cattaneo, Farrell and Titiuni, see rdplot
Calonico, S., M. D. Cattaneo, and R. Titiunik. 2015a. Optimal Data-Driven Regression Discontinuity Plots. Journal of the American Statistical Association 110(512): 1753-1769. https://www.tandfonline.com/doi/abs/10.1080/01621459.2015.1017578.
rdd_bw_ik Local RDD bandwidth selector using the plug-in method of Imbens and Kalyanaraman (2012)
data(house) rd<- rdd_data(x=house$x, y=house$y, cutpoint=0) rdd_bw_cct_plot(rd)data(house) rd<- rdd_data(x=house$x, y=house$y, cutpoint=0) rdd_bw_cct_plot(rd)
Imbens-Kalyanaraman optimal bandwidth for local linear regression in Regression discontinuity designs.
rdd_bw_ik(rdd_object, kernel = c("Triangular", "Uniform", "Normal"))rdd_bw_ik(rdd_object, kernel = c("Triangular", "Uniform", "Normal"))
rdd_object |
of class rdd_data created by |
kernel |
The type of kernel used: either |
The optimal bandwidth
Matthieu Stigler <[email protected]>
Imbens, Guido and Karthik Kalyanaraman. (2012) 'Optimal Bandwidth Choice for the regression discontinuity estimator,' Review of Economic Studies (2012) 79, 933-959
rdd_bw_rsw Global bandwidth selector of Ruppert, Sheather and Wand (1995)
data(house) rd<- rdd_data(x=house$x, y=house$y, cutpoint=0) rdd_bw_ik(rd)data(house) rd<- rdd_data(x=house$x, y=house$y, cutpoint=0) rdd_bw_ik(rd)
Uses the global bandwidth selector of Ruppert, Sheather and Wand (1995) either to the whole function, or to the functions below and above the cutpoint.
rdd_bw_rsw(object, type = c("global", "sided"))rdd_bw_rsw(object, type = c("global", "sided"))
object |
object of class rdd_data created by |
type |
Whether to choose a global bandwidth for the whole function ( |
One (or two for sided) bandwidth value.
See dpill
rdd_bw_ik Local RDD bandwidth selector using the plug-in method of Imbens and Kalyanaraman (2012)
data(house) rd<- rdd_data(x=house$x, y=house$y, cutpoint=0) rdd_bw_rsw(rd)data(house) rd<- rdd_data(x=house$x, y=house$y, cutpoint=0) rdd_bw_rsw(rd)
Function to access the RDD coefficient in the various regressions
rdd_coef(object, allInfo = FALSE, allCo = FALSE, ...) ## Default S3 method: rdd_coef(object, allInfo = FALSE, allCo = FALSE, ...) ## S3 method for class 'rdd_reg_np' rdd_coef(object, allInfo = FALSE, allCo = FALSE, ...)rdd_coef(object, allInfo = FALSE, allCo = FALSE, ...) ## Default S3 method: rdd_coef(object, allInfo = FALSE, allCo = FALSE, ...) ## S3 method for class 'rdd_reg_np' rdd_coef(object, allInfo = FALSE, allCo = FALSE, ...)
object |
A RDD regression object |
allInfo |
whether to return just the coefficients (allInfo=FALSE) or also the se/t stat/pval. |
allCo |
Whether to give only the RDD coefficient (allCo=FALSE) or all coefficients |
... |
Further arguments passed to/from specific methods |
Either a numeric value of the RDD coefficient estimate, or a data frame with the estimate, its standard value, t test and p-value and
Construct the base RDD object, containing x, y and the cutpoint, eventuallay covariates.
rdd_data(y, x, covar, cutpoint, z, labels, data)rdd_data(y, x, covar, cutpoint, z, labels, data)
y |
Output |
x |
Forcing variable |
covar |
Exogeneous variables |
cutpoint |
Cutpoint |
z |
Assignment variable for the fuzzy case. Should be 0/1 or TRUE/FALSE variable. |
labels |
Additional labels to provide as list (with entries |
data |
A data-frame for the |
Arguments x, y (and eventually covar) can be either given as:
vectors (eventually data-frame for covar)
quote/character when data is also provided. For multiple covar, use a vector of characters
Object of class rdd_data, inheriting from data.frame
Matthieu Stigler [email protected]
data(house) rd <- rdd_data(x=house$x, y=house$y, cutpoint=0) rd2 <- rdd_data(x=x, y=y, data=house, cutpoint=0) # The print() function is the same as the print.data.frame: rd # The summary() and plot() function are specific to rdd_data summary(rd) plot(rd) # for the fuzzy case, you need to specify the assignment variable z: rd_dat_fakefuzzy <- rdd_data(x=house$x, y=house$y, z=ifelse(house$x>0+rnorm(nrow(house), sd=0.05),1,0), cutpoint=0) summary(rd_dat_fakefuzzy)data(house) rd <- rdd_data(x=house$x, y=house$y, cutpoint=0) rd2 <- rdd_data(x=x, y=y, data=house, cutpoint=0) # The print() function is the same as the print.data.frame: rd # The summary() and plot() function are specific to rdd_data summary(rd) plot(rd) # for the fuzzy case, you need to specify the assignment variable z: rd_dat_fakefuzzy <- rdd_data(x=house$x, y=house$y, z=ifelse(house$x>0+rnorm(nrow(house), sd=0.05),1,0), cutpoint=0) summary(rd_dat_fakefuzzy)
Compute RDD estimate allowing a locally kernel weighted version of any estimation function possibly on the range specified by bandwidth
rdd_gen_reg( rdd_object, fun = glm, covariates = NULL, order = 1, bw = NULL, slope = c("separate", "same"), covar.opt = list(strategy = c("include", "residual"), slope = c("same", "separate"), bw = NULL), weights, ... )rdd_gen_reg( rdd_object, fun = glm, covariates = NULL, order = 1, bw = NULL, slope = c("separate", "same"), covar.opt = list(strategy = c("include", "residual"), slope = c("same", "separate"), bw = NULL), weights, ... )
rdd_object |
Object of class rdd_data created by |
fun |
The function to estimate the parameters |
covariates |
Formula to include covariates |
order |
Order of the polynomial regression. |
bw |
A bandwidth to specify the subset on which the kernel weighted regression is estimated |
slope |
Whether slopes should be different on left or right (separate), or the same. |
covar.opt |
Options for the inclusion of covariates. Way to include covariates, either in the main regression ( |
weights |
Optional weights to pass to the lm function. Note this cannot be entered together with |
... |
Further arguments passed to fun. See the example. |
This function allows the user to use a custom estimating function, instead of the traditional lm().
It is assumed that the custom funciton has following behaviour:
A formula interface, together with a data argument
A weight argument
A coef(summary(x)) returning a data-frame containing a column Estimate
Note that for the last requirement, this can be accomodated by writing a specific rdd_coef
function for the class of the object returned by fun.
An object of class rdd_reg_lm and class lm, with specific print and plot methods
TODO
## Step 0: prepare data data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) ## Estimate a local probit: house_rdd$y <- with(house_rdd, ifelse(y<quantile(y, 0.25), 0,1)) reg_bin_glm <- rdd_gen_reg(rdd_object=house_rdd, fun= glm, family=binomial(link='probit')) print(reg_bin_glm) summary(reg_bin_glm)## Step 0: prepare data data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) ## Estimate a local probit: house_rdd$y <- with(house_rdd, ifelse(y<quantile(y, 0.25), 0,1)) reg_bin_glm <- rdd_gen_reg(rdd_object=house_rdd, fun= glm, family=binomial(link='probit')) print(reg_bin_glm) summary(reg_bin_glm)
Function to predict the RDD coefficient in presence of covariate (without covariates, returns the same than rdd_coef)
rdd_pred( object, covdata, se.fit = TRUE, vcov. = NULL, newdata, stat = c("identity", "sum", "mean"), weights )rdd_pred( object, covdata, se.fit = TRUE, vcov. = NULL, newdata, stat = c("identity", "sum", "mean"), weights )
object |
A RDD regression object |
covdata |
New data.frame specifying the values of the covariates, can have multiple rows. |
se.fit |
A switch indicating if standard errors are required. |
vcov. |
Specific covariance function (see package sandwich ), by default uses the |
newdata |
Another data on which to evaluate the x/D variables. Useful in very few cases. |
stat |
The statistic to use if there are multiple predictions, 'identity' just returns the single values, 'mean' averages them |
weights |
Eventual weights for the averaging of the predicted values. |
The function rdd_pred does a simple prediction of the RDD effect
When there are no covariates (and z is irrelevant in the equation above), this amounts exactly to the usual RDD coefficient,
shown in the outputs, or obtained with rdd_coef. If there were covariates, and if these covariates were estimated using the
“include” strategy and with different coefficients left and right to the cutoff (i.e.
had argument slope = “separate”), than the RDD effect is also dependent on the value of the covariate(s).
rdd_pred allows to set the value of the covariate(s) at which to evaluate the RDD effect, by providing a data.frame with
the values for the covariates. Note that the effect can be evaluated at multiple points, if you provide multiple rows of covdata.
In pressence of covariate-specific RDD effect, one may wish to estimate an average effect. This can be done by setting the argument stat='mean'.
Weights can additionally be added, with the argument weights, to obtain a weighted-average of the predictions. Note however that in most cases,
this will be equivalent to provide covariates at their (weighted) mean value, which will be much faster also!
Standard errors, obtained setting the argument se.fit=TRUE, are computed using following formula:
where is the estimated variance-covariance matrix ( by default using vcov) and
is the input data (a mix of covdata and input data). If one wishes individual predictions, standard errors are simply obtained
as the square of that diagonal matrix, whereas for mean/sum, covariances are taken into account.
Returns the predicted value(s), and, if se.fit=TRUE, their standard errors.
Froehlich (2007) Regression discontinuity design with covariates, IZA discussion paper 3024
# Load data, add (artificial) covariates: data(house) n_Lee <- nrow(house) z1 <- runif(n_Lee) house_rdd <- rdd_data(y=y, x=x, data=house, covar=z1, cutpoint=0) # estimation without covariates: rdd_pred is the same than rdd_coef: reg_para <- rdd_reg_lm(rdd_object=house_rdd) rdd_pred(reg_para) rdd_coef(reg_para, allInfo=TRUE) # estimation with covariates: reg_para_cov <- rdd_reg_lm(rdd_object=house_rdd, covariates='z1', covar.opt=list(slope='separate') ) # should obtain same result as with RDestimate rdd_pred(reg_para_cov, covdata=data.frame(z1=0)) # evaluate at mean of z1 (as comes from uniform) rdd_pred(reg_para_cov, covdata=data.frame(z1=0.5))# Load data, add (artificial) covariates: data(house) n_Lee <- nrow(house) z1 <- runif(n_Lee) house_rdd <- rdd_data(y=y, x=x, data=house, covar=z1, cutpoint=0) # estimation without covariates: rdd_pred is the same than rdd_coef: reg_para <- rdd_reg_lm(rdd_object=house_rdd) rdd_pred(reg_para) rdd_coef(reg_para, allInfo=TRUE) # estimation with covariates: reg_para_cov <- rdd_reg_lm(rdd_object=house_rdd, covariates='z1', covar.opt=list(slope='separate') ) # should obtain same result as with RDestimate rdd_pred(reg_para_cov, covdata=data.frame(z1=0)) # evaluate at mean of z1 (as comes from uniform) rdd_pred(reg_para_cov, covdata=data.frame(z1=0.5))
Compute a parametric polynomial regression of the ATE, possibly on the range specified by bandwidth
rdd_reg_lm( rdd_object, covariates = NULL, order = 1, bw = NULL, slope = c("separate", "same"), covar.opt = list(strategy = c("include", "residual"), slope = c("same", "separate"), bw = NULL), covar.strat = c("include", "residual"), weights )rdd_reg_lm( rdd_object, covariates = NULL, order = 1, bw = NULL, slope = c("separate", "same"), covar.opt = list(strategy = c("include", "residual"), slope = c("same", "separate"), bw = NULL), covar.strat = c("include", "residual"), weights )
rdd_object |
Object of class rdd_data created by |
covariates |
Formula to include covariates |
order |
Order of the polynomial regression. |
bw |
A bandwidth to specify the subset on which the parametric regression is estimated |
slope |
Whether slopes should be different on left or right (separate), or the same. |
covar.opt |
Options for the inclusion of covariates. Way to include covariates, either in the main regression ( |
covar.strat |
DEPRECATED, use covar.opt instead. |
weights |
Optional weights to pass to the lm function. Note this cannot be entered together with |
This function estimates the standard discontinuity regression:
with the main parameter of interest. Several versions of the regression can be estimated, either restricting the slopes to be the same,
i.e (argument slope). The order of the polynomial in can also be adjusted with argument order.
Note that a value of zero can be used, which corresponds to the simple difference in means, that one would use if the samples were random.
Covariates can also be added in the regression, according to the two strategies discussed in Lee and Lemieux (2010, sec 4.5), through argument covar.strat:
Covariates are simply added as supplementary regressors in the RD equation
The dependent variable is first regressed on the covariates only, then the RDD equation is applied on the residuals from this first step
The regression can also be estimated in a neighborhood of the cutpoint with the argument bw. This make the parametric regression resemble
the non-parametric local kernel rdd_reg_np. Similarly, weights can also be provided (but not simultaneously to bw).
The returned object is a classical lm object, augmented with a RDDslot, so usual methods can be applied. As is done in general in R,
heteroskeadsticity-robust inference can be done later on with the usual function from package sandwich. For the case of clustered observations
a specific function clusterInf is provided.
An object of class rdd_reg_lm and class lm, with specific print and plot methods
## Step 0: prepare data data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) ## Step 2: regression # Simple polynomial of order 1: reg_para <- rdd_reg_lm(rdd_object=house_rdd) print(reg_para) plot(reg_para) # Simple polynomial of order 4: reg_para4 <- rdd_reg_lm(rdd_object=house_rdd, order=4) reg_para4 plot(reg_para4) # Restrict sample to bandwidth area: bw_ik <- rdd_bw_ik(house_rdd) reg_para_ik <- rdd_reg_lm(rdd_object=house_rdd, bw=bw_ik, order=4) reg_para_ik plot(reg_para_ik)## Step 0: prepare data data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) ## Step 2: regression # Simple polynomial of order 1: reg_para <- rdd_reg_lm(rdd_object=house_rdd) print(reg_para) plot(reg_para) # Simple polynomial of order 4: reg_para4 <- rdd_reg_lm(rdd_object=house_rdd, order=4) reg_para4 plot(reg_para4) # Restrict sample to bandwidth area: bw_ik <- rdd_bw_ik(house_rdd) reg_para_ik <- rdd_reg_lm(rdd_object=house_rdd, bw=bw_ik, order=4) reg_para_ik plot(reg_para_ik)
Compute a parametric polynomial regression of the ATE, possibly on the range specified by bandwidth
rdd_reg_np( rdd_object, covariates = NULL, bw = rdd_bw_ik(rdd_object), slope = c("separate", "same"), inference = c("np", "lm"), covar.opt = list(slope = c("same", "separate"), bw = NULL) )rdd_reg_np( rdd_object, covariates = NULL, bw = rdd_bw_ik(rdd_object), slope = c("separate", "same"), inference = c("np", "lm"), covar.opt = list(slope = c("same", "separate"), bw = NULL) )
rdd_object |
Object of class rdd_data created by |
covariates |
TODO |
bw |
A bandwidth to specify the subset on which the parametric regression is estimated |
slope |
Whether slopes should be different on left or right (separate), or the same. |
inference |
Type of inference to conduct: non-parametric one ( |
covar.opt |
Options for the inclusion of covariates. Way to include covariates, either in the main regression ( |
An object of class rdd_reg_np and class lm, with specific print and plot methods
TODO
rdd_bw_ik Bandwidth selection using the plug-in bandwidth of Imbens and Kalyanaraman (2012)
## Step 0: prepare data data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) ## Step 2: regression # Simple polynomial of order 1: reg_nonpara <- rdd_reg_np(rdd_object=house_rdd) print(reg_nonpara) plot(reg_nonpara)## Step 0: prepare data data(house) house_rdd <- rdd_data(y=house$y, x=house$x, cutpoint=0) ## Step 2: regression # Simple polynomial of order 1: reg_nonpara <- rdd_reg_np(rdd_object=house_rdd) print(reg_nonpara) plot(reg_nonpara)
Set of functions for Regression Discontinuity Design ('RDD'), for data visualisation, estimation and testing.
implements dpill
rot_bw(object)rot_bw(object)
object |
object of class rdd_data |
McCrary, Justin. (2008) 'Manipulation of the running variable in the regression discontinuity design: A density test,' Journal of Econometrics. 142(2): 698-714.
#No discontinuity#No discontinuity
Transformation of the STAR dataset as used in Table 8.2.1 of Angrist and Pischke (2008)
A data frame containing 5743 observations and 6 variables. The first variable is from the original dataset, all other are created by Angrist and Pischke STAT code.
School ID in kindergarden (original variable, schoolidk in STAR)
The propensity score (computed by A & P)
The id of the class (computed by A & P)
Class size (computed by A & P)
Various covariates (computed by A & P)
). This is a transformation of the dataset from the project STAR (Student/Teacher Achievement Ratio.
The full dataset is described and available in package AER, STAR.
The transformed data was obtained using the STATA script krueger.do, obtained from Joshua Angrist website, on the webstar.dta.
Data obtained using the script krueger.do on data webstar.rda, found on J. Angrist website
Krueger, A. (1999) 'Experimental Estimates Of Education Production Functions,' The Quarterly Journal of Economics, Vol. 114(2), pages 497-532, May.
Angrist, A. ad Pischke J-S (2008) Mostly Harmless Econometrics: An Empiricist's Companion, Princeton University press
STAR for the original dataset.
data(STAR_MHE) # Compute the group means: STAR_MHE_means <- aggregate(STAR_MHE[, c('classid', 'pscore', 'cs')], by=list(STAR_MHE$classid), mean) # Regression of means, with weighted average: reg_krug_gls <- lm(pscore~cs, data=STAR_MHE_means, weights=cs) coef(summary(reg_krug_gls))[2,2]data(STAR_MHE) # Compute the group means: STAR_MHE_means <- aggregate(STAR_MHE[, c('classid', 'pscore', 'cs')], by=list(STAR_MHE$classid), mean) # Regression of means, with weighted average: reg_krug_gls <- lm(pscore~cs, data=STAR_MHE_means, weights=cs) coef(summary(reg_krug_gls))[2,2]
Offer a cluster variant of the usual Heteroskedasticity-consistent
vcovCluster(object, clusterVar) vcovCluster2(object, clusterVar1, clusterVar2)vcovCluster(object, clusterVar) vcovCluster2(object, clusterVar1, clusterVar2)
object |
Object of class lm, from which rdd_reg also inherits. |
clusterVar |
The variable containing the cluster attributions. |
clusterVar1, clusterVar2
|
The two cluster variables for the 2-cluster case. |
A matrix containing the covariance matrix estimate.
Mahmood Arai, see http://people.su.se/~ma/econometrics.html
Cameron, C., Gelbach, J. and Miller, D. (2011) Robust Inference With Multiway Clustering, Journal of Business and Economic Statistics, vol. 29(2), pages 238-249. #' @references Wooldridge (2003) Cluster-sample methods in applied econometrics. American Economic Review, 93, p. 133-138
Arai, M. (2011) Cluster-robust standard errors using R, Note available http://people.su.se/~ma/clustering.pdf.
clusterInf for a direct function, allowing also alternative cluster inference methods.
data(STAR_MHE) if(all(c(require(sandwich), require(lmtest)))){ # Run simple regression: reg_krug <- lm(pscore~cs, data=STAR_MHE) # Row 1 of Table 8.2.1, inference with standard vcovHC: coeftest(reg_krug,vcov.=vcovHC(reg_krug, 'HC1'))[2,2] # Row 4 of Table 8.2.1, inference with cluster vcovHC: coeftest(reg_krug,vcov.=vcovCluster(reg_krug, clusterVar=STAR_MHE$classid))[2,2] }data(STAR_MHE) if(all(c(require(sandwich), require(lmtest)))){ # Run simple regression: reg_krug <- lm(pscore~cs, data=STAR_MHE) # Row 1 of Table 8.2.1, inference with standard vcovHC: coeftest(reg_krug,vcov.=vcovHC(reg_krug, 'HC1'))[2,2] # Row 4 of Table 8.2.1, inference with cluster vcovHC: coeftest(reg_krug,vcov.=vcovCluster(reg_krug, clusterVar=STAR_MHE$classid))[2,2] }
Version of vcov allowing for confint
waldci(x, parm = NULL, level = 0.95, vcov. = NULL, df = NULL, ...)waldci(x, parm = NULL, level = 0.95, vcov. = NULL, df = NULL, ...)
x |
Object of class lm or else |
parm |
specification of which parameters are to be given confidence intervals, see confint |
level |
the confidence level required, see confint() |
vcov. |
Specific covariance function to pass to coeftest. See help of sandwich |
df |
Degrees of freedom |
... |
Further arguments |