如何在R语言中构建每个ID对应固定IQ及全字母分值的数据集？

需求：构建包含300个受试者的数据集，每个受试者（以id标识）有唯一的正态分布IQ分数，且每个受试者对应全部20个字母（a-t），每个字母对应固定的value分值。

现有错误代码及问题 #

当前编写的代码如下：

id <- 1:300
iq <- rnorm(n=300, mean=120, sd=15)
letter <- rep(c("a","b","c","d","e","f","g","h","i","j",
            "k","l","m","n","o","p","q","r","s","t"),15)
value <-  rep(c(2,2,1,2,2,2,2,2,3,2,
            3,1,3,2,1,2,2,2,1,2),15)
df <- data.frame(id,iq,letter,value)
df$id <- as.character(id)

运行head(df)得到的结果不符合需求，每个受试者仅对应一个字母：

id        iq letter value
1  1 126.35025      a     2
2  2 150.08165      b     2
3  3 105.88712      c     1
4  4 106.86652      d     2
5  5  97.86159      e     2
6  6 116.39497      f     2

期望的数据集格式 #

期望每个受试者对应全部目标字母，示例（单个受试者对应4个字母）：

id2 <- rep(1,4)
iq2 <- 120
letter2 <- c("a","b","c","d")
value2 <-  c(2,2,1,2)
df2 <- data.frame(id2,
                  iq2,
                  letter2,
                  value2)

输出结果：

id2 iq2 letter2 value2
1   1 120       a      2
2   1 120       b      2
3   1 120       c      1
4   1 120       d      2

解决方法 #

方法1：使用expand.grid生成笛卡尔积 #

先分别构建受试者信息表和字母-分值表，再通过笛卡尔积组合所有可能的配对：

# 构建受试者信息：每个id对应唯一iq
subjects <- data.frame(
  id = as.character(1:300),
  iq = rnorm(n=300, mean=120, sd=15)
)

# 构建字母-分值对应表：每个letter对应固定value
letters_values <- data.frame(
  letter = c("a","b","c","d","e","f","g","h","i","j",
             "k","l","m","n","o","p","q","r","s","t"),
  value = c(2,2,1,2,2,2,2,2,3,2,
            3,1,3,2,1,2,2,2,1,2)
)

# 生成所有受试者与字母的组合，自动匹配对应的iq和value
df <- expand.grid(id = subjects$id, letter = letters_values$letter)
df <- merge(df, subjects, by = "id")
df <- merge(df, letters_values, by = "letter")

# 可选：按id排序，让同一受试者的记录连在一起
df <- df[order(df$id), ]
rownames(df) <- NULL  # 重置行号

方法2：手动重复向量（基础R写法） #

通过重复受试者信息20次，重复字母-分值信息300次来构建数据集：

id <- rep(1:300, each = 20)  # 每个id重复20次（对应20个字母）
iq <- rep(rnorm(n=300, mean=120, sd=15), each = 20)  # 每个iq重复20次
letter <- rep(c("a","b","c","d","e","f","g","h","i","j",
                "k","l","m","n","o","p","q","r","s","t"), 300)  # 字母序列重复300次
value <- rep(c(2,2,1,2,2,2,2,2,3,2,
               3,1,3,2,1,2,2,2,1,2), 300)  # 分值序列重复300次

df <- data.frame(id = as.character(id), iq, letter, value)

两种方法都能得到符合需求的数据集，每个受试者对应全部20个字母，且iq和letter的value保持恒定。

内容的提问来源于stack exchange，提问作者Shawn Hemelstrand