trivial effect plot

pair_13_asz.R

library(data.table)
library(ggplot2)
library(scales)

set.seed(12345)
post_df <- data.table(
  est = rnorm(13 * 12 / 2, 0, .05),
  se = rlnorm(13 * 12 / 2, log(.09), log(.20 / .09) / qnorm(.9999))
)
post_df[, lo := qnorm(.025, est, se)]
post_df[, hi := qnorm(.975, est, se)]
post_df[, study_pos := frank(est)]
post_df

# Using .2 as limit for minor effect
d_lim <- .2

ggplot(post_df, aes(study_pos, est, ymin = lo, ymax = hi)) +
  geom_rect(aes(xmin = -10, xmax = 85, ymin = -d_lim, ymax = d_lim), fill = "#e3e3e3") +
  geom_segment(x = 0, xend = 79, y = 0, yend = 0, linetype = 2, size = .125) +
  geom_segment(x = -5.75, xend = -5.75, y = -d_lim, yend = d_lim, linetype = 1, size = .125 / 4,
               arrow = arrow(length = unit(0.03, "npc"))) +
  geom_segment(x = -5.75, xend = -5.75, y = d_lim, yend = -d_lim, linetype = 1, size = .125 / 4,
               arrow = arrow(length = unit(0.03, "npc"))) +
  annotate("text", x = -7, y = 0, hjust = 0.5, size = 3,
           label = "Range for small effects", angle = 90) +
  geom_point(size = 1, alpha = .5) + geom_linerange(alpha = .5, size = .25) +
  # Fake y-axis
  geom_vline(xintercept = -.75, size = .25) +
  # Fake y-axis labels
  annotate("text", label = .2, x = -1.625, y = .2, hjust = 1, size = 3.25, alpha = .65) +
  annotate("text", label = "0.0", x = -1.625, y = 0, hjust = 1, size = 3.25, alpha = .65) +
  annotate("text", label = -.2, x = -1.625, y = -.2, hjust = 1, size = 3.25, alpha = .65) +
  annotate("text", label = -.4, x = -1.625, y = -.4, hjust = 1, size = 3.25, alpha = .65) +
  # Fake y-axis ticks
  geom_segment(x = -.75, xend = -1.25, y = .2, yend = .2, size = .25) +
  geom_segment(x = -.75, xend = -1.25, y = 0, yend = 0, size = .25) +
  geom_segment(x = -.75, xend = -1.25, y = -.2, yend = -.2, size = .25) +
  geom_segment(x = -.75, xend = -1.25, y = -.4, yend = -.4, size = .25) +
  coord_cartesian(xlim = c(-5, 75.5)) +
  theme_bw() +
  labs(y = "difference in differences",
       subtitle = "All pairwise difference estimates are small") +
  theme(axis.ticks = element_blank(),
        axis.text = element_blank(),
        axis.title = element_blank(),
        plot.subtitle = element_text(hjust = .17),
        panel.border = element_blank(),
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank())
ggsave("asz_01_l.png", width = 6.5, height = 4)

ggplot(post_df, aes(study_pos, est, ymin = lo, ymax = hi)) +
  geom_rect(aes(xmin = -1, xmax = 85, ymin = -d_lim, ymax = d_lim), fill = "#e3e3e3") +
  geom_segment(x = 0, xend = 79, y = 0, yend = 0, linetype = 2, size = .125) +
  geom_segment(x = 81, xend = 81, y = -d_lim, yend = d_lim, linetype = 1, size = .125 / 4,
               arrow = arrow(length = unit(0.03, "npc"))) +
  geom_segment(x = 81, xend = 81, y = d_lim, yend = -d_lim, linetype = 1, size = .125 / 4,
               arrow = arrow(length = unit(0.03, "npc"))) +
  annotate("text", x = 82, y = 0, hjust = 0.5, size = 3,
           label = "Range for small effects", angle = 270) +
  geom_point(size = 1, alpha = .5) + geom_linerange(alpha = .5, size = .25) +
  coord_cartesian(xlim = c(3, 80)) +
  theme_bw() +
  labs(y = "difference in differences",
       subtitle = "All pairwise difference estimates are small") +
  theme(axis.ticks.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.x = element_blank(),
        axis.line.y = element_line(size = .25),
        panel.border = element_blank(),
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank())
ggsave("asz_01_r.png", width = 6.5, height = 4)

# Calculate prob(eff > d_lim OR eff < -d_lim)
post_df[, p_gt_d_lim := pnorm(d_lim, est, se, lower.tail = FALSE) +
          pnorm(-d_lim, est, se, lower.tail = TRUE)]
post_df

# Histogram of probability differences excced abs(d_lim)
ggplot(post_df, aes(p_gt_d_lim)) + geom_histogram(col = 1) + theme_classic() +
  scale_x_continuous(
    labels = percent_format(),
    name = paste0("Probability effect exceeds ", d_lim))
ggsave("asz_02.png", width = 6.5, height = 4)