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#### nlrob.<meth>() functions for high breakdown point nlrob() methods
## concept (and original version) from lme4/R/lmer.R
getOptfun <- function(optimizer, needArgs = c("fn","par","lower","control"))
{
if (((is.character(optimizer) && optimizer=="optimx") ||
deparse(substitute(optimizer))=="optimx") &&
!("package:optimx") %in% search())
stop(shQuote("optimx")," package must be loaded in order to ",
"use ",shQuote('optimizer="optimx"'))
optfun <- if (is.character(optimizer))
tryCatch(get(optimizer), error=function(e) NULL) else optimizer
if (is.null(optfun))
stop("couldn't find optimizer function ",optimizer )
if (!is.function(optfun)) stop("non-function specified as optimizer")
if (any(is.na(match(needArgs, names(formals(optfun))))))
stop("optimizer function must use (at least) formal parameters ",
pasteK(sQuote(needArgs)))
optfun
}
##' Utility for all nlrob.<meth>(): Find how and where to get parameter
##' names from, also check lower, upper, and replicate if needed.
##'
##' @param lower possibly unnamed numeric vector
##' @param upper as \code{lower}; both will be replicated to
##' \code{length(pnames)} if that is specified and longer.
##' @param var.nms character vector of which 'pnames' must be a subset of.
##' @param envir if not missing and an \code{\link{environment}: possibly assign
##' 'lower', 'upper' of full length in the environment \code{envir}.
.fixupArgs <- function(lower, upper, var.nms, envir) {
if(is.null(pnames <- names(lower))) pnames <- names(upper)
if(is.null(pnames))
stop("Provide 'upper' or 'lower' with names()")
if(any(is.na(match(pnames, var.nms))))
stop("parameter names must appear in 'formula'")
hasE <- !missing(envir) && is.environment(envir)
npar <- length(pnames)
if (npar > 1 && length(lower) == 1) {
if(hasE) envir$lower <- rep.int(lower, npar)
} else if (length(lower) != npar)
stop(gettextf("lower must be either of length %d, or length 1", npar))
if (npar > 1 && length(upper) == 1) {
if(hasE) envir$upper <- rep.int(upper, npar)
} else if (length(upper) != npar)
stop(gettextf("upper must be either of length %d, or length 1", npar))
stopifnot(is.numeric(lower), is.numeric(upper), lower <= upper)
pnames
}
nlrob.MM <-
function(formula, data, lower, upper, tol = 1e-6,
psi = c("bisquare", "lqq", "optimal", "hampel"),
init = c("S", "lts"),
ctrl = nlrob.control("MM", psi=psi, init=init, fnscale=NULL,
tuning.chi.scale = .psi.conv.cc(psi, .Mchi.tuning.defaults[[psi]]),
tuning.psi.M = .psi.conv.cc(psi, .Mpsi.tuning.defaults[[psi]]),
optim.control = list(), optArgs = list(...)),
...)
{
if(missing(ctrl)) {
init <- match.arg(init)
psi <- match.arg(psi)
force(ctrl) #
} else {
init <- ctrl$ init
psi <- ctrl$ psi
}
c1 <- ctrl$tuning.chi.scale
c2 <- ctrl$tuning.psi.M
if(is.character(ctrl$optimizer)) {
### TODO
} else if(is.function(ctrl$optimizer)) {
### TODO
} else
stop(gettextf("'%s' must be character string or function, but is \"%s\"",
"ctrl$optimizer", class(ctrl$optimizer)), domain=NA)
## Preliminary psi-specific checks / computations:
switch(psi,
"lqq" = { # lqqMax = rho(Inf), used in rho.inv() *and* 'constant':
c12 <- c1[1]+c1[2]
lqqMax <- (c1[1]*c1[3] - 2*c12)/(1-c1[3]) + c12})
rho1 <- function(t) Mchi(t, c1, psi)
rho2 <- function(t) Mchi(t, c2, psi)
rho.inv <- switch(psi, "bisquare" = function(y) {
## Find x := u^2 which solves cubic eq. 3*x - 3*x^2 + x^3 = y
## <==> (x-1)^3 + 1 = y <==> (1-x)^3 = 1-y <==> x = 1 - (1-y)^(1/3)
## (where we assume 0 <= y <= 1, i.e, y-1 < 0)
c1 * sqrt(1 - (1 - y)^(1/3))
}, "lqq" = function(y) {
uniroot( function(x) rho1(x) - y, lower = 0, upper = lqqMax )$root
}, "optimal" = function(y) {
## Salibian-Barrera, Matias, Willems, Gert, and Zamar, Ruben (2008).
## The fast-tau estimator for regression.
## Journal of Computational and Graphical Statistics 17, 659-682.
sqrt(y/1.38) * c1 * 3
}, "hampel" = function(y) {
C <- MrhoInf(c1, psi)
a <- c1[1]; b <- c1[2]; r <- c1[3]
if (y <= a/C)
sqrt(2*C*y)
else if (y <= (2*b - a)/C)
0.5*a + C/a*y
else r + sqrt( r^2 - ( (r - b)*(2*C/a*y + (b - a)) - b*r ) )
}, stop(gettextf("Psi function '%s' not supported yet", psi)))
M_scale <- function(sigma, u) sum( rho1(u/sigma) )/nobs - 0.5
objective.initial <-
switch(init,
"lts" = function(par) { ## and (h, formula, data, pnames)
y.hat <- eval( formula[[3L]], c(data, setNames(par, pnames)) )
sum(sort.int( (y - y.hat)^2, partial = h )[1:h])
},
"S" = function(par) { ## and (constant, formula, data, pnames)
y.hat <- eval( formula[[3L]], c(data, setNames(par, pnames)) )
res <- y - y.hat
## Rousseeuw, Peter J., and Leroy, Annick M. (1987).
## Robust Regression & Outlier Detection.
## John Wiley & Sons, New York, p. 137.
med_abs_res <- median(abs(res))
uniroot(M_scale,
lower = constant[1L] * med_abs_res,
upper = constant[2L] * med_abs_res,
u = res )$ root ## == 'sigma'
}, stop(gettextf("Initialization 'init = \"%s\"' not supported (yet)",
init)))
objective.M <- function(par, sigma) {
y.hat <- eval( formula[[3L]], c(data, setNames(par, pnames)) )
sum(rho2( (y - y.hat)/sigma ))
}
## => psi(.) / wgt(.) for robustness weights is
## Mpsi(x, c2, psi) or Mwgt(x, c2, psi)
formula <- as.formula(formula)
dataName <- substitute(data)
varNames <- all.vars(formula)
obsNames <- rownames(data <- as.data.frame(data))
data <- as.list(data)# to be used as such
if (length(formula) == 2L) { ## as nls
formula[[3L]] <- formula[[2L]]
formula[[2L]] <- 0
}
npar <- length(pnames <- .fixupArgs(lower, upper, varNames, environment()))
## ^^^^^^^^^ -> possibly changes (lower, upper) in envir.
y <- eval(formula[[2L]], data)
nobs <- length(y)
stopifnot(nobs >= npar)
if (is.null(fnscale <- ctrl$ fnscale))
fnscale <- sum((y - mean(y))^2)
ctrl$fnscale <- NULL # remove it there
stopifnot(is.numeric(fnscale), fnscale > 0)
## is used in M_scale() in any case, and in init-estim. if "S"
constant <- c(
switch(psi, bisquare = 1/c1,
lqq = 1/lqqMax,
optimal = 1/c1 * 1/3,
hampel = 1/c1[3]),
if(nobs %% 2) 2/rho.inv(2/(nobs+2)) else 1/rho.inv(1/(nobs+1)))
switch(init, lts = h <- (nobs + npar + 1)%/%2)
## FIXME: "optimizer":
initial <- do.call(JDEoptim, c(list(lower, upper, objective.initial,
tol=tol, fnscale=fnscale), ctrl$optArgs))
names(initial$par) <- pnames
res <- y - eval( formula[[3L]], c(data, initial$par) )
med_abs_res <- median(abs(res))
sigma <- uniroot( M_scale,
lower = constant[1L] * med_abs_res,
upper = constant[2L] * med_abs_res,
u = res )$root
M <- optim(initial$par, objective.M, sigma = sigma,
method = "L-BFGS-B", lower = lower, upper = upper,
control = c(list(fnscale = initial$value, parscale = initial$par),
ctrl$optim.control), hessian = TRUE)
## 'hessian': experimental - FIXME: eliminate if unused
coef <- setNames(M$par, pnames)
status <-
if (M$convergence == 0) "converged"
else if (M$convergence == 1)
"maximum number of iterations reached without convergence"
else M$message
fit <- eval( formula[[3L]], c(data, coef) )
names(fit) <- obsNames
structure(list(call = match.call(), formula=formula, nobs=nobs,
coefficients = coef,
fitted.values = fit,
residuals = y - fit,
crit = M$value,
initial = initial,
Scale = sigma,
status = status, counts = M$counts, data = dataName,
hessian = M$hessian, ctrl=ctrl),
class = "nlrob")
} ## nlrob.MM
nlrob.tau <- function(formula, data, lower, upper, tol = 1e-6,
psi = c("bisquare", "optimal"),
ctrl = nlrob.control("tau", psi=psi, fnscale=NULL,
tuning.chi.scale = NULL, tuning.chi.tau = NULL,
optArgs = list(...)),
...)
{
if(missing(ctrl)) {
psi <- match.arg(psi)
force(ctrl) #
} else {
psi <- ctrl$ psi
}
if(is.null(.chi.s <- ctrl$tuning.chi.scale))
.chi.s <- switch(psi, bisquare = list(b = 0.20, cc = 1.55),
optimal = list(b = 0.5, cc = 0.405))
if(is.null(.chi.t <- ctrl$tuning.chi.tau))
.chi.t <- switch(psi, bisquare = list(b = 0.46, cc = 6.04),
optimal = list(b = 0.128, cc = 1.060))
b1 <- .chi.s$b
c1 <- .chi.s$cc
b2 <- .chi.t$b
c2 <- .chi.t$cc
## Preliminary psi-specific checks / computations:
switch(psi, "bisquare" = {
b1 <- b1/MrhoInf(c1, psi)
b2 <- b2/MrhoInf(c2, psi)
})
rho1 <- function(t) Mchi(t, c1, psi)
rho2 <- function(t) Mchi(t, c2, psi)
rho.inv <- switch(psi, "bisquare" = function(y) {
c1 * sqrt(1 - (1 - y)^(1/3))
}, "optimal" = function(y) {
## Salibian-Barrera, Matias, Willems, Gert, and Zamar, Ruben (2008).
## The fast-tau estimator for regression.
## Journal of Computational and Graphical Statistics 17, 659-682.
sqrt(y/1.38) * c1 * 3
})
M_scale <- function(sigma, u) sum( rho1(u/sigma) )/nobs - b1
tau_scale2 <- function(u, sigma) sigma^2 * 1/b2*sum( rho2(u/sigma) )/nobs
objective <- function(par) {
fit <- eval( formula[[3L]], c(data, setNames(par, pnames)) )
res <- y - fit
## Rousseeuw, Peter J., and Leroy, Annick M. (1987).
## Robust Regression & Outlier Detection.
## John Wiley & Sons, New York, p. 137.
med_abs_res <- median(abs(res))
sigma <- uniroot( M_scale,
lower = constant[1L] * med_abs_res,
upper = constant[2L] * med_abs_res,
u = res )$root
tau_scale2(res, sigma)
}
formula <- as.formula(formula)
dataName <- substitute(data)
varNames <- all.vars(formula)
obsNames <- rownames(data <- as.data.frame(data))
data <- as.list(data)# to be used as such
if (length(formula) == 2L) { ## as nls
formula[[3L]] <- formula[[2L]]
formula[[2L]] <- 0
}
npar <- length(pnames <- .fixupArgs(lower, upper, varNames, environment()))
## ^^^^^^^^^ -> possibly changes (lower, upper) in envir.
y <- eval(formula[[2L]], data)
nobs <- length(y)
stopifnot(nobs >= npar)
if (is.null(fnscale <- ctrl$ fnscale))
fnscale <- mean((y - mean(y))^2)
ctrl$fnscale <- NULL # remove it there
stopifnot(is.numeric(fnscale), fnscale > 0)
constant <- c(
switch(psi,
bisquare = 1/c1,
optimal = 1/c1 * 1/3),
if (nobs %% 2) 2/rho.inv(2/(nobs+2)) else 1/rho.inv(1/(nobs+1)))
optRes <- do.call(JDEoptim, c(list(lower, upper, objective, tol=tol, fnscale=fnscale),
ctrl$optArgs))
iter <- optRes$iter
status <-
if (optRes$convergence == 0)
"converged"
else paste("failed to converge in", iter, "steps")
coef <- setNames(optRes$par, pnames)
fit <- eval( formula[[3L]], c(data, coef) )
names(fit) <- obsNames
structure(list(call = match.call(), formula=formula, nobs=nobs,
coefficients = coef,
fitted.values = fit,
residuals = y - fit,
crit = optRes$value,
Scale = sqrt(optRes$value),
status = status, iter = iter, data = dataName, ctrl=ctrl),
class = "nlrob")
} ## nlrob.tau
nlrob.CM <- function(formula, data, lower, upper, tol = 1e-6,
psi = c("bisquare", "lqq", "welsh", "optimal", "hampel", "ggw"),
ctrl = nlrob.control("CM", psi=psi, fnscale=NULL,
tuning.chi = NULL, optArgs = list(...)),
...)
{
if(missing(ctrl)) {
psi <- match.arg(psi)
force(ctrl) #
} else {
psi <- ctrl$ psi
}
if (is.null(t.chi <- ctrl$tuning.chi))
t.chi <- switch(psi, bisquare = list(b = 0.5, cc = 1, c = 4.835),
stop("unable to find constants for psi function"))
## FIXME:
b <- t.chi$b ## b = epsilon (in paper) = fraction of outlier ~= breakdown
cc <- t.chi$cc ## cc = k; make
c <- t.chi$c ## c = the factor in objective c*rho(.) - log(sigma)
rho <- function(t) Mchi(t, cc, psi)
M_scale <- function(sigma, u) sum( rho(u/sigma) )/nobs - b
formula <- as.formula(formula)
dataName <- substitute(data)
varNames <- all.vars(formula)
obsNames <- rownames(data <- as.data.frame(data))
data <- as.list(data)# to be used as such
if (length(formula) == 2L) { ## as nls
formula[[3L]] <- formula[[2L]]
formula[[2L]] <- 0
}
npar <- length(pnames <- .fixupArgs(lower,upper, c(varNames,"sigma"),environment()))
## ^^^^^^^^^ -> possibly changes (lower, upper) in envir.
if ("sigma" %in% pnames) {
if ("sigma" %in% varNames || "sigma" %in% names(data))
stop("As \"sigma\" is in 'pnames', do not use it as variable or parameter name in 'formula'")
stopifnot(lower[pnames == "sigma"] >= 0)
objective <- function(par) {
par <- setNames(par, pnames)
fit <- eval( formula[[3L]], c(data, par) )
sigma <- par[["sigma"]]
c * sum(rho( (y - fit)/sigma ))/nobs + log(sigma)
}
con <- function(par) {
par <- setNames(par, pnames)
fit <- eval( formula[[3L]], c(data, par) )
M_scale(par[["sigma"]], y - fit)
}
} else { ## hmm, this case *really* is not CM properly
objective <- function(par) {
fit <- eval( formula[[3L]], c(data, setNames(par, pnames)) )
resid <- y - fit
sigma <- mad(resid)
c * sum(rho( resid/sigma ))/nobs + log(sigma)
}
con <- NULL
}
y <- eval(formula[[2L]], data)
nobs <- length(y)
stopifnot(nobs >= npar)
if (is.null(fnscale <- ctrl$ fnscale))
fnscale <- mean((y - mean(y))^2)
ctrl$fnscale <- NULL # remove it there
stopifnot(is.numeric(fnscale), fnscale > 0)
optRes <- do.call(JDEoptim, c(list(lower, upper, objective, constr=con,
tol=tol, fnscale=fnscale),
ctrl$optArgs))
iter <- optRes$iter
status <- if (optRes$convergence == 0)
"converged"
else paste("failed to converge in", iter, "steps")
coef <- setNames(optRes$par, pnames)
fit <- eval( formula[[3L]], c(data, coef) )
names(fit) <- obsNames
structure(list(call = match.call(), formula=formula, nobs=nobs,
coefficients = coef,
fitted.values = fit,
residuals = y - fit,
crit = optRes$value,
status = status, iter = iter, data = dataName, ctrl=ctrl),
class = "nlrob")
} ## nlrob.CM
nlrob.mtl <- function(formula, data, lower, upper, tol = 1e-6,
ctrl = nlrob.control("mtl", cutoff = 2.5, optArgs = list(...)),
...)
{
stopifnot(is.numeric(cutoff <- ctrl[["cutoff"]]), length(cutoff) >= 1)
trim <- function(t) { # t = residuals Res, or Res / sigma
t <- sort.int(t)
i <- which(t >= cutoff)
h <- if (length(i) > 0)
max(hlow, floor(min( (i - 1)/(2*pnorm(t[i]) - 1) ))) else nobs
list(h = h, t = t)
}
formula <- as.formula(formula)
dataName <- substitute(data)
varNames <- all.vars(formula)
obsNames <- rownames(data <- as.data.frame(data))
data <- as.list(data)# to be used as such
if (length(formula) == 2L) { ## as nls
formula[[3L]] <- formula[[2L]]
formula[[2L]] <- 0
}
npar <- length(pnames <- .fixupArgs(lower,upper, c(varNames,"sigma"), environment()))
## ^^^^^^^^^ -> possibly changes (lower, upper) in envir.
constant <- log(2*pi)
if ("sigma" %in% pnames) {
if ("sigma" %in% varNames || "sigma" %in% names(data))
stop("As \"sigma\" is in 'pnames', do not use it as variable or parameter name in 'formula'")
stopifnot(lower[pnames == "sigma"] >= 0)
objective <- function(par) {
par <- setNames(par, pnames)
fit <- eval( formula[[3L]], c(data, par) )
sigma <- par[["sigma"]]
tp <- trim( abs( (y - fit)/sigma ) )
h <- tp$h
h*(constant + 2*log(sigma)) + sum(tp$t[1L:h]^2)
}
} else { ## hmm... this is not really MTL
objective <- function(par) {
fit <- eval( formula[[3L]], c(data, setNames(par, pnames)) )
resid <- y - fit
sigma <- mad(resid)
tp <- trim( abs(resid/sigma) )
h <- tp$h
h*(constant + 2*log(sigma)) + sum(tp$t[1L:h]^2)
}
}
y <- eval(formula[[2L]], data)
nobs <- length(y)
stopifnot(nobs >= npar)
if (is.null(fnscale <- ctrl$ fnscale))
fnscale <- sum((y - mean(y))^2)
ctrl$fnscale <- NULL # remove it there
stopifnot(is.numeric(fnscale), fnscale > 0)
hlow <- (nobs + npar + 1)%/%2
optRes <- do.call(JDEoptim, c(list(lower, upper, objective, tol=tol, fnscale=fnscale),
ctrl$optArgs))
coef <- setNames(optRes$par, pnames)
crit <- optRes$value
iter <- optRes$iter
status <- if (optRes$convergence == 0)
"converged"
else paste("failed to converge in", iter, "steps")
fit <- eval( formula[[3L]], c(data, coef) )
names(fit) <- obsNames
resid <- y - fit
quan <-
trim( resid/(if ("sigma" %in% pnames) coef["sigma"] else mad(resid)) )$h
structure(list(call = match.call(), formula=formula, nobs=nobs,
coefficients = coef,
fitted.values = fit,
residuals = resid,
crit = crit,
quan = quan,
status = status, iter = iter, data = dataName, ctrl = ctrl),
class = "nlrob")
} ## nlrob.mtl
nlrob.control <- function(method,
psi = c("bisquare", "lqq", "welsh", "optimal", "hampel", "ggw"),
init = c("S", "lts"),
optimizer = "JDEoptim", optArgs = list(),
...)
{
psi <- match.arg(psi)
init <- match.arg(init)
dots <- list(...)
argNms <- names(dots)
##' argument or default -> return list of length 1
a. <- function(nm,def) {
L <- list( if(nm %in% argNms) dots[[nm]] else def )
names(L) <- nm
L
}
switch(method,
"M" = {
list(method = method) # not yet used
},
"MM" = {
c(list(method = method, init = init, psi = psi),
a.("fnscale", NULL),
a.("tuning.chi.scale", .psi.conv.cc(psi, .Mchi.tuning.defaults[[psi]])),
a.("tuning.psi.M", .psi.conv.cc(psi, .Mpsi.tuning.defaults[[psi]])),
a.("optim.control", list()),
list(optimizer = optimizer, optArgs = optArgs))
},
"tau" = {
c(list(method = method, psi = psi),
a.("fnscale", NULL),
a.("tuning.chi.scale", NULL),
a.("tuning.chi.tau", NULL),
list(optimizer = optimizer, optArgs = optArgs))
},
"CM" = {
c(list(method = method, psi = psi),
a.("fnscale", NULL),
a.("tuning.chi", NULL),
list(optimizer = optimizer, optArgs = optArgs))
},
"mtl" = {
c(list(method = method),
a.("fnscale", NULL),
a.("cutoff", 2.5),
list(optimizer = optimizer, optArgs = optArgs))
},
stop("Method ", method, "not correctly supported yet"))
}
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