187:# Reproducible R code # Load necessary libraries library(ggplot2) library(patchwork) # Set seed for reproducibility set.seed(123) # Generate data n <- 10000 x <- sort(runif(n, min = 1, max = 100)) intercept <- 0.000001 slope <- 0.5 y_true_log <- intercept + slope * log10(x) noise <- rnorm(n, mean = 0, sd = .1) y_observed_log <- y_true_log + noise y_observed <- 10^y_observed_log y_true <- 10^y_true_log # Create data frame df <- data.frame(x = x, y_true = y_true, y_observed = y_observed) # Load necessary libraries library(dplyr) library(ggplot2) library(zoo) # Define window size window_size <- 28 # Calculate error metrics over sliding window df <- df %>% arrange(x) %>% mutate(MAE = rollapply(abs(y_true - y_observed), width = window_size, FUN = mean, align = "right", fill = NA), RMSE = sqrt(rollapply((y_true - y_observed)^2, width = window_size, FUN = mean, align = "right", fill = NA)), MALE = rollapply(abs(log10(y_true) - log10(y_observed)), width = window_size, FUN = mean, align = "right", fill = NA)) # Load necessary library library(tidyr) # Reshape data to long format df_long <- df %>% gather(key = "error_type", value = "error_value", MAE, RMSE, MALE) options( repr.plot.width = 12, # in inches (default = 7) repr.plot.height = 10 # in inches (default = 7) ) # Plot error metrics ggplot(df_long, aes(x = x, y = error_value, color = error_type)) + geom_line(alpha = .5) + geom_smooth() + # scale_x_log10() + # scale_y_log10() + coord_cartesian(ylim = c(0, 2.5)) + # Set the limits of the plot without excluding obs theme_bw() + theme(text = element_text(size = 25)) + theme(legend.position="bottom") + labs(x = 'X', y = 'Error', title = 'Sliding Window Analysis of Error Metrics\nin Loglog Normal Data')
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This image presents a line plot of three error metrics (Mean
Absolute Error - MAE, Root Mean Square Error - RMSE, and Mean Absolute Logarithmic Error - MALE) calculated over a sliding window of size 28, plotted against the independent variable (x). Each error metric is represented by a different
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color, with the corresponding smoothed line overlaying the original line. The y-axis is limited to a range of 0 to 2.5.
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Sliding Window
Analysis of Error Metrics in Loglog Normal Data
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Sliding Window Error
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