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# I have named the function "hetprobit2", because another colleague did the heteroscedastic probit model before me.
# I had the luxury to countercheck my code with hers. For this reason: thank you Judith Santer, I owe you several
# lines of code. The core of the code is done based on prof.Zeiles htobit 1; 2a; 2b; 2c.
hetprobit2 <- function(formula, data, subset, na.action,
model = TRUE, y = TRUE, x = FALSE,
control = hetprobit2_control(...), ...)
{
## call
cl <- match.call()
if(missing(data))
data <- environment(formula)
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data", "subset", "na.action"), names(mf), 0L)
mf <- mf[c(1L, m)]
mf$drop.unused.levels <- TRUE
## formula
oformula <- as.formula(formula)
formula <- as.Formula(formula)
if(length(formula)[2L] < 2L) {
formula <- as.Formula(formula(formula), formula(formula, lhs = 0L))
} else {
if(length(formula)[2L] > 2L) {
formula <- Formula(formula(formula, rhs = 1L:2L))
warning("formula must not have more than two RHS parts")
}
}
mf$formula <- formula
## evaluate model.frame
mf[[1L]] <- as.name("model.frame")
mf <- eval(mf, parent.frame())
## extract terms, model matrix, response
mt <- terms(formula, data = data)
mtX <- terms(formula, data = data, rhs = 1L)
mtZ <- delete.response(terms(formula, data = data, rhs = 2L))
Y <- model.response(mf, "numeric")
X <- model.matrix(mtX, mf)
Z <- model.matrix(mtZ, mf)[, -1, drop = FALSE] # remove intercept in z matrix but keep the dimension of z # thanks Judith
## sanity check
if(length(Y) < 1) stop("empty model")
n <- length(Y)
## call the actual workhorse: hetprobit2_fit()
rval <- hetprobit2_fit(X, Y, Z, control)
## further model information
rval$call <- cl
rval$formula <- oformula
rval$terms <- list(mean = mtX, scale = mtZ, full = mt)
rval$levels <- list(mean = .getXlevels(mtX, mf), scale = .getXlevels(mtZ, mf), full = .getXlevels(mt, mf))
rval$contrasts <- list(mean = attr(X, "contrasts"), scale = attr(Z, "contrasts"))
if(model) rval$model <- mf
if(y) rval$y <- Y
if(x) rval$x <- list(mean = X, scale = Z)
class(rval) <- "hetprobit2"
return(rval)
}
hetprobit2_control <- function(maxit = 5000, start = NULL, ...)
{
ctrl <- c(
list(maxit = maxit,
start = start), list(...)
)
if(!is.null(ctrl$fnscale)) warning("fnscale must not be modified")
ctrl$fnscale <- 1
if(is.null(ctrl$reltol)) ctrl$reltol <- .Machine$double.eps^(1/1.2)
ctrl
}
hetprobit2_fit <- function(x, y, z = NULL, control, ...)
{
if(is.null(z)) matrix(1, n, 1, dimnames = list(rownames(x), "(Intercept)")) # Thanks Judith!
## dimensions
n <- length(y)
m <- ncol(x)
p <- ncol(z)
stopifnot(n == nrow(x), n == nrow(z))
## negative log-likelihood
nll <- function(par) {
beta <- par[1:m]
gamma <- par[m + (1:p)]
mu <- x %*% beta
sigma <- exp(z %*% gamma)
pi <- pnorm(mu/sigma)
ll <- dbinom(as.numeric(y), prob = pi, size = 1, log = TRUE)
-sum(ll)
}
## starting values by default -> glm.fit(x, y, family = binomial())
if(is.null(control$start)) {
start <- glm.fit(x, y, family = binomial(link = "probit"))
start <- start <- c(start$coefficients, rep.int(0, p))
} else {
start <- control$start
stopifnot(length(start) == m + p)
}
control$start <- NULL
## optimization
opt <- optim(par = start, fn = nll, control = control)
## collect information
names(opt)[1:2] <- c("coefficients", "loglik")
opt$coefficients <- list(
mean = opt$coefficients[1:m],
scale = opt$coefficients[m + 1:p]
)
names(opt$coefficients$mean) <- colnames(x)
names(opt$coefficients$scale) <- colnames(z)
opt$loglik <- -opt$loglik
opt$nobs <- n
opt$df <- m + p
return(opt)
}
logLik.hetprobit2 <- function(object, ...) {
structure(object$loglik, df = object$df, class = "logLik")
}
coef.hetprobit2 <- function(object, model = c("full", "location", "scale"), ...) {
model <- match.arg(model)
cf <- object$coefficients
switch(model,
"mean" = cf$mean,
"scale" = cf$scale,
"full" = {
structure(c(cf$mean, cf$scale),
.Names = c(names(cf$mean), paste("(scale)", names(cf$scale), sep = "_")))
}
)
} # Thanks Judith
print.hetprobit2 <- function(x, digits = max(3, getOption("digits") - 3), ...)
{
cat("Heteroscedastic probit model 2\n\n")
cat("\nCall:", deparse(x$call, width.cutoff = floor(getOption("width") * 0.85)), "", sep = "\n")
cat("Coefficients (binomial model with probit link):\n")
print.default(format(x$coefficients$mean, digits = digits), print.gap = 2, quote = FALSE)
cat("\nCoefficients (scale model with log link):\n")
print.default(format(x$coefficients$scale, digits = digits), print.gap = 2, quote = FALSE)
cat(sprintf("\nLog-likelihood: %s on %s Df\n", format(x$loglik, digits = digits), x$df))
invisible(x)
}
terms.hetprobit2 <- function(x, model = c("mean", "scale", "full"), ...) x$terms[[match.arg(model)]]
model.frame.hetprobit2 <- function(formula, ...) {
if(!is.null(formula$model)) return(formula$model)
formula$terms <- formula$terms$full
formula$call$formula <- formula$formula <- formula(formula$terms)
NextMethod()
}
model.matrix.hetprobit2 <- function(object, model = c("mean", "scale"), ...) {
model <- match.arg(model)
rval <- if(!is.null(object$x[[model]])) object$x[[model]]
else model.matrix(object$terms[[model]], model.frame(object), contrasts = object$contrasts[[model]])
return(rval)
}
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