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regression_base.R
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regression_base.R
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# Base code to perform regression analysis of PDI vs duration
# Author: Alfredo Hernández <[email protected]>
# Libraries ------------------------------------------------
library(tidyverse)
library(lubridate)
# Scatterplots ---------------------------------------------
plot_scatterplot <- function(basin, var1, var2, min.speed = 0) {
# Parse the basin PDI data frame
basin.df <- eval(parse(text=paste("pdi.", tolower(basin), sep = "")))
# Filter data frames
basin.df <- basin.df %>%
dplyr::filter(max.wind > min.speed)
df.low <- basin.df %>%
dplyr::filter(sst.class == "low")
df.high <- basin.df %>%
dplyr::filter(sst.class == "high")
# Extract data vectors
col.x.low <- df.low[[var1]]
col.y.low <- df.low[[var2]]
col.x.high <- df.high[[var1]]
col.y.high <- df.high[[var2]]
lm.high.y <- lm(log10(col.y.high) ~ log10(col.x.high))
lm.low.y <- lm(log10(col.y.low) ~ log10(col.x.low))
lm.high.x <- lm(log10(col.x.high) ~ log10(col.y.high))
lm.low.x <- lm(log10(col.x.low) ~ log10(col.y.low))
# Automatic plot title
if (min.speed == 0) {
storms.str <- "all storms"
} else {
storms.str <- paste("wind speed >", min.speed)
}
years.str <- paste0( min(basin.df$storm.year), "-", max(basin.df$storm.year))
title.str <- paste0(basin, " (", storms.str, "; ", years.str, ")" )
gg <- ggplot() +
# Scatterplot
geom_point(data = df.low, aes(x = col.x.low, y = col.y.low, colour = "low"), shape = 5, size = 1) +
geom_point(data = df.high, aes(x = col.x.high, y = col.y.high, colour = "high"), shape = 1, size = 1) +
# Regression lines
geom_abline(aes(slope = coef(lm.low.y)[[2]],
intercept = coef(lm.low.y)[[1]],
colour = "low", linetype = "Y(X)")) +
geom_abline(aes(slope = 1/coef(lm.low.x)[[2]],
intercept = -coef(lm.low.x)[[1]]/coef(lm.low.x)[[2]],
colour = "low", linetype = "X(Y)")) +
geom_abline(aes(slope = coef(lm.high.y)[[2]],
intercept = coef(lm.high.y)[[1]],
colour = "high", linetype = "Y(X)")) +
geom_abline(aes(slope = 1/coef(lm.high.x)[[2]],
intercept = -coef(lm.high.x)[[1]]/coef(lm.high.x)[[2]],
colour = "high", linetype = "X(Y)")) +
# Scales and legend
scale_x_log10(breaks = c(25, 50, 100, 200, 400, 800)) +
scale_y_log10() +
guides(colour = guide_legend(order = 1, override.aes = list(linetype = c(0,0), shape = c(1,5))),
linetype = guide_legend(order = 2, override.aes = list(colour = c("black", "black")))) +
scale_colour_manual(labels = c(bquote(.(paste0("high; ")) ~ r^2 ~
.(paste0("= ", format(summary(lm.high.y)$r.squared, digits = 2)))),
bquote(.(paste0("low; ")) ~ r^2 ~
.(paste0("= ", format(summary(lm.low.y)$r.squared, digits = 2))))),
values = c("high" = "brown1", "low" = "dodgerblue1")) +
scale_linetype_manual(values = c("X(Y)" = "longdash", "Y(X)" = "solid")) +
labs(title = title.str,
x = paste(eval(var1)), y = paste(eval(var2)),
colour = "SST class", linetype = "Regression")
return(gg + theme_bw())
}
# Explore p-values -----------------------------------------
explore_p_values <- function(p.values.list, alpha = 0.05) {
for (i in 1:length(p.values.list)) {
for (j in 1:2) {
if ( (p.values.list[[i]][["slope.p.val"]][j] <= alpha) |
(p.values.list[[i]][["inter.p.val"]][j] <= alpha) |
(p.values.list[[i]][["total.p.val"]][j] <= alpha) |
(p.values.list[[i]][["r.sqr.p.val"]][j] <= alpha) ) {
# Print regression results
print(paste("Element in list:", i))
print(p.values.list[[i]][j, ])
}
}
}
}
# Calculate T statistics -----------------------------------
# get_T_statistics <- function(a, b, ci) {
# T1 <- abs( ci[[a, 4]] - ci[[b, 4]])
# T2 <- abs( ci[[a, 2]] - ci[[b, 2]])
# T3 <- abs( ci[[a, 6]] - ci[[b, 6]])
# T4 <- abs( ci[[a, 4]] - ci[[b, 4]]) / sqrt(ci[[a, 5]]^2 + ci[[b, 5]]^2 )
# T5 <- abs( ci[[a, 2]] - ci[[b, 2]]) / sqrt(ci[[a, 3]]^2 + ci[[b, 3]]^2 )
# T6 <- T5 + T4
#
# result <- c(T1,T2,T3,T4,T5,T6)
#
# return(round(result, digits = 3))
# }
get_t_statistics <- function(coefs.low, coefs.high) {
# Low SST coefficients
slope.low <- coefs.low[1]
slope.sd.low <- coefs.low[2]
inter.low <- coefs.low[3]
inter.sd.low <- coefs.low[4]
r2.low <- coefs.low[5]
# High SST coefficients
slope.high <- coefs.high[1]
slope.sd.high <- coefs.high[2]
inter.high <- coefs.high[3]
inter.sd.high <- coefs.high[4]
r2.high <- coefs.high[5]
T1 <- abs( inter.high - inter.low )
T2 <- abs( slope.high - slope.low )
T3 <- abs( r2.high - r2.low )
T4 <- T1 / sqrt( inter.sd.high^2 + inter.sd.low^2 )
T5 <- T2 / sqrt( slope.sd.high^2 + slope.sd.low^2 )
T6 <- T5 + T4
result <- c(T1, T2, T3, T4, T5, T6)
return(round(result, digits = 3))
}
# Compare statistics and CI methods ------------------------
compare_perm_statistics <- function(p.values.list) {
dim <- 2*length(p.values.list)
slope.factor <- numeric(dim)
inter.factor <- numeric(dim)
k <- 1
for (i in 1:length(p.values.list)) {
for (j in 1:2) {
slope.factor[k] <- p.values.list[[i]][j, "slope.alt.p.val"] / p.values.list[[i]][j, "slope.p.val"]
inter.factor[k] <- p.values.list[[i]][j, "inter.alt.p.val"] / p.values.list[[i]][j, "inter.p.val"]
k <- k + 1
}
}
data <- tibble(
n = seq(1:dim),
slope.factor = slope.factor,
inter.factor = inter.factor
)
results <- tibble(
stat = c("slope", "intercept"),
mean = c(mean(slope.factor), mean(inter.factor)),
sd = c(sd(slope.factor) ,sd(inter.factor))
)
gg.slope <- ggplot(data) +
geom_histogram(aes(x = slope.factor), binwidth = 0.01, fill = "white", colour = "black") +
labs(title = "Slope factor")
gg.inter <- ggplot(data) +
geom_histogram(aes(x = inter.factor), binwidth = 0.01, fill = "white", colour = "black") +
labs(title = "Intercept factor")
# return(data)
# return(results)
return(list(gg.slope, gg.inter))
}
compare_perm_methods <- function(p.values.list, boot.p.values.list, alpha = 1.75, beta =0.7) {
dim <- 6 * 2 * length(p.values.list)
count = 0
comp.vect <- numeric(dim)
for (i in 1:length(p.values.list)) {
A <- p.values.list[[i]]
B <- boot.p.values.list[[i]]
num.vars <- grep("p.val$", names(A), value = T)
chr.vars <- A[!grepl("p.val", names(A))]
S <- A[num.vars] / B[match(A$dep.var, B$dep.var), num.vars]
for (k in 1:length(S)) {
for (j in 1:2) {
comp.vect[count] <- S[j, k]
count = count + 1
}
}
R <- cbind(S, chr.vars)
print(R)
print("=================================================================================")
for (k in 1:(length(R)-4)) {
for (j in 1:2) {
if ( R[j, k] >= alpha | R[j, k] <= beta ) {
print(paste("Element in list:", i))
print(paste("row:", j, "col:", k))
print(paste("Value:", R[j, k]))
}
}
}
}
gg <- ggplot(tibble(n = seq(1:length(comp.vect)),
comp.vect = comp.vect)) +
geom_histogram(aes(x = comp.vect), binwidth = 0.05, fill = "white", colour = "black") +
labs(title = "Ordinary / Bootstrap factor")
return(gg)
}
compare_ci_methods <- function(factors.ci.list) {
dim <- 4*length(factors.ci.list)
slope.factor <- numeric(dim)
slope.sd.factor <- numeric(dim)
inter.factor <- numeric(dim)
inter.sd.factor <- numeric(dim)
r.sqr.factor <- numeric(dim)
r.sqr.sd.factor <- numeric(dim)
k <- 1
for (i in 1:length(factors.ci.list)) {
for (j in 1:4) {
slope.factor[k] <- factors.ci.list[[i]][j, "slope"]
slope.sd.factor[k] <- factors.ci.list[[i]][j, "slope.sd"]
inter.factor[k] <- factors.ci.list[[i]][j, "inter"]
inter.sd.factor[k] <- factors.ci.list[[i]][j, "inter.sd"]
r.sqr.factor[k] <- factors.ci.list[[i]][j, "r2"]
r.sqr.sd.factor[k] <- factors.ci.list[[i]][j, "r2.sd"]
k <- k + 1
}
}
data <- tibble(
n = seq(1:dim),
slope.factor = slope.factor,
slope.sd.factor = slope.sd.factor,
inter.factor = inter.factor,
inter.sd.factor = inter.sd.factor,
r.sqr.factor = r.sqr.factor,
r.sqr.sd.factor = r.sqr.sd.factor
)
return(summary(data))
}
# Histograms of sample -------------------------------------
plot_boot_coefs_hist <- function(data.low, data.high, stat) {
all.data <- rbind(
cbind(data.low, sst.class = "low"),
cbind(data.high, sst.class = "high")
)
ggplot(all.data) +
aes_string(x = stat) +
geom_histogram(aes(fill = sst.class, group = sst.class),
position = "identity", colour = "black", bins = 50, alpha = 0.5) +
scale_fill_manual(values = c("high" = "brown1",
"low" = "dodgerblue1")) +
theme_bw()
}
# Arbitraty Q-Q plots --------------------------------------
plot_dists_qqplot <- function(col.x, col.y) {
data <- tibble(var1 = sort(col.x),
var2 = sort(col.y))
gg <- ggplot(data, aes(sample = var2 )) +
geom_point(aes(x = var1, y = var2), shape = 1, size = 1.5) +
labs(x = "Var 1", y = "Var 2") +
theme_bw()
return(gg)
}