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prelim.profiling <- function(fitted, quantile = qchisq(0.95, 1), objective = stop("'objective' is missing."),
verbose = TRUE, which = 1:length(coef(fitted)), stepsize = 0.5,
stdn = 5, agreement = TRUE, trace.prelim = FALSE, stdErrors = NULL,
...) {
## which should be a vector of integers
if (is.null(stdErrors))
stdErrors <- summary(fitted)$coefficients[, 2]
Betas <- coef(fitted)
BetasNames <- names(Betas)
noNA <- !is.na(Betas) # aliased out
fm.call <- fitted$call
mf <- model.frame(fitted$terms,data=eval(fm.call$data))
if (inherits(fitted,"BTm")) {
Y <- fitted$y0
X <- fitted$x0
}
else {
Y <- model.response(mf)
X <- model.matrix(fitted$terms,mf,contrasts = fitted$contrasts)
}
if (is.null(fitted$X.max.scaleFit) & inherits(fitted,"polr"))
X <- X[, -1, drop = FALSE]
O <- model.offset(mf)
if (is.null(O))
O <- rep(0, nrow(X))
# fitted.formula <- formula(fitted)
fm.call$offset <- NULL
LP.or <- fitted$linear.predictor
if (length(Betas) == 1)
fm.call$formula <- Y ~ -1 + offset(o)
else {
if (inherits(fitted,"BTm")) {
fm.call$formula <- Y ~ -1 + offset(o) + Xnoi
}
else {
XnoiNams <- paste(paste("Xnoi[,", 1:(ncol(X) - sum(!noNA) -1),
"]", sep=""))
fm.call$formula <- as.formula(paste("Y ~ -1 + offset(o) + ",
paste(XnoiNams, collapse = "+")))
}
}
fm.call$offset <- NULL
fitted.formals <- names(formals(as.character(fm.call)[[1]]))
test1 <- "etastart" %in% fitted.formals
if (test1) {
LP.or <- fitted$linear.predictor
fm.call$etastart <- as.symbol("LP")
}
ObjValue.or <- objective(fitted, ...)
p <- length(which)
grid.bounds <- intersects <- matrix(NA, p, 2, dimnames = list(BetasNames[which],
c("Left", "Right")))
## The information in prelim.profile could be used... TBD
## if (return.profiles) {
## res <- as.list(rep(NA,p))
## names(res) <- BetasNames[which]
## }
should.intersect <- intersects.temp <- rep(NA, 2)
numberofsteps <- stdn/stepsize
if (verbose & !trace.prelim)
cat("Preliminary iteration ")
for (i in which) {
if (verbose & !trace.prelim)
cat(".")
if (!noNA[i]) # aliased out
next
tb.included <- noNA
tb.included[i] <- FALSE # without the aliased
profiledName <- BetasNames[i]
if (trace.prelim)
cat(profiledName, "\n")
stepsize.temp <- c(stepsize, stepsize)
stdErrors.i <- stdErrors[i]
Xnoi <- X[, tb.included, drop = FALSE] # without the aliased
Xonlyi <- X[, i]
################
### left
################
cc <- 1
tempDiff <- quantile + 10
test.intersections <- TRUE
b <- Betas[i]
b <- b.old <- sign(b) * min(abs(b), 30)
LP <- (abs(b) <= 30) * LP.or
while (test.intersections) {
b <- b.old
## if (trace.prelim) {
## title1 <- paste(profiledName,"left","with stepsize",stepsize.temp[1]) #TR
## plot(1,1,xlim=c(Betas[i]-5*min(30,stdErrors.i),Betas[i]+5*min(30,stdErrors.i)), #TR
## ylim=c(0,100),type="n",main=title1) #TR
## points(x=c(Betas[i]-5*min(30,stdErrors.i),Betas[i]+5*min(30,stdErrors.i)), #TR
## y=c(quantile,quantile),type="l") #TR
## }
test <- TRUE
curPoint <- 0
slope.pp <- 1
slopes.pp <- rep(1, numberofsteps + 5)
while (test & curPoint < numberofsteps) {
tempDiff.old <- tempDiff
b.old <- b
## if (trace.prelim) {
## if (!curPoint) {points(x=b,y=tempDiff,pch='s');Sys.sleep(1)} #TR
## else {points(x=b,y=tempDiff);Sys.sleep(1)} #TR
## }
curPoint <- curPoint + 1
b <- c(b - min(30, stdErrors.i)/slope.pp * curPoint * stepsize.temp[1])
o <- O + Xonlyi * b
suppressWarnings(fm <- eval(fm.call))
LP <- fm$linear.predictor
tempDiff <- objective(fm, ...) - ObjValue.or
if (is.na(tempDiff))
stop("Profiling failed. NA's introduced by the objective.")
if (is.infinite(tempDiff)) {
warning("Infinite values were introduced by the objective.")
slope.pp <- 1
}
else {
slope.pp <- abs(ss <- (tempDiff.old - tempDiff)/(b.old -
b))
slopes.pp[curPoint] <- slope.pp
## set to give the objective a chance to increase and at the
# same time to avoid huge steps while being conservative
if (slope.pp < 1)
slope.pp <- 1
if (slope.pp > 500)
slope.pp <- 500
}
## if you have done the first three iterations and nothing
# is found stop
if (curPoint < 4)
nonzero.slopes <- TRUE
else nonzero.slopes <- !all(slopes.pp[(curPoint -
3):curPoint] < 1e-08)
test <- (tempDiff < quantile | ss > 1e-08) &
nonzero.slopes
if (trace.prelim)
cat("<-- iteration:", curPoint, "\t", paste(c("CPV:",
"SL:", "OV:"), format(round(c(b, ss, tempDiff),
digits = 3), zero.print = TRUE)), "SS:",
stepsize.temp[1], "\n")
}
grid.bounds[profiledName, 1] <- b
should.intersect[1] <- nonzero.slopes
intersects.temp[1] <- tempDiff > quantile
## test.intersections is interpreted as should intersect but it does not
# ss>0 stands for the case where the search on the left side starts outside
# the right end of the profiled objective (if agreement is false then this is
# necessary. if agreement is true then ss>0 does not violate the facts)
test.intersections <- (should.intersect[1] | ss >
1e-08) & (!intersects.temp[1] | ss > 1e-08)
}
################
### right
################
cc <- 1
tempDiff <- quantile + 10
test.intersections <- TRUE
b <- Betas[i]
b <- b.old <- sign(b) * min(abs(b), 30)
LP <- (abs(b) <= 30) * LP.or
while (test.intersections) {
b <- b.old
## if (trace.prelim) {
## title1 <- paste(profiledName,"right","with stepsize",stepsize.temp[2]) #TR
## plot(1,1,xlim=c(Betas[i]-5*min(30,stdErrors.i),Betas[i]+5*min(30,stdErrors.i)), #TR
## ylim=c(0,200),type="n",main=title1) #TR
## points(x=c(Betas[i]-5*min(30,stdErrors.i),Betas[i]+5*min(30,stdErrors.i)), #TR
## y=c(quantile,quantile),type="l") #TR
## }
test <- TRUE
curPoint <- 0
slope.pp <- 1
slopes.pp <- rep(1, numberofsteps + 5)
while (test & curPoint < numberofsteps) {
tempDiff.old <- tempDiff
b.old <- b
## if (trace.prelim) {
## if (!curPoint) {points(x=b,y=tempDiff,pch='s');Sys.sleep(1)} #TR
## else {points(x=b,y=tempDiff);Sys.sleep(1)} #TR
## }
curPoint <- curPoint + 1
b <- c(b + min(30, stdErrors.i)/slope.pp * curPoint * stepsize.temp[2])
o <- O + Xonlyi * b
suppressWarnings(fm <- eval(fm.call))
LP <- fm$linear.predictor
tempDiff <- objective(fm, ...) - ObjValue.or
if (is.na(tempDiff))
stop("Profiling failed. NA's introduced by the objective.")
if (is.infinite(tempDiff)) {
warning("Infinite values were introduced by the objective.")
slope.pp <- 1
}
else {
slope.pp <- abs(ss <- (tempDiff.old - tempDiff)/(b.old -
b))
slopes.pp[curPoint] <- slope.pp
## set to give the objective a chance to increase and at the
# same time to avoid huge steps while being conservative
if (slope.pp < 1)
slope.pp <- 1
if (slope.pp > 500)
slope.pp <- 500
}
## if you have done the first three iterations and nothing
# is found stop
if (curPoint < 4)
nonzero.slopes <- TRUE
else nonzero.slopes <- !all(slopes.pp[(curPoint -
3):curPoint] < 1e-08)
test <- (tempDiff < quantile | ss < -1e-08) &
nonzero.slopes
if (trace.prelim)
cat("--> iteration:", curPoint, "\t", paste(c("CPV:",
"SL:", "OV:"), format(round(c(b, ss, tempDiff),
digits = 3), zero.print = TRUE)), "SS:",
stepsize.temp[1], "\n")
}
grid.bounds[profiledName, 2] <- b
should.intersect[2] <- nonzero.slopes
intersects.temp[2] <- tempDiff > quantile
## test.intersections is interpreted as should intersect but it does not
# ss>0 stands for the case where the search on the left side starts outside
# the right end of the profiled objective (if agreement is false then this is
# necessary. if agreement is true then ss>0 does not violate the facts)
test.intersections <- (should.intersect[2] | ss <
-1e-08) & (!intersects.temp[2] | ss < -1e-08)
stepsize.temp[2] <- stepsize.temp[2] + stepsize
cc <- cc + 1
}
intersects[profiledName, ] <- intersects.temp
if (i == which[p] & verbose & !trace.prelim)
cat(" Done\n\n")
}
if (trace.prelim) {
cat("<--: Left | -->: Right | CPV: Current Parameter value\n")
cat("SL: slope | OV: Objective Value | SS: StepSize\n")
}
list(grid.bounds = grid.bounds, intersects = intersects)
}
profileModel <- function(fitted, gridsize = 20, stdn = 5, stepsize = 0.5, grid.bounds = NULL,
quantile = NULL, objective = stop("'objective' is missing."),
agreement = TRUE, verbose = TRUE, trace.prelim = FALSE, which = 1:length(coef(fitted)),
profTraces = TRUE, zero.bound = 1e-08, scale = FALSE, stdErrors = NULL,
...) {
Betas <- coef(fitted)
BetasNames <- names(Betas)
noNA <- !is.na(Betas)
if (is.null(stdErrors)) {
stdErrors <- rep(NA, length(Betas))
stdErrors[noNA] <- summary(fitted)$coefficients[BetasNames[noNA], 2]
}
if (scale) {
fitted <- scaleFit(fitted)
Xmax <- fitted$X.max.scaleFit
}
if ((zero.bound < 0) | (zero.bound > 1e-06)) {
stop("zero.bound takes values between 0 and 1e-6.")
}
if (is.character(which)) {
which <- match(which, BetasNames)
ttt <- is.na(which)
if (any(ttt))
stop("A least a parameter name specified in 'which' does not exist in the fitted model.")
}
if (any(duplicated(which))) {
warning("At least a parameter was specified more than once in 'which'. Profiling for the duplicated parameter(s) was done only once.")
which <- unique(which)
}
if (min(which) < 1 | max(which) > length(Betas)) {
stop("At least a parameter position specified in 'which' is not valid.")
}
p <- length(which)
na.in.which <- !noNA[which]
if (all(na.in.which)) {
stop("'which' refers to parameters which have value 'NA' in the original fit.")
}
if (any(na.in.which)) {
warning("At least a parameter with value 'NA' exists in the original fit. Profiling did not take place for these parameters.")
}
if (!is.null(grid.bounds))
if (length(grid.bounds) != 2 * p)
stop("The dimension of 'grid.bounds' is not compatible with the length of 'which'.")
objective <- match.fun(objective)
if (is.null(grid.bounds)) {
if (is.null(quantile)) {
grid.bounds <- cbind(Betas[which] - stdn * stdErrors[which],
Betas[which] + stdn * stdErrors[which])
if (scale)
grid.bounds <- grid.bounds * Xmax[which]
result <- profiling(fitted, grid.bounds = grid.bounds,
gridsize = gridsize, verbose = verbose, objective = objective,
which = which, agreement = agreement, profTraces = profTraces,
zero.bound = zero.bound, ...)
intersects <- NULL
attr(grid.bounds, "from.prelim") <- FALSE
}
else {
if (scale)
stdErrors <- stdErrors * Xmax
prelim.res <- prelim.profiling(fitted, quantile = quantile,
objective = objective, verbose = verbose, which = which,
stepsize = stepsize, stdn = stdn, agreement = agreement,
trace.prelim = trace.prelim, stdErrors = stdErrors,
...)
grid.bounds <- prelim.res$grid.bounds
result <- profiling(fitted, grid.bounds = grid.bounds,
gridsize = gridsize, verbose = verbose, objective = objective,
which = which, agreement = agreement, profTraces = profTraces,
zero.bound = zero.bound, ...)
intersects <- prelim.res$intersects
rownames(intersects) <- BetasNames[which]
attr(grid.bounds, "from.prelim") <- TRUE
}
}
else {
if (is.null(dim(grid.bounds)))
grid.bounds <- matrix(grid.bounds, ncol = 2, byrow = TRUE)
if (scale)
grid.bounds <- grid.bounds * Xmax[which]
result <- profiling(fitted, grid.bounds = grid.bounds,
gridsize = gridsize, verbose = verbose, objective = objective,
which = which, agreement = agreement, profTraces = profTraces,
zero.bound = zero.bound, ...)
intersects <- NULL
attr(grid.bounds, "from.prelim") <- FALSE
}
names(result) <- rownames(grid.bounds) <- BetasNames[which]
if (scale) {
grid.bounds <- grid.bounds/Xmax[which]
for (i in 1:p) {
if (!noNA[which[i]])
next
result[[i]][, 1] <- result[[i]][, 1]/Xmax[which[i]]
colnames(result[[i]])[1] <- BetasNames[which[i]]
}
if (profTraces) {
for (i in 1:p) {
if (!noNA[which[i]])
next
tb.included <- noNA
tb.included[which[i]] <- FALSE
result[[i]][, -c(1, 2)] <- sweep(result[[i]][,
-c(1, 2), drop = FALSE], 2, Xmax[tb.included], "/")
colnames(result[[i]])[-c(1, 2)] <- BetasNames[tb.included]
}
}
}
dotss <- match.call(expand.dots = FALSE)[["..."]]
dotssNames <- names(dotss)
for (i in dotssNames) formals(objective)[[i]] <- eval(dotss[[i]])
result <- list(profiles = result, fit = fitted, quantile = quantile,
gridsize = gridsize, intersects = intersects, profiled.parameters = which,
profiled.objective = objective, isNA = !noNA[which],
agreement = agreement, zero.bound = zero.bound, call = match.call(),
grid.bounds = grid.bounds)
attr(result, "includes.traces") <- profTraces
class(result) <- "profileModel"
result
}
profiling <- function(fitted, grid.bounds, gridsize = 20, verbose = TRUE,
objective = stop("'objective' is missing."), agreement = TRUE,
which = 1:length(coef(fitted)), profTraces = TRUE, zero.bound = 1e-08,
...) {
## which should be a vector of integers
## grid.bounds should be a 2*length(which) vector of reals or
# a 2 by length(which) matrix of reals
if (is.null(dim(grid.bounds)))
grid.bounds <- matrix(grid.bounds, ncol = 2, byrow = TRUE)
Betas <- coef(fitted)
p.or <- length(Betas)
BetasNames <- names(Betas)
noNA <- !is.na(Betas)
p <- length(which)
fm.call <- fitted$call
mf <- model.frame(fitted$terms,data=eval(fm.call$data))
Y <- model.response(mf)
if (inherits(fitted,"BTm")) {
Y <- fitted$y0
X <- fitted$x0
}
else {
Y <- model.response(mf)
X <- model.matrix(fitted$terms,mf,contrasts = fitted$contrasts)
}
if (is.null(fitted$X.max.scaleFit) & inherits(fitted, "polr"))
X <- X[, -1, drop = FALSE]
O <- model.offset(mf)
if (is.null(O))
O <- rep(0, nrow(X))
# fitted.formula <- formula(fitted)
if (p.or == 1)
fm.call$formula <- Y ~ -1 + offset(o)
else {
if (inherits(fitted,"BTm"))
fm.call$formula <- Y ~ -1 + offset(o) + Xnoi
else {
XnoiNams <- paste(paste("Xnoi[,", 1:(ncol(X) - sum(!noNA) -1),
"]", sep=""))
fm.call$formula <- as.formula(paste("Y ~ -1 + offset(o) + ",
paste(XnoiNams, collapse = "+")))
}
}
fm.call$offset <- NULL
fitted.formals <- names(formals(as.character(fm.call)[[1]]))
test1 <- "etastart" %in% fitted.formals
if (test1) {
LP.or <- fitted$linear.predictor
fm.call$etastart <- as.symbol("LP")
}
ObjValue.or <- objective(fitted, ...)
res <- as.list(rep(NA, p))
names(res) <- BetasNames[which]
for (i in 1:p) {
iprof <- which[i]
if (!noNA[iprof]) # aliased out
next
tb.included <- noNA
tb.included[iprof] <- FALSE # without the aliased
profiledName <- BetasNames[iprof]
gridd <- seq(grid.bounds[i, 1], grid.bounds[i, 2], length = gridsize)
curPoint <- 0
Xnoi <- X[, tb.included, drop = FALSE] # without the aliased
Xonlyi <- X[, iprof]
inds.right <- which(gridd >= Betas[iprof])
inds.left <- which(gridd < Betas[iprof])
# Make sure you start as close as possible to the estimate
if (grid.bounds[i, 1] <= grid.bounds[i, 2])
inds.left <- inds.left[order(inds.left, decreasing = TRUE)]
else inds.right <- inds.right[order(inds.right, decreasing = TRUE)]
inds <- list(inds.left, inds.right)
ObjValues <- cbind(gridd, 0)
if (profTraces) {
tracesNames <- BetasNames[tb.included]
profile.traces <- matrix(0, nrow = gridsize, ncol = sum(noNA) -
1)
colnames(profile.traces) <- tracesNames
}
colnames(ObjValues) <- c(profiledName, "Differences")
if (verbose)
cat("Profiling for parameter", profiledName, "...")
for (k in 1:2) {
if (test1)
LP <- LP.or
## else supply no starting valiues...
## maybe an argument to control starting values??? TBD
for (curPoint in inds[[k]]) {
bp <- c(gridd[curPoint])
o <- O + Xonlyi * bp
suppressWarnings(fm <- eval(fm.call))
## LP will be NULL if fm$linear.predictor does not exist...OK
LP <- fm$linear.predictor
ObjValue.current <- (objective(fm, ...) - ObjValue.or)
if (is.na(ObjValue.current))
stop("Profiling failed. NA's introduced by the objective.")
if (is.infinite(ObjValue.current))
warning("Infinite values were introduced by the objective.")
if (agreement) {
if (ObjValue.current < -(zero.bound * 1000)) {
stop("Profiling has found a better solution. Original fit had not converged.")
}
ObjValues[curPoint, 2] <- (ObjValue.current >=
zero.bound) * ObjValue.current
}
else {
ObjValues[curPoint, 2] <- ObjValue.current
}
if (profTraces)
profile.traces[curPoint, ] <- coef(fm)
}
}
if (verbose)
cat(" Done\n")
res[[profiledName]] <- if (profTraces)
cbind(ObjValues, profile.traces)
else ObjValues
}
res
}
|
