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R/20241206_test_function_edit.R
In hdthreshold: Inference on Many Jumps in Nonparametric Panel Regression Models
Defines functions
threshold.derivative.test
threshold.heterogeneity.test
threshold.test
Documented in
threshold.derivative.test
threshold.heterogeneity.test
threshold.test
#' Uniform test for existence of threshold effects
#'
#' Uniform test for existence of threshold effects in a nonparametric panel regression. Both the
#' known and unknown threshold location case are covered. Apart from the uniform test statistic and
#' the corresponding p-value, a table for the results of the individual threshold estimates and test statistics
#' is provided.
#'
#' @param data a data frame containing the response, running and id variables
#' @param response name of the dependent variable (aka response variable)
#' @param running name of the running variable (aka forcing variable)
#' @param id name of the id variable
#' @param bw an optional scalar bandwidth parameter for the local linear estimation. If not specified, the bandwidth
#' is selected by the command [rdrobust::rdbwselect()].
#' @param C a scalar value for the true threshold location (for the known case) or a grid of candidate threshold locations
#' (for the unknown case)
#' @param alpha specifies a threshold to determine which and how many individual-specific threshold effects and test
#' statistics are displayed in the output table. Only individuals which are significant at the alpha confidence level are selected.
#' @param alternative specifies whether we consider a two-sided alternative (default) or left-/right-sided alternative.
#'
#' @seealso [threshold.example()], [rdrobust::rdbwselect()].
#'
#' @return A list containing:\tabular{ll}{
#' \code{I_hat} \tab the value of the uniform test statistic \cr
#' \tab \cr
#' \code{p_value} \tab the corresponding p-value \cr
#' \tab \cr
#' \code{N} \tab the cross-sectional dimension \cr
#' \tab \cr
#' \code{Critical_values} \tab critical values at 10%, 5%, 1%, and 0.1% confidence level \cr
#' \tab \cr
#' \code{Table} \tab a table displaying the estimation result for a selection of individuals, including the id variable, the threshold location,
#' the estimated coefficient, the estimated standard error, and the individual test statistic. \cr
#' }
#' @export
#'
#' @examples
#' d = threshold.example(10, 200, 0.1, 2)
#' threshold.test(data = d, response = "y", running = "x", id = "id", C = 0)
threshold.test = function(data,
response,
running,
id,
bw = NULL,
C = 0,
alpha = NULL,
alternative = "two") {
names = unique(data[, id])
N = length(names)
result = data.frame(matrix(ncol = 5, nrow = 0))
colnames(result) = c("ID", "c_0j", "gamma_hat_j", "v_hat_j", "I_hat_j")
result_j = data.frame(matrix(nrow = length(C), ncol = 5))
colnames(result_j) = c("ID", "c_0j", "gamma_hat_j", "v_hat_j", "I_hat_j")
for (j in 1:N) {
message(paste("Individual ", j))
y = data[data[, id] == names[j], response]
x = data[data[, id] == names[j], running]
result_j[, 1] = names[j]
result_j[, 2] = C
for (i in 1:length(C)) {
c = C[i]
h = ifelse(is.null(bw),
rdrobust::rdbwselect(y, x, kernel = "uniform", c = c)$bws[1],
bw)
K = function(x) {
ifelse((abs(x)) <= 1, 1 / 2, 0)
}
S0p = sum(ifelse(x - c > 0, K((x - c) / h), 0))
S1p = sum(ifelse(x - c > 0, (x - c) * K((x - c) / h), 0))
S2p = sum(ifelse(x - c > 0, (x - c) ^ 2 * K((x - c) / h), 0))
S0n = sum(ifelse(x - c <= 0, K((x - c) / h), 0))
S1n = sum(ifelse(x - c <= 0, (x - c) * K((x - c) / h), 0))
S2n = sum(ifelse(x - c <= 0, (x - c) ^ 2 * K((x - c) / h), 0))
wp = ifelse(x - c > 0, K((x - c) / h), 0) * (S2p - (x - c) * S1p) / (S2p *
S0p - S1p ^ 2)
wn = ifelse(x - c <= 0, K((x - c) / h), 0) * (S2n - (x - c) * S1n) / (S2n *
S0n - S1n ^ 2)
tauhat = sum((wp - wn) * y)
result_j[i, 3] = tauhat
fit1 = KernSmooth::locpoly(x,
y - ifelse(x > c, 1, 0) * tauhat,
bandwidth = h,
truncate = FALSE)
e = y - ifelse((x - c) > 0, 1, 0) * tauhat - approx(fit1$x, fit1$y, xout =
x)$y
wpos = ifelse(x - c > 0, ifelse((x - c) < h, 1, 0), 0)
wneg = ifelse(x - c < 0, ifelse((x - c) > -h, 1, 0), 0)
result_j[i, 4] = sqrt(var(e[wpos + wneg != 0]) * sum(wp ^ 2 + wn ^
2))
}
result_j[, 5] = as.numeric(result_j[, 3]) / as.numeric(result_j[, 4])
if (alternative == "two") {
result_j_max = result_j[abs(result_j[, 5]) == max(abs(result_j[, 5])), ]
}
if (alternative == "right") {
result_j_max = result_j[result_j[, 5] == max(result_j[, 5]), ]
}
if (alternative == "left") {
result_j_max = result_j[result_j[, 5] == min(result_j[, 5]), ]
}
result = rbind(result, result_j_max)
}
I_hat = ifelse(alternative == "left", min(result[, 5]), max(abs(result[, 5])))
if (alternative == "two") {
p_value = 1 - fdrtool::phalfnorm(I_hat) ^ (N * length(C))
}
if (alternative == "right") {
p_value = 1 - pnorm(I_hat) ^ (N * length(C))
}
if (alternative == "left") {
p_value = 1 - pnorm(-I_hat) ^ (N * length(C))
}
alpha = ifelse(is.null(alpha), 1, alpha)
if (alternative == "two") {
result_1 = subset(result, abs(result$I_hat_j) > fdrtool::qhalfnorm((1 - alpha) ^ (1 / (N *
length(
C
)))))
}
else {
result_1 = subset(result, abs(result$I_hat_j) > qnorm((1 - alpha) ^ (1 / (N * length(
C
)))))
}
result_1 = result_1[order(result_1$c_0j), ]
result_1[, 2:5] = round(result_1[, 2:5], digits = 3)
rownames(result_1) <- NULL
if (alternative == "two") {
critical = c(fdrtool::qhalfnorm((0.90) ^ (1 / (N * length(
C
)))),
fdrtool::qhalfnorm((0.95) ^ (1 / (N * length(
C
)))),
###5
fdrtool::qhalfnorm((0.99) ^ (1 / (N * length(
C
)))),
fdrtool::qhalfnorm((0.999) ^ (1 / (N * length(
C
)))))
}
if (alternative == "right") {
critical = c(qnorm((0.90) ^ (1 / (N * length(
C
)))), qnorm((0.95) ^ (1 / (N * length(
C
)))),
qnorm((0.99) ^ (1 / (N * length(
C
)))), qnorm((0.999) ^ (1 / (N * length(
C
)))))
}
if (alternative == "left") {
critical = -c(qnorm((0.90) ^ (1 / (N * length(
C
)))), qnorm((0.95) ^ (1 / (N * length(
C
)))),
qnorm((0.99) ^ (1 / (N * length(
C
)))), qnorm((0.999) ^ (1 / (N * length(
C
)))))
}
critical = setNames(critical, c("90%", "95%", "99%", "99.9%"))
list = list(I_hat, p_value, N, critical, result_1)
list = setNames(list, c("I_hat", "p_value", "N", "Critical_values", "Table"))
return(list)
}
#' Uniform test for heterogeneity of threshold effects
#'
#' Uniform test for heterogeneity of threshold effects in a nonparametric panel regression under known threshold locations.
#' Apart from the uniform test statistic and the corresponding p-value, a table for the results of the individual threshold
#' estimates and test statistics is provided.
#'
#' @param data a data frame containing the response, running and id variables
#' @param response name of the dependent variable (aka response variable)
#' @param running name of the running variable (aka forcing variable)
#' @param id name of the id variable
#' @param bw an optional scalar bandwidth parameter for the local linear estimation. If not specified, the bandwidth
#' is selected by the command [rdrobust::rdbwselect()].
#' @param c a scalar value for the true threshold location
#' @param alpha specifies a threshold to determine which and how many individual-specific threshold effects and test
#' statistics are displayed in the output table. Only individuals which are significant at the alpha confidence level are selected.
#' @param alternative specifies whether we consider a two-sided alternative (default) or left-/right-sided alternative.
#' @param use.median if \code{TRUE}, the median replaces the mean as a robust alternative in the test for heterogeneity
#'
#' @seealso [threshold.example()], [rdrobust::rdbwselect()].
#'
#' @return A list containing:\tabular{ll}{
#' \code{Q_hat} \tab the value of the uniform test statistic \cr
#' \tab \cr
#' \code{p_value} \tab the corresponding p-value \cr
#' \tab \cr
#' \code{N} \tab the cross-sectional dimension \cr
#' \tab \cr
#' \code{Critical_values} \tab critical values at 10%, 5%, 1%, and 0.1% confidence level \cr
#' \tab \cr
#' \code{Table} \tab a table displaying the estimation result for a selection of individuals, including the id variable, the threshold location,
#' the estimated coefficient, the estimated standard error, and the individual test statistic. \cr
#' }
#' @export
#'
#' @examples
#' d = threshold.example(10, 200, 0.1, 2)
#' threshold.heterogeneity.test(data = d, response = "y", running = "x", id = "id", c = 0)
threshold.heterogeneity.test = function(data,
response,
running,
id,
bw = NULL,
c = 0,
alpha = NULL,
alternative = "two",
use.median = FALSE) {
names = unique(data[, id])
N = length(names)
result = data.frame(matrix(ncol = 5, nrow = 0))
colnames(result) = c("ID",
"c_0j",
"gamma_hat_j-gamma_bar",
"v_tilde_j",
"Q_hat_j")
result_j = data.frame(matrix(nrow = 1, ncol = 5))
colnames(result_j) = c("ID",
"c_0j",
"gamma_hat_j-gamma_bar",
"v_tilde_j",
"Q_hat_j")
for (j in 1:N) {
message(paste("Individual ", j))
y = data[data[, id] == names[j], response]
x = data[data[, id] == names[j], running]
result_j[, 1] = names[j]
result_j[, 2] = c
h = ifelse(is.null(bw),
rdrobust::rdbwselect(y, x, kernel = "uniform", c = c)$bws[1],
bw)
K = function(x) {
ifelse((abs(x)) <= 1, 1 / 2, 0)
}
S0p = sum(ifelse(x - c > 0, K((x - c) / h), 0))
S1p = sum(ifelse(x - c > 0, (x - c) * K((x - c) / h), 0))
S2p = sum(ifelse(x - c > 0, (x - c) ^ 2 * K((x - c) / h), 0))
S0n = sum(ifelse(x - c <= 0, K((x - c) / h), 0))
S1n = sum(ifelse(x - c <= 0, (x - c) * K((x - c) / h), 0))
S2n = sum(ifelse(x - c <= 0, (x - c) ^ 2 * K((x - c) / h), 0))
wp = ifelse(x - c > 0, K((x - c) / h), 0) * (S2p - (x - c) * S1p) / (S2p *
S0p - S1p ^ 2)
wn = ifelse(x - c <= 0, K((x - c) / h), 0) * (S2n - (x - c) * S1n) / (S2n *
S0n - S1n ^ 2)
tauhat = sum((wp - wn) * y)
result_j[, 3] = tauhat
fit1 = KernSmooth::locpoly(x,
y - ifelse(x > c, 1, 0) * tauhat,
bandwidth = h,
truncate = FALSE)
e = y - ifelse((x - c) > 0, 1, 0) * tauhat - approx(fit1$x, fit1$y, xout =
x)$y
wpos = ifelse(x - c > 0, ifelse((x - c) < h, 1, 0), 0)
wneg = ifelse(x - c < 0, ifelse((x - c) > -h, 1, 0), 0)
result_j[, 4] = sqrt(var(e[wpos + wneg != 0]) * sum(wp ^ 2 + wn ^ 2))
result_j[, 5] = as.numeric(result_j[, 3]) / as.numeric(result_j[, 4])
result = rbind(result, result_j)
}
if (use.median == TRUE) {
result[, 3] = result[, 3] - median(result[, 3])
}
else{
result[, 3] = result[, 3] - mean(result[, 3])
}
for (j in 1:N) {
result[j, 4] = result[j, 4] * (1 - 1 / N) ^ 2 + sum(result[-j, 4]) / N ^
2
}
result[, 5] = as.numeric(result[, 3]) / as.numeric(result[, 4])
Q_hat = ifelse(alternative == "left", min(result$Q_hat_j), max(abs(result$Q_hat_j)))
if (alternative == "two") {
p_value = 1 - fdrtool::phalfnorm(Q_hat) ^ N
}
if (alternative == "right") {
p_value = 1 - pnorm(Q_hat) ^ N
}
if (alternative == "left") {
p_value = 1 - pnorm(-Q_hat) ^ N
}
alpha = ifelse(is.null(alpha), 1, alpha)
if (alternative == "two") {
result_1 = subset(result, abs(result$Q_hat_j) > fdrtool::qhalfnorm((1 - alpha) ^ (1 / N)))
}
else {
result_1 = subset(result, abs(result$Q_hat_j) > qnorm((1 - alpha) ^ (1 / N)))
}
result_1 = result_1[order(result_1$c_0j), ]
result_1[, 2:5] = round(result_1[, 2:5], digits = 3)
rownames(result_1) <- NULL
if (alternative == "two") {
critical = c(fdrtool::qhalfnorm((0.90) ^ (1 / N)),
fdrtool::qhalfnorm((0.95) ^ (1 / N)),
fdrtool::qhalfnorm((0.99) ^ (1 / N)),
fdrtool::qhalfnorm((0.999) ^ (1 / N)))
}
if (alternative == "right") {
critical = c(qnorm((0.90) ^ (1 / N)), qnorm((0.95) ^ (1 / N)),
qnorm((0.99) ^ (1 / N)), qnorm((0.999) ^ (1 / N)))
}
if (alternative == "left") {
critical = -c(qnorm((0.90) ^ (1 / N)), qnorm((0.95) ^ (1 / N)),
qnorm((0.99) ^ (1 / N)), qnorm((0.999) ^ (1 / N)))
}
critical = setNames(critical, c("90%", "95%", "99%", "99.9%"))
list = list(Q_hat, p_value, N, critical, result_1)
list = setNames(list, c("Q_hat", "p_value", "N", "Critical_values", "Table"))
return(list)
}
#' Uniform test for existence of derivative threshold effects
#'
#' Uniform test for existence of threshold effects in the first derivative for nonparametric panel regressions. Both the
#' known and unknown threshold location case are covered. Apart from the uniform test statistic and
#' the corresponding p-value, a table for the results of the individual threshold estimates and test statistics
#' is provided.
#'
#' @param data a data frame containing the response, running and id variables
#' @param response name of the dependent variable (aka response variable)
#' @param running name of the running variable (aka forcing variable)
#' @param id name of the id variable
#' @param bw an optional scalar bandwidth parameter for the local linear estimation. If not specified, the bandwidth
#' is selected by the command [rdrobust::rdbwselect()].
#' @param C a scalar value for the true threshold location (for the known case) or a grid of candidate threshold locations
#' (for the unknown case)
#' @param alpha specifies a threshold to determine which and how many individual-specific threshold effects and test
#' statistics are displayed in the output table. Only individuals which are significant at the alpha confidence level are selected.
#' @param alternative specifies whether we consider a two-sided alternative (default) or left-/right-sided alternative.
#'
#' @seealso [threshold.example()], [rdrobust::rdbwselect()].
#'
#' @return A list containing:\tabular{ll}{
#' \code{I_hat} \tab the value of the uniform test statistic \cr
#' \tab \cr
#' \code{p_value} \tab the corresponding p-value \cr
#' \tab \cr
#' \code{N} \tab the cross-sectional dimension \cr
#' \tab \cr
#' \code{Critical_values} \tab critical values at 10%, 5%, 1%, and 0.1% confidence level \cr
#' \tab \cr
#' \code{Table} \tab a table displaying the estimation result for a selection of individuals, including the id variable, the threshold location,
#' the estimated coefficient, the estimated standard error, and the individual test statistic. \cr
#' }
#' @export
#'
#' @examples
#' d = threshold.example(10, 200, 0.1, 2)
#' threshold.derivative.test(data = d, response = "y", running = "x", id = "id", C = 0)
threshold.derivative.test = function(data,
response,
running,
id,
bw = NULL,
C = 0,
alpha = NULL,
alternative = "two") {
names = unique(data[, id])
N = length(names)
result = data.frame(matrix(ncol = 5, nrow = 0))
colnames(result) = c("ID", "c_0j", "gamma_hat_j", "v_hat_j", "I_hat_j")
result_j = data.frame(matrix(nrow = length(C), ncol = 5))
colnames(result_j) = c("ID", "c_0j", "gamma_hat_j", "v_hat_j", "I_hat_j")
for (j in 1:N) {
message(paste("Individual ", j))
y = data[data[, id] == names[j], response]
x = data[data[, id] == names[j], running]
result_j[, 1] = names[j]
result_j[, 2] = C
for (i in 1:length(C)) {
c = C[i]
h = ifelse(is.null(bw),
rdrobust::rdbwselect(y, x, kernel = "uniform", c = c)$bws[1],
bw)
K = function(x) {
ifelse((abs(x)) <= 1, 1 / 2, 0)
}
S0p = sum(ifelse(x - c > 0, K((x - c) / h), 0))
S1p = sum(ifelse(x - c > 0, (x - c) * K((x - c) / h), 0))
S2p = sum(ifelse(x - c > 0, (x - c) ^ 2 * K((x - c) / h), 0))
S0n = sum(ifelse(x - c <= 0, K((x - c) / h), 0))
S1n = sum(ifelse(x - c <= 0, (x - c) * K((x - c) / h), 0))
S2n = sum(ifelse(x - c <= 0, (x - c) ^ 2 * K((x - c) / h), 0))
wp = ifelse(x - c > 0, K((x - c) / h), 0) * (S2p - (x - c) * S1p) / (S2p *
S0p - S1p ^ 2)
wn = ifelse(x - c <= 0, K((x - c) / h), 0) * (S2n - (x - c) * S1n) / (S2n *
S0n - S1n ^ 2)
wp1 = ifelse(x > c, K((x - c) / h), 0) * (S1p - (x - c) * S0p) / (-S2p *
S0p + S1p ^ 2)
wn1 = ifelse(x <= c, K((x - c) / h), 0) * (S1n - (x - c) * S0n) / (-S2n *
S0n + S1n ^ 2)
tauhat = sum((wp - wn) * y)
result_j[i, 3] = sum((wp1 - wn1) * y)
fit1 = KernSmooth::locpoly(x,
y - ifelse(x > c, 1, 0) * tauhat,
bandwidth = h,
truncate = FALSE)
e = y - ifelse((x - c) > 0, 1, 0) * tauhat - approx(fit1$x, fit1$y, xout =
x)$y
wpos = ifelse(x - c > 0, ifelse((x - c) < h, 1, 0), 0)
wneg = ifelse(x - c < 0, ifelse((x - c) > -h, 1, 0), 0)
result_j[i, 4] = sqrt(var(e[wpos + wneg != 0]) * sum(wp1 ^ 2 + wn1 ^
2))
}
result_j[, 5] = as.numeric(result_j[, 3]) / as.numeric(result_j[, 4])
if (alternative == "two") {
result_j_max = result_j[abs(result_j$I_hat_j) == max(abs(result_j$I_hat_j)), ]
}
if (alternative == "right") {
result_j_max = result_j[result_j$I_hat_j == max(result_j$I_hat_j), ]
}
if (alternative == "left") {
result_j_max = result_j[result_j$I_hat_j == min(result_j$I_hat_j), ]
}
result = rbind(result, result_j_max)
}
I_hat = ifelse(alternative == "left", min(result$I_hat_j), max(abs(result$I_hat_j)))
if (alternative == "two") {
p_value = 1 - fdrtool::phalfnorm(I_hat) ^ (N * length(C))
}
if (alternative == "right") {
p_value = 1 - pnorm(I_hat) ^ (N * length(C))
}
if (alternative == "left") {
p_value = 1 - pnorm(-I_hat) ^ (N * length(C))
}
alpha = ifelse(is.null(alpha), 1, alpha)
if (alternative == "two") {
result_1 = subset(result, abs(result$I_hat_j) > fdrtool::qhalfnorm((1 - alpha) ^ (1 / (N *
length(C)))))
}
else {
result_1 = subset(result, abs(result$I_hat_j) > qnorm((1 - alpha) ^ (1 / (N *
length(C)))))
}
result_1 = result_1[order(result_1$c_0j), ]
result_1[, 2:5] = round(result_1[, 2:5], digits = 3)
rownames(result_1) <- NULL
if (alternative == "two") {
critical = c(fdrtool::qhalfnorm((0.90) ^ (1 / (N * length(C)))),
fdrtool::qhalfnorm((0.95) ^ (1 / (N * length(C)))),
fdrtool::qhalfnorm((0.99) ^ (1 / (N * length(C)))),
fdrtool::qhalfnorm((0.999) ^ (1 / (N * length(C)))))
}
if (alternative == "right") {
critical = c(qnorm((0.90) ^ (1 / (N * length(C)))),
qnorm((0.95) ^ (1 / (N * length(C)))),
qnorm((0.99) ^ (1 / (N * length(C)))),
qnorm((0.999) ^ (1 / (N * length(C)))))
}
if (alternative == "left") {
critical = -c(qnorm((0.90) ^ (1 / (N * length(C)))),
qnorm((0.95) ^ (1 / (N * length(C)))),
qnorm((0.99) ^ (1 / (N * length(C)))),
qnorm((0.999) ^ (1 / (N * length(C)))))
}
critical = setNames(critical, c("90%", "95%", "99%", "99.9%"))
list = list(I_hat, p_value, N, critical, result_1)
list = setNames(list, c("I_hat", "p_value", "N", "Critical_values", "Table"))
return(list)
}
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Defines functions threshold.derivative.test threshold.heterogeneity.test threshold.test
Documented in threshold.derivative.test threshold.heterogeneity.test threshold.test
#' Uniform test for existence of threshold effects
#'
#' Uniform test for existence of threshold effects in a nonparametric panel regression. Both the
#' known and unknown threshold location case are covered. Apart from the uniform test statistic and
#' the corresponding p-value, a table for the results of the individual threshold estimates and test statistics
#' is provided.
#'
#' @param data a data frame containing the response, running and id variables
#' @param response name of the dependent variable (aka response variable)
#' @param running name of the running variable (aka forcing variable)
#' @param id name of the id variable
#' @param bw an optional scalar bandwidth parameter for the local linear estimation. If not specified, the bandwidth
#' is selected by the command [rdrobust::rdbwselect()].
#' @param C a scalar value for the true threshold location (for the known case) or a grid of candidate threshold locations
#' (for the unknown case)
#' @param alpha specifies a threshold to determine which and how many individual-specific threshold effects and test
#' statistics are displayed in the output table. Only individuals which are significant at the alpha confidence level are selected.
#' @param alternative specifies whether we consider a two-sided alternative (default) or left-/right-sided alternative.
#'
#' @seealso [threshold.example()], [rdrobust::rdbwselect()].
#'
#' @return A list containing:\tabular{ll}{
#' \code{I_hat} \tab the value of the uniform test statistic \cr
#' \tab \cr
#' \code{p_value} \tab the corresponding p-value \cr
#' \tab \cr
#' \code{N} \tab the cross-sectional dimension \cr
#' \tab \cr
#' \code{Critical_values} \tab critical values at 10%, 5%, 1%, and 0.1% confidence level \cr
#' \tab \cr
#' \code{Table} \tab a table displaying the estimation result for a selection of individuals, including the id variable, the threshold location,
#' the estimated coefficient, the estimated standard error, and the individual test statistic. \cr
#' }
#' @export
#'
#' @examples
#' d = threshold.example(10, 200, 0.1, 2)
#' threshold.test(data = d, response = "y", running = "x", id = "id", C = 0)
threshold.test = function(data,
response,
running,
id,
bw = NULL,
C = 0,
alpha = NULL,
alternative = "two") {
names = unique(data[, id])
N = length(names)
result = data.frame(matrix(ncol = 5, nrow = 0))
colnames(result) = c("ID", "c_0j", "gamma_hat_j", "v_hat_j", "I_hat_j")
result_j = data.frame(matrix(nrow = length(C), ncol = 5))
colnames(result_j) = c("ID", "c_0j", "gamma_hat_j", "v_hat_j", "I_hat_j")
for (j in 1:N) {
message(paste("Individual ", j))
y = data[data[, id] == names[j], response]
x = data[data[, id] == names[j], running]
result_j[, 1] = names[j]
result_j[, 2] = C
for (i in 1:length(C)) {
c = C[i]
h = ifelse(is.null(bw),
rdrobust::rdbwselect(y, x, kernel = "uniform", c = c)$bws[1],
bw)
K = function(x) {
ifelse((abs(x)) <= 1, 1 / 2, 0)
}
S0p = sum(ifelse(x - c > 0, K((x - c) / h), 0))
S1p = sum(ifelse(x - c > 0, (x - c) * K((x - c) / h), 0))
S2p = sum(ifelse(x - c > 0, (x - c) ^ 2 * K((x - c) / h), 0))
S0n = sum(ifelse(x - c <= 0, K((x - c) / h), 0))
S1n = sum(ifelse(x - c <= 0, (x - c) * K((x - c) / h), 0))
S2n = sum(ifelse(x - c <= 0, (x - c) ^ 2 * K((x - c) / h), 0))
wp = ifelse(x - c > 0, K((x - c) / h), 0) * (S2p - (x - c) * S1p) / (S2p *
S0p - S1p ^ 2)
wn = ifelse(x - c <= 0, K((x - c) / h), 0) * (S2n - (x - c) * S1n) / (S2n *
S0n - S1n ^ 2)
tauhat = sum((wp - wn) * y)
result_j[i, 3] = tauhat
fit1 = KernSmooth::locpoly(x,
y - ifelse(x > c, 1, 0) * tauhat,
bandwidth = h,
truncate = FALSE)
e = y - ifelse((x - c) > 0, 1, 0) * tauhat - approx(fit1$x, fit1$y, xout =
x)$y
wpos = ifelse(x - c > 0, ifelse((x - c) < h, 1, 0), 0)
wneg = ifelse(x - c < 0, ifelse((x - c) > -h, 1, 0), 0)
result_j[i, 4] = sqrt(var(e[wpos + wneg != 0]) * sum(wp ^ 2 + wn ^
2))
}
result_j[, 5] = as.numeric(result_j[, 3]) / as.numeric(result_j[, 4])
if (alternative == "two") {
result_j_max = result_j[abs(result_j[, 5]) == max(abs(result_j[, 5])), ]
}
if (alternative == "right") {
result_j_max = result_j[result_j[, 5] == max(result_j[, 5]), ]
}
if (alternative == "left") {
result_j_max = result_j[result_j[, 5] == min(result_j[, 5]), ]
}
result = rbind(result, result_j_max)
}
I_hat = ifelse(alternative == "left", min(result[, 5]), max(abs(result[, 5])))
if (alternative == "two") {
p_value = 1 - fdrtool::phalfnorm(I_hat) ^ (N * length(C))
}
if (alternative == "right") {
p_value = 1 - pnorm(I_hat) ^ (N * length(C))
}
if (alternative == "left") {
p_value = 1 - pnorm(-I_hat) ^ (N * length(C))
}
alpha = ifelse(is.null(alpha), 1, alpha)
if (alternative == "two") {
result_1 = subset(result, abs(result$I_hat_j) > fdrtool::qhalfnorm((1 - alpha) ^ (1 / (N *
length(
C
)))))
}
else {
result_1 = subset(result, abs(result$I_hat_j) > qnorm((1 - alpha) ^ (1 / (N * length(
C
)))))
}
result_1 = result_1[order(result_1$c_0j), ]
result_1[, 2:5] = round(result_1[, 2:5], digits = 3)
rownames(result_1) <- NULL
if (alternative == "two") {
critical = c(fdrtool::qhalfnorm((0.90) ^ (1 / (N * length(
C
)))),
fdrtool::qhalfnorm((0.95) ^ (1 / (N * length(
C
)))),
###5
fdrtool::qhalfnorm((0.99) ^ (1 / (N * length(
C
)))),
fdrtool::qhalfnorm((0.999) ^ (1 / (N * length(
C
)))))
}
if (alternative == "right") {
critical = c(qnorm((0.90) ^ (1 / (N * length(
C
)))), qnorm((0.95) ^ (1 / (N * length(
C
)))),
qnorm((0.99) ^ (1 / (N * length(
C
)))), qnorm((0.999) ^ (1 / (N * length(
C
)))))
}
if (alternative == "left") {
critical = -c(qnorm((0.90) ^ (1 / (N * length(
C
)))), qnorm((0.95) ^ (1 / (N * length(
C
)))),
qnorm((0.99) ^ (1 / (N * length(
C
)))), qnorm((0.999) ^ (1 / (N * length(
C
)))))
}
critical = setNames(critical, c("90%", "95%", "99%", "99.9%"))
list = list(I_hat, p_value, N, critical, result_1)
list = setNames(list, c("I_hat", "p_value", "N", "Critical_values", "Table"))
return(list)
}
#' Uniform test for heterogeneity of threshold effects
#'
#' Uniform test for heterogeneity of threshold effects in a nonparametric panel regression under known threshold locations.
#' Apart from the uniform test statistic and the corresponding p-value, a table for the results of the individual threshold
#' estimates and test statistics is provided.
#'
#' @param data a data frame containing the response, running and id variables
#' @param response name of the dependent variable (aka response variable)
#' @param running name of the running variable (aka forcing variable)
#' @param id name of the id variable
#' @param bw an optional scalar bandwidth parameter for the local linear estimation. If not specified, the bandwidth
#' is selected by the command [rdrobust::rdbwselect()].
#' @param c a scalar value for the true threshold location
#' @param alpha specifies a threshold to determine which and how many individual-specific threshold effects and test
#' statistics are displayed in the output table. Only individuals which are significant at the alpha confidence level are selected.
#' @param alternative specifies whether we consider a two-sided alternative (default) or left-/right-sided alternative.
#' @param use.median if \code{TRUE}, the median replaces the mean as a robust alternative in the test for heterogeneity
#'
#' @seealso [threshold.example()], [rdrobust::rdbwselect()].
#'
#' @return A list containing:\tabular{ll}{
#' \code{Q_hat} \tab the value of the uniform test statistic \cr
#' \tab \cr
#' \code{p_value} \tab the corresponding p-value \cr
#' \tab \cr
#' \code{N} \tab the cross-sectional dimension \cr
#' \tab \cr
#' \code{Critical_values} \tab critical values at 10%, 5%, 1%, and 0.1% confidence level \cr
#' \tab \cr
#' \code{Table} \tab a table displaying the estimation result for a selection of individuals, including the id variable, the threshold location,
#' the estimated coefficient, the estimated standard error, and the individual test statistic. \cr
#' }
#' @export
#'
#' @examples
#' d = threshold.example(10, 200, 0.1, 2)
#' threshold.heterogeneity.test(data = d, response = "y", running = "x", id = "id", c = 0)
threshold.heterogeneity.test = function(data,
response,
running,
id,
bw = NULL,
c = 0,
alpha = NULL,
alternative = "two",
use.median = FALSE) {
names = unique(data[, id])
N = length(names)
result = data.frame(matrix(ncol = 5, nrow = 0))
colnames(result) = c("ID",
"c_0j",
"gamma_hat_j-gamma_bar",
"v_tilde_j",
"Q_hat_j")
result_j = data.frame(matrix(nrow = 1, ncol = 5))
colnames(result_j) = c("ID",
"c_0j",
"gamma_hat_j-gamma_bar",
"v_tilde_j",
"Q_hat_j")
for (j in 1:N) {
message(paste("Individual ", j))
y = data[data[, id] == names[j], response]
x = data[data[, id] == names[j], running]
result_j[, 1] = names[j]
result_j[, 2] = c
h = ifelse(is.null(bw),
rdrobust::rdbwselect(y, x, kernel = "uniform", c = c)$bws[1],
bw)
K = function(x) {
ifelse((abs(x)) <= 1, 1 / 2, 0)
}
S0p = sum(ifelse(x - c > 0, K((x - c) / h), 0))
S1p = sum(ifelse(x - c > 0, (x - c) * K((x - c) / h), 0))
S2p = sum(ifelse(x - c > 0, (x - c) ^ 2 * K((x - c) / h), 0))
S0n = sum(ifelse(x - c <= 0, K((x - c) / h), 0))
S1n = sum(ifelse(x - c <= 0, (x - c) * K((x - c) / h), 0))
S2n = sum(ifelse(x - c <= 0, (x - c) ^ 2 * K((x - c) / h), 0))
wp = ifelse(x - c > 0, K((x - c) / h), 0) * (S2p - (x - c) * S1p) / (S2p *
S0p - S1p ^ 2)
wn = ifelse(x - c <= 0, K((x - c) / h), 0) * (S2n - (x - c) * S1n) / (S2n *
S0n - S1n ^ 2)
tauhat = sum((wp - wn) * y)
result_j[, 3] = tauhat
fit1 = KernSmooth::locpoly(x,
y - ifelse(x > c, 1, 0) * tauhat,
bandwidth = h,
truncate = FALSE)
e = y - ifelse((x - c) > 0, 1, 0) * tauhat - approx(fit1$x, fit1$y, xout =
x)$y
wpos = ifelse(x - c > 0, ifelse((x - c) < h, 1, 0), 0)
wneg = ifelse(x - c < 0, ifelse((x - c) > -h, 1, 0), 0)
result_j[, 4] = sqrt(var(e[wpos + wneg != 0]) * sum(wp ^ 2 + wn ^ 2))
result_j[, 5] = as.numeric(result_j[, 3]) / as.numeric(result_j[, 4])
result = rbind(result, result_j)
}
if (use.median == TRUE) {
result[, 3] = result[, 3] - median(result[, 3])
}
else{
result[, 3] = result[, 3] - mean(result[, 3])
}
for (j in 1:N) {
result[j, 4] = result[j, 4] * (1 - 1 / N) ^ 2 + sum(result[-j, 4]) / N ^
2
}
result[, 5] = as.numeric(result[, 3]) / as.numeric(result[, 4])
Q_hat = ifelse(alternative == "left", min(result$Q_hat_j), max(abs(result$Q_hat_j)))
if (alternative == "two") {
p_value = 1 - fdrtool::phalfnorm(Q_hat) ^ N
}
if (alternative == "right") {
p_value = 1 - pnorm(Q_hat) ^ N
}
if (alternative == "left") {
p_value = 1 - pnorm(-Q_hat) ^ N
}
alpha = ifelse(is.null(alpha), 1, alpha)
if (alternative == "two") {
result_1 = subset(result, abs(result$Q_hat_j) > fdrtool::qhalfnorm((1 - alpha) ^ (1 / N)))
}
else {
result_1 = subset(result, abs(result$Q_hat_j) > qnorm((1 - alpha) ^ (1 / N)))
}
result_1 = result_1[order(result_1$c_0j), ]
result_1[, 2:5] = round(result_1[, 2:5], digits = 3)
rownames(result_1) <- NULL
if (alternative == "two") {
critical = c(fdrtool::qhalfnorm((0.90) ^ (1 / N)),
fdrtool::qhalfnorm((0.95) ^ (1 / N)),
fdrtool::qhalfnorm((0.99) ^ (1 / N)),
fdrtool::qhalfnorm((0.999) ^ (1 / N)))
}
if (alternative == "right") {
critical = c(qnorm((0.90) ^ (1 / N)), qnorm((0.95) ^ (1 / N)),
qnorm((0.99) ^ (1 / N)), qnorm((0.999) ^ (1 / N)))
}
if (alternative == "left") {
critical = -c(qnorm((0.90) ^ (1 / N)), qnorm((0.95) ^ (1 / N)),
qnorm((0.99) ^ (1 / N)), qnorm((0.999) ^ (1 / N)))
}
critical = setNames(critical, c("90%", "95%", "99%", "99.9%"))
list = list(Q_hat, p_value, N, critical, result_1)
list = setNames(list, c("Q_hat", "p_value", "N", "Critical_values", "Table"))
return(list)
}
#' Uniform test for existence of derivative threshold effects
#'
#' Uniform test for existence of threshold effects in the first derivative for nonparametric panel regressions. Both the
#' known and unknown threshold location case are covered. Apart from the uniform test statistic and
#' the corresponding p-value, a table for the results of the individual threshold estimates and test statistics
#' is provided.
#'
#' @param data a data frame containing the response, running and id variables
#' @param response name of the dependent variable (aka response variable)
#' @param running name of the running variable (aka forcing variable)
#' @param id name of the id variable
#' @param bw an optional scalar bandwidth parameter for the local linear estimation. If not specified, the bandwidth
#' is selected by the command [rdrobust::rdbwselect()].
#' @param C a scalar value for the true threshold location (for the known case) or a grid of candidate threshold locations
#' (for the unknown case)
#' @param alpha specifies a threshold to determine which and how many individual-specific threshold effects and test
#' statistics are displayed in the output table. Only individuals which are significant at the alpha confidence level are selected.
#' @param alternative specifies whether we consider a two-sided alternative (default) or left-/right-sided alternative.
#'
#' @seealso [threshold.example()], [rdrobust::rdbwselect()].
#'
#' @return A list containing:\tabular{ll}{
#' \code{I_hat} \tab the value of the uniform test statistic \cr
#' \tab \cr
#' \code{p_value} \tab the corresponding p-value \cr
#' \tab \cr
#' \code{N} \tab the cross-sectional dimension \cr
#' \tab \cr
#' \code{Critical_values} \tab critical values at 10%, 5%, 1%, and 0.1% confidence level \cr
#' \tab \cr
#' \code{Table} \tab a table displaying the estimation result for a selection of individuals, including the id variable, the threshold location,
#' the estimated coefficient, the estimated standard error, and the individual test statistic. \cr
#' }
#' @export
#'
#' @examples
#' d = threshold.example(10, 200, 0.1, 2)
#' threshold.derivative.test(data = d, response = "y", running = "x", id = "id", C = 0)
threshold.derivative.test = function(data,
response,
running,
id,
bw = NULL,
C = 0,
alpha = NULL,
alternative = "two") {
names = unique(data[, id])
N = length(names)
result = data.frame(matrix(ncol = 5, nrow = 0))
colnames(result) = c("ID", "c_0j", "gamma_hat_j", "v_hat_j", "I_hat_j")
result_j = data.frame(matrix(nrow = length(C), ncol = 5))
colnames(result_j) = c("ID", "c_0j", "gamma_hat_j", "v_hat_j", "I_hat_j")
for (j in 1:N) {
message(paste("Individual ", j))
y = data[data[, id] == names[j], response]
x = data[data[, id] == names[j], running]
result_j[, 1] = names[j]
result_j[, 2] = C
for (i in 1:length(C)) {
c = C[i]
h = ifelse(is.null(bw),
rdrobust::rdbwselect(y, x, kernel = "uniform", c = c)$bws[1],
bw)
K = function(x) {
ifelse((abs(x)) <= 1, 1 / 2, 0)
}
S0p = sum(ifelse(x - c > 0, K((x - c) / h), 0))
S1p = sum(ifelse(x - c > 0, (x - c) * K((x - c) / h), 0))
S2p = sum(ifelse(x - c > 0, (x - c) ^ 2 * K((x - c) / h), 0))
S0n = sum(ifelse(x - c <= 0, K((x - c) / h), 0))
S1n = sum(ifelse(x - c <= 0, (x - c) * K((x - c) / h), 0))
S2n = sum(ifelse(x - c <= 0, (x - c) ^ 2 * K((x - c) / h), 0))
wp = ifelse(x - c > 0, K((x - c) / h), 0) * (S2p - (x - c) * S1p) / (S2p *
S0p - S1p ^ 2)
wn = ifelse(x - c <= 0, K((x - c) / h), 0) * (S2n - (x - c) * S1n) / (S2n *
S0n - S1n ^ 2)
wp1 = ifelse(x > c, K((x - c) / h), 0) * (S1p - (x - c) * S0p) / (-S2p *
S0p + S1p ^ 2)
wn1 = ifelse(x <= c, K((x - c) / h), 0) * (S1n - (x - c) * S0n) / (-S2n *
S0n + S1n ^ 2)
tauhat = sum((wp - wn) * y)
result_j[i, 3] = sum((wp1 - wn1) * y)
fit1 = KernSmooth::locpoly(x,
y - ifelse(x > c, 1, 0) * tauhat,
bandwidth = h,
truncate = FALSE)
e = y - ifelse((x - c) > 0, 1, 0) * tauhat - approx(fit1$x, fit1$y, xout =
x)$y
wpos = ifelse(x - c > 0, ifelse((x - c) < h, 1, 0), 0)
wneg = ifelse(x - c < 0, ifelse((x - c) > -h, 1, 0), 0)
result_j[i, 4] = sqrt(var(e[wpos + wneg != 0]) * sum(wp1 ^ 2 + wn1 ^
2))
}
result_j[, 5] = as.numeric(result_j[, 3]) / as.numeric(result_j[, 4])
if (alternative == "two") {
result_j_max = result_j[abs(result_j$I_hat_j) == max(abs(result_j$I_hat_j)), ]
}
if (alternative == "right") {
result_j_max = result_j[result_j$I_hat_j == max(result_j$I_hat_j), ]
}
if (alternative == "left") {
result_j_max = result_j[result_j$I_hat_j == min(result_j$I_hat_j), ]
}
result = rbind(result, result_j_max)
}
I_hat = ifelse(alternative == "left", min(result$I_hat_j), max(abs(result$I_hat_j)))
if (alternative == "two") {
p_value = 1 - fdrtool::phalfnorm(I_hat) ^ (N * length(C))
}
if (alternative == "right") {
p_value = 1 - pnorm(I_hat) ^ (N * length(C))
}
if (alternative == "left") {
p_value = 1 - pnorm(-I_hat) ^ (N * length(C))
}
alpha = ifelse(is.null(alpha), 1, alpha)
if (alternative == "two") {
result_1 = subset(result, abs(result$I_hat_j) > fdrtool::qhalfnorm((1 - alpha) ^ (1 / (N *
length(C)))))
}
else {
result_1 = subset(result, abs(result$I_hat_j) > qnorm((1 - alpha) ^ (1 / (N *
length(C)))))
}
result_1 = result_1[order(result_1$c_0j), ]
result_1[, 2:5] = round(result_1[, 2:5], digits = 3)
rownames(result_1) <- NULL
if (alternative == "two") {
critical = c(fdrtool::qhalfnorm((0.90) ^ (1 / (N * length(C)))),
fdrtool::qhalfnorm((0.95) ^ (1 / (N * length(C)))),
fdrtool::qhalfnorm((0.99) ^ (1 / (N * length(C)))),
fdrtool::qhalfnorm((0.999) ^ (1 / (N * length(C)))))
}
if (alternative == "right") {
critical = c(qnorm((0.90) ^ (1 / (N * length(C)))),
qnorm((0.95) ^ (1 / (N * length(C)))),
qnorm((0.99) ^ (1 / (N * length(C)))),
qnorm((0.999) ^ (1 / (N * length(C)))))
}
if (alternative == "left") {
critical = -c(qnorm((0.90) ^ (1 / (N * length(C)))),
qnorm((0.95) ^ (1 / (N * length(C)))),
qnorm((0.99) ^ (1 / (N * length(C)))),
qnorm((0.999) ^ (1 / (N * length(C)))))
}
critical = setNames(critical, c("90%", "95%", "99%", "99.9%"))
list = list(I_hat, p_value, N, critical, result_1)
list = setNames(list, c("I_hat", "p_value", "N", "Critical_values", "Table"))
return(list)
}
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