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# Two-Stage Least Squares
# John Fox
# last modified 2019-11-15 by J. Fox
tsls <- function (y, ...) {
UseMethod("tsls")
}
tsls.default <- function (y, X, Z, w, names = NULL, ...) {
if (is.null(w)) w <- 1
if (any(w < 0 | is.na(w)))
stop("missing or negative weights not allowed")
n <- length(y)
p <- ncol(X)
sqrt.w <- sqrt(w)
invZtZ <- solve(crossprod(Z*sqrt.w))
XtZ <- crossprod(X*w, Z)
V <- chol2inv(chol(XtZ %*% invZtZ %*% t(XtZ)))
b <- V %*% XtZ %*% invZtZ %*% crossprod(Z*w, y)
residuals <- (y - X %*% b)*sqrt.w
s2 <- sum(residuals^2)/(n - p)
V <- s2 * V
result <- list()
result$n <- n
result$p <- p
b <- as.vector(b)
names(b) <- names
result$coefficients <- b
rownames(V) <- colnames(V) <- names
result$V <- V
result$s <- sqrt(s2)
result$residuals <- as.vector(residuals)
result$response <- y
result$model.matrix <- X
result$instruments <- Z
result$weights <- w
result
}
tsls.formula <- function (formula, instruments, data, subset, weights, na.action, contrasts = NULL, ...) {
if (missing(na.action))
na.action <- options()$na.action
m <- match.call(expand.dots = FALSE)
if (is.matrix(eval(m$data, sys.frame(sys.parent()))))
m$data <- as.data.frame(data)
response.name <- deparse(formula[[2]])
form <- as.formula(paste(paste(response.name, collapse = ""),
"~", paste(deparse(formula[[3]]), collapse = ""), "+",
paste(deparse(instruments[[2]]), collapse = "")))
m$formula <- form
m$instruments <- m$contrasts <- NULL
m[[1]] <- as.name("model.frame")
mf <- eval(m, sys.frame(sys.parent()))
na.act <- attr(mf, "na.action")
w <- as.vector(model.weights(mf))
wt.var <- if(!is.null(w)) deparse(substitute(weights)) else NULL
Z <- model.matrix(instruments, data = mf, contrasts)
y <- mf[, response.name]
X <- model.matrix(formula, data = mf, contrasts)
result <- tsls(y, X, Z, w, colnames(X))
result$response.name <- response.name
result$formula <- formula
result$instruments <- instruments
result$wt.var <- wt.var
if (!is.null(na.act))
result$na.action <- na.act
class(result) <- "tsls"
result
}
print.tsls <- function (x, ...) {
cat("\nModel Formula: ")
print(x$formula)
cat("\nInstruments: ")
print(x$instruments)
if (!is.null(x$wt.var)){
cat("\nWeights: ", x$wt.var, "\n")
}
cat("\nCoefficients:\n")
print(x$coefficients)
cat("\n")
invisible(x)
}
summary.tsls <- function (object, digits=getOption("digits"), ...) {
save.digits <- options(digits = digits)
on.exit(options(save.digits))
df <- object$n - object$p
std.errors <- sqrt(diag(object$V))
b <- object$coefficients
t <- b/std.errors
p <- 2 * (1 - pt(abs(t), df))
table <- cbind(b, std.errors, t, p)
rownames(table) <- names(b)
colnames(table) <- c("Estimate", "Std. Error", "t value",
"Pr(>|t|)")
result <- list(formula=object$formula, instruments=object$instruments, wt.var=object$wt.var,
residuals=summary(residuals(object)), coefficients=table, digits=digits, s=object$s, df=df)
class(result) <- "summary.tsls"
result
}
print.summary.tsls <- function(x, ...){
cat("\n 2SLS Estimates\n")
cat("\nModel Formula: ")
print(x$formula)
cat("\nInstruments: ")
print(x$instruments)
if (!is.null(x$wt.var)){
cat("\nWeights: ", x$wt.var, "\n")
}
cat("\nResiduals:\n")
print(x$residuals)
cat("\n")
printCoefmat(x$coefficients, digits=x$digits)
cat(paste("\nResidual standard error:", round(x$s, x$digits),
"on", x$df, "degrees of freedom\n\n"))
invisible(x)
}
residuals.tsls <- function(object, ...){
res <- object$residuals
if (is.null(object$na.action))
res
else naresid(object$na.action, res)
}
coef.tsls <- function(object, ...){
object$coefficients
}
fitted.tsls <- function(object, ...){
yhat <- as.vector(object$model.matrix %*% object$coefficients)
if (is.null(object$na.action))
yhat
else napredict(object$na.action, yhat)
}
vcov.tsls <- function(object, ...) object$V
anova.tsls <- function(object, model.2, s2, dfe, ...){
if(!inherits(model.2, "tsls")) stop('requires two models of class tsls')
s2.1 <- object$s^2
n.1 <- object$n
p.1 <- object$p
dfe.1 <- n.1 - p.1
s2.2 <- model.2$s^2
n.2 <- model.2$n
p.2 <- model.2$p
dfe.2 <- n.2 - p.2
SS.1 <- s2.1 * dfe.1
SS.2 <- s2.2 * dfe.2
SS <- abs(SS.1 - SS.2)
Df <- abs(dfe.2 - dfe.1)
if (missing(s2)){
s2 <- if (dfe.1 > dfe.2) s2.2 else s2.1
f <- (SS/Df) / s2
RSS <- c(SS.1, SS.2)
Res.Df <- c(dfe.1, dfe.2)
SS <- c(NA, SS)
P <- c(NA, 1 - pf(f, Df, min(dfe.1, dfe.2)))
Df <- c(NA, Df)
f <- c(NA, f)
rows <- c("Model 1", "Model 2")
}
else{
f <- (SS/Df) / s2
RSS <- c(SS.1, SS.2, s2*dfe)
Res.Df <- c(dfe.1, dfe.2, dfe)
SS <- c(NA, SS, NA)
P <- c(NA, 1 - pf(f, Df, dfe), NA)
Df <- c(NA, Df, NA)
f <- c(NA, f, NA)
rows <- c("Model 1", "Model 2", "Error")
}
table <- data.frame(Res.Df, RSS, Df, SS, f, P)
head.1 <- paste("Model 1: ",format(object$formula), " Instruments:",
format(object$instruments))
head.2 <- paste("Model 2: ",format(model.2$formula), " Instruments:",
format(model.2$instruments))
names(table) <- c("Res.Df", "RSS", "Df", "Sum of Sq", "F", "Pr(>F)")
row.names(table) <- rows
structure(table, heading = c("Analysis of Variance", "", head.1, head.2, ""),
class = c("anova", "data.frame"))
}
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