如何在ggplot2混合效应模型中仅显示最差回归线的95%下界及优化图例

1. 加载依赖包并模拟数据集 #

library(tidyverse)

# 固定随机种子确保结果可复现
set.seed(123)
n_lots <- 5  # 批次数量
n_per_lot <- 10  # 每个批次的观测数

# 生成各批次的斜率（越负下降越快）和截距
slopes <- runif(n_lots, -2, -0.5)
intercepts <- runif(n_lots, 90, 100)

# 构造数据集
df <- expand_grid(Lot = paste0("Lot_", 1:n_lots),
                  Time = seq(1, 10, length.out = n_per_lot)) %>%
  left_join(tibble(Lot = paste0("Lot_", 1:n_lots),
                   slope = slopes,
                   intercept = intercepts), by = "Lot") %>%
  mutate(Purity = intercept + slope * Time + rnorm(n(), 0, 1)) %>%
  select(-slope, -intercept)

2. 识别「最差回归线」批次 #

# 对每个批次拟合线性模型，计算与y=80的交点时间
lot_models <- df %>%
  group_by(Lot) %>%
  nest() %>%
  mutate(model = map(data, ~lm(Purity ~ Time, data = .x)),
         intercept = map_dbl(model, ~coef(.x)[[1]]),
         slope = map_dbl(model, ~coef(.x)[[2]]),
         # 计算回归线与y=80的交点时间
         cross_time = (80 - intercept)/slope) %>%
  ungroup()

# 筛选出最早与y=80相交的批次
worst_lot <- lot_models %>%
  filter(cross_time == min(cross_time)) %>%
  pull(Lot)

3. 生成最差批次的95%下界置信限数据 #

# 为最差批次生成预测数据，仅保留下界置信限
worst_pred <- lot_models %>%
  filter(Lot == worst_lot) %>%
  pull(model) %>%
  first() %>%
  predict(newdata = tibble(Time = seq(min(df$Time), max(df$Time), length.out = 100)),
          interval = "confidence", level = 0.95) %>%
  as_tibble() %>%
  mutate(Time = seq(min(df$Time), max(df$Time), length.out = 100)) %>%
  select(Time, lwr)

4. 绘制符合需求的图形 #

ggplot(df, aes(x = Time, y = Purity, color = Lot)) +
  # 绘制所有批次的散点
  geom_point(size = 2) +
  # 绘制所有批次的回归线（无置信区间，不显示图例线条）
  geom_smooth(method = "lm", se = FALSE, show.legend = FALSE) +
  # 绘制最差批次的95%下界置信限（虚线）
  geom_line(data = worst_pred, aes(y = lwr, color = worst_lot), linetype = "dashed") +
  # 添加y=80的参考水平线
  geom_hline(yintercept = 80, color = "red", linetype = "solid") +
  # 优化图例：仅显示点符号，隐藏线条
  guides(color = guide_legend(override.aes = list(linetype = "blank"))) +
  # 图形标签设置
  labs(title = "Purity vs Time by Lot",
       x = "Time",
       y = "Purity",
       color = "Lot") +
  theme_minimal()

关键说明 #

• 识别最差批次：通过计算每条回归线与y=80的交点时间，取时间最小的批次即为「最早相交」的最差批次。
• 下界置信限绘制：单独提取最差批次的模型预测结果，仅保留95%置信区间的下界，用虚线绘制。
• 图例优化：通过show.legend = FALSE隐藏回归线的图例项，再用guide_legend(override.aes = list(linetype = "blank"))确保图例仅显示散点符号。

内容的提问来源于stack exchange，提问作者Joe the Second