线性模型回归系数的相关矩阵

Question

使用 cor(mtcars, method='pearson') 生成一个矩阵，显示 mtcars 中所有变量与 mtcars 中所有其他变量的皮尔逊相关性。例如：

head(cor(mtcars, method='pearson'))
            mpg        cyl       disp         hp       drat         wt        qsec         vs         am       gear
mpg   1.0000000 -0.8521620 -0.8475514 -0.7761684  0.6811719 -0.8676594  0.41868403  0.6640389  0.5998324  0.4802848
cyl  -0.8521620  1.0000000  0.9020329  0.8324475 -0.6999381  0.7824958 -0.59124207 -0.8108118 -0.5226070 -0.4926866
disp -0.8475514  0.9020329  1.0000000  0.7909486 -0.7102139  0.8879799 -0.43369788 -0.7104159 -0.5912270 -0.5555692
hp   -0.7761684  0.8324475  0.7909486  1.0000000 -0.4487591  0.6587479 -0.70822339 -0.7230967 -0.2432043 -0.1257043
drat  0.6811719 -0.6999381 -0.7102139 -0.4487591  1.0000000 -0.7124406  0.09120476  0.4402785  0.7127111  0.6996101
wt   -0.8676594  0.7824958  0.8879799  0.6587479 -0.7124406  1.0000000 -0.17471588 -0.5549157 -0.6924953 -0.5832870
           carb
mpg  -0.5509251
cyl   0.5269883
disp  0.3949769
hp    0.7498125
drat -0.0907898
wt    0.4276059

除了每个值不是每个变量之间的皮尔逊相关，而是来自线性模型的 r.squared 值之外，我如何才能得到与上面相同的矩阵？因此，例如第一列，第二行将与 summary(lm(mtcars$mpg~ mtcars$cyl))$r.squared 相同。谢谢

Answer 1

library(tidyverse)

# kepp names of dataset
names = names(mtcars)

expand.grid(names, names, stringsAsFactors = F) %>%  # create pairs of names
  filter(Var1 != Var2) %>%                           # exclude same variables (creates warnings)
  rowwise() %>%                                      # for each row
  mutate(r = summary(lm(paste(Var1, "~" ,Var2), data = mtcars))$r.squared) %>%  # get the r squared
  spread(Var2, r)                                    # reshape

# # A tibble: 11 x 12
# Var1        am     carb    cyl   disp     drat    gear      hp    mpg
# <chr>    <dbl>    <dbl>  <dbl>  <dbl>    <dbl>   <dbl>   <dbl>  <dbl>
# 1 am    NA        0.00331  0.273  0.350  0.508    0.631   0.0591  0.360
# 2 carb   0.00331 NA        0.278  0.156  0.00824  0.0751  0.562   0.304
# 3 cyl    0.273    0.278   NA      0.814  0.490    0.243   0.693   0.726
# 4 disp   0.350    0.156    0.814 NA      0.504    0.309   0.626   0.718
# 5 drat   0.508    0.00824  0.490  0.504 NA        0.489   0.201   0.464
# 6 gear   0.631    0.0751   0.243  0.309  0.489   NA       0.0158  0.231
# 7 hp     0.0591   0.562    0.693  0.626  0.201    0.0158 NA       0.602
# 8 mpg    0.360    0.304    0.726  0.718  0.464    0.231   0.602  NA    
# 9 qsec   0.0528   0.431    0.350  0.188  0.00832  0.0452  0.502   0.175
# 10 vs     0.0283   0.324    0.657  0.505  0.194    0.0424  0.523   0.441
# 11 wt     0.480    0.183    0.612  0.789  0.508    0.340   0.434   0.753
# # ... with 3 more variables: qsec <dbl>, vs <dbl>, wt <dbl>

如果您想要行名称而不是第一列 (Var1)，您可以在上面管道的末尾添加

... %>%
  data.frame() %>%
  column_to_rownames("Var1")

这将更接近您从 cor(mtcars, method='pearson')

获得的输出

Answer 2

我创建了一个 corlm 函数，它用 for 循环填充条目

corlm <- function(df){
mat <- matrix(NA, ncol(df), ncol(df), dimnames = list(colnames(df),colnames(df)))
suppressWarnings(for(i in 1:ncol(df)){
    for(j in 1:ncol(df)){
      mat[i,j] = summary(lm(df[,j]  ~ df[,i]))$r.squared}})
diag(mat) = NA; return(mat)
}

round(corlm(mtcars),3)
       mpg   cyl  disp    hp  drat    wt  qsec    vs    am  gear  carb
mpg     NA 0.726 0.718 0.602 0.464 0.753 0.175 0.441 0.360 0.231 0.304
cyl  0.726    NA 0.814 0.693 0.490 0.612 0.350 0.657 0.273 0.243 0.278
disp 0.718 0.814    NA 0.626 0.504 0.789 0.188 0.505 0.350 0.309 0.156
hp   0.602 0.693 0.626    NA 0.201 0.434 0.502 0.523 0.059 0.016 0.562
drat 0.464 0.490 0.504 0.201    NA 0.508 0.008 0.194 0.508 0.489 0.008
wt   0.753 0.612 0.789 0.434 0.508    NA 0.031 0.308 0.480 0.340 0.183
qsec 0.175 0.350 0.188 0.502 0.008 0.031    NA 0.554 0.053 0.045 0.431
vs   0.441 0.657 0.505 0.523 0.194 0.308 0.554    NA 0.028 0.042 0.324
am   0.360 0.273 0.350 0.059 0.508 0.480 0.053 0.028    NA 0.631 0.003
gear 0.231 0.243 0.309 0.016 0.489 0.340 0.045 0.042 0.631    NA 0.075
carb 0.304 0.278 0.156 0.562 0.008 0.183 0.431 0.324 0.003 0.075    NA

线性模型回归系数的相关矩阵

Correlation matrix for linear model regression coefficient

r

matrix

linear-regression

correlation