261 lines
8.8 KiB
R
261 lines
8.8 KiB
R
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library(tensorPredictors)
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# Data set sample size in every simulation
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sample.size <- 500L
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# Nr. of per simulation replications
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reps <- 100L
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# number of observation/response axes (order of the tensors)
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orders <- c(2L, 3L, 4L)
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# auto correlation coefficient for the mode-wise auto scatter matrices `Omegas`
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rhos <- seq(0, 0.8, by = 0.1)
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setwd("~/Work/tensorPredictors/sim/")
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base.name <- format(Sys.time(), "failure_of_tsir-%Y%m%dT%H%M")
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# data sampling routine
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sample.data <- function(sample.size, betas, Omegas) {
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dimF <- mapply(ncol, betas)
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# responce is a standard normal variable
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y <- rnorm(sample.size)
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y.pow <- Reduce(function(a, b) outer(a, b, `+`), Map(seq, 0L, len = dimF))
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F <- t(outer(y, as.vector(y.pow), `^`))
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dim(F) <- c(dimF, sample.size)
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# sample predictors from tensor normal X | Y = y (last axis is sample axis)
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sample.axis <- length(betas) + 1L
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Sigmas <- Map(solve, Omegas)
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mu_y <- mlm(F, Map(`%*%`, Sigmas, betas))
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X <- mu_y + rtensornorm(sample.size, 0, Sigmas, sample.axis)
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list(X = X, F = F, y = y, sample.axis = sample.axis)
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}
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# Create a CSV logger to write simulation results to
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log.file <- paste(base.name, "csv", sep = ".")
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logger <- CSV.logger(
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file.name = log.file,
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header = c("rho", "order", "sample.size", "rep", "beta.version", outer(
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"dist.subspace", c("gmlm", "tsir", "sir"),
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paste, sep = "."
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))
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)
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for (order in orders) {
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# setup problem dimensions given the tensor order
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dimX <- rep(2L, order)
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dimF <- rep(2L, order)
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# as well as the projections onto rank 1 matrices
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proj.betas <- Map(.projRank, rep(1L, order))
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for (rho in rhos) {
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# Scatter matrices (Omegas) given as autoregression structure `AR(rho)`
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Omegas <- Map(function(p) rho^abs(outer(1:p, 1:p, `-`)), dimX)
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# Version 1 betas (reductions)
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beta.version <- 1L
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betas <- Map(function(nr, nc) {
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`[<-`(matrix(0, nr, nc), 1, , 1)
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}, dimX, dimF)
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B.true <- Reduce(kronecker, rev(betas))
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# `(B.min %*% vec(X)) | Y = y` proportional to `(1 + y)^order`)
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B.min.true <- B.true[, 1L, drop = FALSE]
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# Version 1: repeated simulations
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for (rep in seq_len(reps)) {
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# Sample training data
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c(X, F, y, sample.axis) %<-% sample.data(sample.size, betas, Omegas)
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# Fit models to provided data
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fit.gmlm <- gmlm_tensor_normal(X, F, sample.axis = sample.axis, proj.betas = proj.betas)
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fit.tsir <- TSIR(X, y, d = rep(1L, order), sample.axis = sample.axis)
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fit.sir <- SIR(mat(X, sample.axis), y, d = 1L)
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# Extract minimal reduction matrices from fitted models
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B.gmlm <- qr.Q(qr(Reduce(kronecker, rev(fit.gmlm$betas))))[, 1L, drop = FALSE]
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B.tsir <- Reduce(kronecker, rev(fit.tsir))
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B.sir <- fit.sir
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# Compute estimation to true minimal `B` distance
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dist.subspace.gmlm <- dist.subspace(B.min.true, B.gmlm, normalize = TRUE)
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dist.subspace.tsir <- dist.subspace(B.min.true, B.tsir, normalize = TRUE)
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dist.subspace.sir <- dist.subspace(B.min.true, B.sir, normalize = TRUE)
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# Write to simulation log file (CSV file)
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logger()
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# and print progress
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cat(sprintf("order %d, rho %.2f, version %d: rep: %d/%d\n",
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order, rho, beta.version, rep, reps))
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}
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# Version 2 betas (reductions)
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beta.version <- 2L
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betas <- Map(function(nr, nc) {
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tcrossprod((-1)^seq_len(nr), (-1)^seq_len(nc))
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}, dimX, dimF)
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B.true <- Reduce(kronecker, rev(betas))
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# `(B.min %*% vec(X)) | Y = y` proportional to `(1 - y)^order`)
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B.min.true <- B.true[, 1L, drop = FALSE]
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# Version 2: repeated simulations (identical to Version 1)
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for (rep in seq_len(reps)) {
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# Sample training data
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c(X, F, y, sample.axis) %<-% sample.data(sample.size, betas, Omegas)
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# Fit models to provided data
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fit.gmlm <- gmlm_tensor_normal(X, F, sample.axis = sample.axis, proj.betas = proj.betas)
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fit.tsir <- TSIR(X, y, d = rep(1L, order), sample.axis = sample.axis)
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fit.sir <- SIR(mat(X, sample.axis), y, d = 1L)
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# Extract minimal reduction matrices from fitted models
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B.gmlm <- qr.Q(qr(Reduce(kronecker, rev(fit.gmlm$betas))))[, 1L, drop = FALSE]
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B.tsir <- Reduce(kronecker, rev(fit.tsir))
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B.sir <- fit.sir
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# Compute estimation to true minimal `B` distance
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dist.subspace.gmlm <- dist.subspace(B.min.true, B.gmlm, normalize = TRUE)
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dist.subspace.tsir <- dist.subspace(B.min.true, B.tsir, normalize = TRUE)
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dist.subspace.sir <- dist.subspace(B.min.true, B.sir, normalize = TRUE)
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# Write to simulation log file (CSV file)
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logger()
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# and print progress
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cat(sprintf("order %d, rho %.2f, version %d: rep: %d/%d\n",
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order, rho, beta.version, rep, reps))
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}
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}
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}
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### read simulation results and generate plots
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if (!interactive()) { pdf(file = paste(base.name, "pdf", sep = ".")) }
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# Read simulation results back from log file
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sim <- read.csv(log.file)
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# Source utility function used in most simulations (extracted for convenience)
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source("./sim_utils.R")
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# aggregate results
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grouping <- sim[c("rho", "order", "beta.version")]
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sim.dist <- sim[startsWith(names(sim), "dist")]
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aggr <- aggregate(sim.dist, grouping, mean)
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# reset (possible lost) config
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orders <- sort(unique(aggr$order))
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rhos <- sort(unique(aggr$rho))
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# new grouping for the aggregates
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layout(rbind(
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matrix(seq_len(2 * length(orders)), ncol = 2),
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2 * length(orders) + 1
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), heights = c(rep(6L, length(orders)), 1L))
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for (group in split(aggr, aggr[c("order", "beta.version")])) {
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order <- group$order[[1]]
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beta.version <- group$beta.version[[1]]
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rho <- group$rho
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plot(range(rho), 0:1, main = sprintf("V%d, order %d", beta.version, order),
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type = "n", bty = "n", axes = FALSE, xlab = expression(rho), ylab = "Subspace Distance")
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axis(1, at = rho)
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axis(2, at = seq(0, 1, by = 0.2))
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with(group, {
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lines(rho, dist.subspace.gmlm, col = col.methods["gmlm"], lwd = 3, type = "b", pch = 16)
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lines(rho, dist.subspace.tsir, col = col.methods["tsir"], lwd = 2, type = "b", pch = 16)
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lines(rho, dist.subspace.sir, col = col.methods["sir"], lwd = 2, type = "b", pch = 16)
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})
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if (order == 3L && beta.version == 2L) {
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abline(v = 0.5, lty = "dotted", col = "black")
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abline(h = group$dist.subspace.tsir[which(rho == 0.5)],
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lty = "dotted", col = "black")
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}
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}
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methods <- c("GMLM", "TSIR", "SIR")
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restor.par <- par(
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fig = c(0, 1, 0, 1),
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oma = c(0, 0, 0, 0),
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mar = c(1, 0, 0, 0),
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new = TRUE
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)
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plot(0, type = "n", bty = "n", axes = FALSE, xlab = "", ylab = "")
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legend("bottom", col = col.methods[tolower(methods)], legend = methods,
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horiz = TRUE, lty = 1, bty = "n", lwd = c(3, 2, 2), pch = 16)
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par(restor.par)
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# new grouping for the aggregates
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layout(rbind(
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matrix(seq_len(2 * 3), ncol = 2),
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2 * 3 + 1
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), heights = c(rep(6L, 3), 1L))
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for (group in split(aggr, aggr[c("rho", "beta.version")])) {
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rho <- group$rho[[1]]
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beta.version <- group$beta.version[[1]]
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if (!(rho %in% c(0, .5, .8))) { next }
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order <- group$order
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plot(range(order), 0:1, main = sprintf("V%d, rho %.1f", beta.version, rho),
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type = "n", bty = "n", axes = FALSE, xlab = expression(order), ylab = "Subspace Distance")
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axis(1, at = order)
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axis(2, at = seq(0, 1, by = 0.2))
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with(group, {
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lines(order, dist.subspace.gmlm, col = col.methods["gmlm"], lwd = 3, type = "b", pch = 16)
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lines(order, dist.subspace.tsir, col = col.methods["tsir"], lwd = 2, type = "b", pch = 16)
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lines(order, dist.subspace.sir, col = col.methods["sir"], lwd = 2, type = "b", pch = 16)
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})
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if (rho == 0.5 && beta.version == 2L) {
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abline(v = 0.5, lty = "dotted", col = "black")
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abline(h = group$dist.subspace.tsir[which(order == 3L)],
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lty = "dotted", col = "black")
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}
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}
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methods <- c("GMLM", "TSIR", "SIR")
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restor.par <- par(
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fig = c(0, 1, 0, 1),
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oma = c(0, 0, 0, 0),
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mar = c(1, 0, 0, 0),
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new = TRUE
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)
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plot(0, type = "n", bty = "n", axes = FALSE, xlab = "", ylab = "")
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legend("bottom", col = col.methods[tolower(methods)], legend = methods,
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horiz = TRUE, lty = 1, bty = "n", lwd = c(3, 2, 2), pch = 16)
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par(restor.par)
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### Version 1
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# 2'nd order
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# 1 + 2 y + y^2
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# (1 + y)^2
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# 3'rd order
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# 1 + 3 y + 3 y^2 + y^4
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# (1 + y)^3
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# 4'th order
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# 1 + 4 y + 6 y^2 + 4 y^3 + y^4
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# (1 + y)^4
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### Version 2
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# 2'nd order
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# 1 - 2 y + y^2
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# (1 - y)^2 = 1 - 2 y + y^2
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# 3'rd order
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# 1 - 3 y + 3 y^2 - y^3
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# -(y - 1)^3
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# 4'th order
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# 1 - 4 y + 6 y^2 - 4 y^3 + y^4
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# (y - 1)^4
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