如何用R绘制展示自变量负交互效应减弱趋势的可视化图形？

问题背景 #

我对数据集做了有序回归分析，发现两个显著自变量：ER_Ratio和Goals_Score。其中：

• Goals_Score与ER_Ratio存在负交互作用：当ER_Ratio降低时，Goals_Score对因变量Academic.Performance的效应会减弱；
• Goals_Score与不显著自变量Adj_Score也存在负交互作用：当Adj_Score升高时，Goals_Score对Academic.Performance的效应会减弱。

交互模型输出结果 #

Adj_Score:Goals_Score had a value of -0.064, and Std. Error of 
  0.026, and a t value of -2.428.

Goals_Score:ER_Ratio had a value of -0.055, an Std.Error of 0.0096, 
  and a t value of -5.7654.

尝试的代码及问题 #

我用下面的ggplot2代码绘图：

ggplot(data, aes(x=Goals_Score, y=Academic.Performance)) + 
    geom_point(aes(color = Adj_Score)) + 
    geom_smooth(method = “lm”, se = FALSE) + 
    scale_color_gradient (low = “blue”, high = “red”)

但这个图只显示高Academic.Performance对应高Goals_Score和高Adj_Score，没法展示“当Adj_Score升高时，Goals_Score对Academic.Performance的效应减弱”（以及ER_Ratio的类似情况）的效果，请问该怎么用R绘制符合需求的图？

修正后的示例数据集 #

（注：原示例数据存在语法错误，已修正补全并将因变量设为有序因子）

n <- 10
dat <- data.frame(id=1:n,
                  Adj_Score = c(0.555, 0.444, 0.4888, 0.7333, 0.4888, 0.8222, 0.7555, 0.666, 0.9111, 0.5222),
                  Goals_Score= c(32, 54, 38, 47, 35, 50, 53, 42, 49, 39),
                  Academic.Performance = factor(c("0-40%", "41-50%", "51-60%", "61-70%", "71-80%", "81-90%", "91-100%", "51-60%", "71-80%", "41-50%"), 
                                                levels = c("0-40%", "41-50%", "51-60%", "61-70%", "71-80%", "81-90%", "91-100%"),
                                                ordered = TRUE))

解决方案 #

要展示交互效应，核心是按调节变量的分组（或关键水平）分别拟合回归线，直观呈现自变量斜率随调节变量变化的趋势。以下分两种交互情况给出实现代码：

1. 展示Goals_Score与Adj_Score的交互效应 #

方法：按Adj_Score分位数分组拟合

将Adj_Score分为高、中、低三组，分别绘制Goals_Score对Academic.Performance的回归线：

library(ggplot2)
library(dplyr)

# 给Adj_Score按三分位数分组
dat <- dat %>%
  mutate(Adj_Group = cut(Adj_Score, 
                         breaks = quantile(Adj_Score, probs = c(0, 0.33, 0.66, 1)),
                         labels = c("低Adj_Score", "中Adj_Score", "高Adj_Score"),
                         include.lowest = TRUE))

# 绘制交互效应图
ggplot(dat, aes(x = Goals_Score, y = as.numeric(Academic.Performance))) +
  geom_point(aes(color = Adj_Group), alpha = 0.7) +
  geom_smooth(aes(color = Adj_Group), method = "lm", se = FALSE, linewidth = 1) +
  scale_color_manual(values = c("低Adj_Score" = "blue", "中Adj_Score" = "green", "高Adj_Score" = "red")) +
  labs(x = "目标得分", y = "学业表现（数值化）", color = "调节变量分组") +
  theme_minimal()

说明：

• 有序因变量需转为数值型（as.numeric(Academic.Performance)）才能用线性拟合展示趋势；
• 绘图后可清晰看到：高Adj_Score组的回归线斜率比低组更平缓，对应“Adj_Score升高时，Goals_Score对学业表现的效应减弱”的结论。

2. 展示Goals_Score与ER_Ratio的交互效应 #

逻辑与上述一致，按ER_Ratio分位数分组后绘图：

# 假设数据集包含ER_Ratio列，先按三分位数分组
dat <- dat %>%
  mutate(ER_Group = cut(ER_Ratio, 
                        breaks = quantile(ER_Ratio, probs = c(0, 0.33, 0.66, 1)),
                        labels = c("低ER_Ratio", "中ER_Ratio", "高ER_Ratio"),
                        include.lowest = TRUE))

# 绘制交互效应图
ggplot(dat, aes(x = Goals_Score, y = as.numeric(Academic.Performance))) +
  geom_point(aes(color = ER_Group), alpha = 0.7) +
  geom_smooth(aes(color = ER_Group), method = "lm", se = FALSE, linewidth = 1) +
  scale_color_manual(values = c("低ER_Ratio" = "blue", "中ER_Ratio" = "green", "高ER_Ratio" = "red")) +
  labs(x = "目标得分", y = "学业表现（数值化）", color = "调节变量分组") +
  theme_minimal()

说明：

• 绘图后会看到低ER_Ratio组的回归线斜率更平缓，对应“ER_Ratio降低时，Goals_Score对学业表现的效应减弱”的结论。

进阶方法：用interactions包直接绘制有序回归交互效应 #

如果不想手动分组，可使用interactions包的interact_plot函数，自动处理有序因变量并展示交互趋势：

library(interactions)
library(MASS) # 用于拟合有序回归模型

# 拟合包含交互项的有序回归模型（以Adj_Score为例）
ord_model <- polr(Academic.Performance ~ Goals_Score * Adj_Score, data = dat, Hess = TRUE)

# 绘制交互效应图
interact_plot(ord_model, pred = Goals_Score, modx = Adj_Score, 
              modx.values = c("min", "mean", "max"),
              y.label = "学业表现", x.label = "目标得分", legend.main = "Adj_Score")

说明：

• 该函数会直接输出不同Adj_Score水平（最小值、均值、最大值）下，Goals_Score对学业表现的预测趋势线，无需手动转换因变量类型；
• 替换modx = ER_Ratio即可绘制另一组交互效应。

内容的提问来源于stack exchange，提问作者Lina Kader