超过 2 个解释变量

R 中级回归

Richie Cotton

Data Evangelist at DataCamp

回顾上次内容

ggplot(
  fish,
  aes(length_cm, height_cm, color = mass_g)
) +
  geom_point() +
  scale_color_viridis_c(option = "inferno")

鱼的长度、高度与质量的散点图（Inferno 配色）

按物种分面

ggplot(
  fish,
  aes(length_cm, height_cm, color = mass_g)
) +
  geom_point() +
  scale_color_viridis_c(option = "inferno") +
  facet_wrap(vars(species))

按物种分面展示鱼的长度、高度与质量的散点图

不同层级的交互

无交互项

lm(mass_g ~ length_cm + height_cm + species + 0, data = fish)

变量两两之间的二阶交互

lm(
  mass_g ~ length_cm + height_cm + species + length_cm:height_cm + length_cm:species + height_cm:species + 0, 
  data = fish
)

三个变量之间的三阶交互

lm(
  mass_g ~ length_cm + height_cm + species + length_cm:height_cm + length_cm:species + height_cm:species + length_cm:height_cm:species + 0, 
  data = fish
)

包含所有交互

lm(
  mass_g ~ length_cm + height_cm + species + length_cm:height_cm + length_cm:species + height_cm:species + length_cm:height_cm:species + 0, 
  data = fish
)

lm(
  mass_g ~ length_cm * height_cm * species + 0, 
  data = fish
)

仅含二阶交互项

lm(
  mass_g ~ length_cm + height_cm + species + length_cm:height_cm + length_cm:species + height_cm:species + 0, 
  data = fish
)

lm(
  mass_g ~ (length_cm + height_cm + species) ^ 2 + 0, 
  data = fish
)

lm(
  mass_g ~ I(length_cm) ^ 2 + height_cm + species + 0, 
  data = fish
)

¹ 关于对解释变量求平方，参见"Introduction to Regression in R"，第 2 章"Transforming variables"

预测流程

mdl_mass_vs_all <- lm(mass_g ~ length_cm * height_cm * species * 0, data = fish)

explanatory_data <- expand_grid(
  length_cm = seq(5, 60, 6),
  height_cm = seq(2, 20, 2),
  species = unique(fish$species)
)

prediction_data <- explanatory_data %>% 
  mutate(mass_g = predict(mdl_mass_vs_all, explanatory_data))

可视化预测

ggplot(
  fish,
  aes(length_cm, height_cm, color = mass_g)
) +
  geom_point() +
  scale_color_viridis_c(option = "inferno") +
  facet_wrap(vars(species)) +
  geom_point(
    data = prediction_data, 
    size = 3, shape = 15
  )

按物种分面展示鱼的长度、高度与质量的散点图（含预测点）

Vamos praticar!

R 中级回归