R语言回归方程添加求和项时的data参数重复错误解决问询

我想在R中实现如下回归公式（i为category的每个取值，category可选1、2、3、4）：
公式核心为：针对每个category=i，拟合quantity关于year×state×district交互项、各主效应的回归，其中交互项覆盖所有年份的组合。

运行尝试代码时触发错误：

Error in lm(category ~ (year * state * district) + year + state + district + :
formal argument "data" matched by multiple actual arguments

我试图通过多次传入不同年份子集的data参数来实现公式中的求和逻辑，但触发了上述错误，想知道正确的实现方式。

我的尝试代码：

ID <-  c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
         17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
         33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)
year <- c(1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,
      1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,
      1982,1982,1982,1982,1982,1982,1982,1982,1982,1982,1982,1982,1982,1982,1982,1982)
 state <-     c("NY","NY","NY","NY","NY","NY","NY","NY","CA","CA","CA","CA","CA","CA","CA","CA",
      "NY","NY","NY","NY","NY","NY","NY","NY","CA","CA","CA","CA","CA","CA","CA","CA",
      "NY","NY","NY","NY","NY","NY","NY","NY","CA","CA","CA","CA","CA","CA","CA","CA")
district <- c(1,1,1,1,2,2,2,2,1,1,1,1,2,2,2,2,
          1,1,1,1,2,2,2,2,1,1,1,1,2,2,2,2,
          1,1,1,1,2,2,2,2,1,1,1,1,2,2,2,2)
quantity <- c(100,200,45,87,65,32,94,52,67,72,14,53,28,94,12,41,
          10,20,45,87,65,32,8,52,67,1,14,53,28,94,12,41,
          1000,2000,45,87,9,32,94,5,6,7,1,5,2,9,1,4)
category <- c(1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,
   1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,
   1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4)

df <- data.frame(ID,year,state,district,quantity,category)

df$year <- as.factor(df$year)
df$state <- as.factor(df$state)
df$district <- as.factor(df$district)
df$category <- as.factor(df$category)

print(df)

# force regression baseline values 
relevel(df$year, ref = '1981')
relevel(df$district, ref = '2')

# r1 is when y = 1
r1 <- lm( category ~ (year*state*district) +  
           quantity + district + state + year,
           data = subset(df, year == 1980)
      +
        (year*state*district) +  
         quantity + district + state + year,
         data = subset(df, year == 1981)
      +
        (year*state*district) +  
         quantity + district + state + year,
         data = subset(df, year == 1980)
     )
summary(r1)

# r2 is when y = 2
r2 <- lm( category ~ (year*state*district) +  
        year + state + district + quantity,
      data = subset(df, year == 1980)
      +
        (year*state*district) +  
        year + state + district + quantity,
      data = subset(df, year == 1981)
      +
        (year*state*district) +  
        year + state + district + quantity,
      data = subset(df, year == 1980)
)
summary(r2)

then r3 and r4

解决方案 #

你误解了lm()的使用逻辑：不能通过多次传入data参数实现求和，回归公式中的求和项本质是让模型覆盖所有年份的交互效应，只需在全数据集的对应category子集上拟合即可。

修正后的代码：

ID <-  c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
         17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
         33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)
year <- c(1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,1980,
      1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,1981,
      1982,1982,1982,1982,1982,1982,1982,1982,1982,1982,1982,1982,1982,1982,1982,1982)
state <-     c("NY","NY","NY","NY","NY","NY","NY","NY","CA","CA","CA","CA","CA","CA","CA","CA",
      "NY","NY","NY","NY","NY","NY","NY","NY","CA","CA","CA","CA","CA","CA","CA","CA",
      "NY","NY","NY","NY","NY","NY","NY","NY","CA","CA","CA","CA","CA","CA","CA","CA")
district <- c(1,1,1,1,2,2,2,2,1,1,1,1,2,2,2,2,
          1,1,1,1,2,2,2,2,1,1,1,1,2,2,2,2,
          1,1,1,1,2,2,2,2,1,1,1,1,2,2,2,2)
quantity <- c(100,200,45,87,65,32,94,52,67,72,14,53,28,94,12,41,
          10,20,45,87,65,32,8,52,67,1,14,53,28,94,12,41,
          1000,2000,45,87,9,32,94,5,6,7,1,5,2,9,1,4)
category <- c(1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,
   1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,
   1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4)

df <- data.frame(ID,year,state,district,quantity,category)

# 转换因子并设置基准水平（需重新赋值生效）
df$year <- relevel(as.factor(df$year), ref = '1981')
df$state <- as.factor(df$state)
df$district <- relevel(as.factor(df$district), ref = '2')
df$category <- as.factor(df$category)

# 针对每个category取值拟合模型
# 注：year*state*district已包含所有交互项及主效应，无需重复添加
r1 <- lm(quantity ~ year*state*district, 
         data = subset(df, category == 1))
summary(r1)

r2 <- lm(quantity ~ year*state*district, 
         data = subset(df, category == 2))
summary(r2)

r3 <- lm(quantity ~ year*state*district, 
         data = subset(df, category == 3))
summary(r3)

r4 <- lm(quantity ~ year*state*district, 
         data = subset(df, category == 4))
summary(r4)

关键修正点 #

1. 因变量修正：原代码错误地将category作为因变量，实际应是quantity（对应公式中被解释变量）。
2. 基准水平生效：relevel()需要重新赋值给原变量，否则不会修改数据框中的因子水平。
3. 公式简化：year*state*district已包含三者的所有交互项及主效应，无需重复添加year + state + district。
4. 数据子集逻辑：只需针对每个category取值筛选数据，year作为因子变量会自动覆盖所有年份的效应，对应公式中的求和项。

内容的提问来源于stack exchange，提问作者ithoughtso