Descriptive statistics for data in matrices

TODO

• link to matrix, linearAlgebra

Sums and means

age    <- c(19, 19, 31, 19, 24)
weight <- c(95, 76, 94, 76, 76)
height <- c(197, 178, 189, 184, 173)
(mat   <- cbind(age, weight, height))

     age weight height
[1,]  19     95    197
[2,]  19     76    178
[3,]  31     94    189
[4,]  19     76    184
[5,]  24     76    173

sum(mat)

[1] 1450

rowSums(mat)

[1] 311 273 314 279 273

mean(mat)

[1] 96.66667

colMeans(mat)

   age weight height 
  22.4   83.4  184.2 

Apply any arithmetic function to rows or columns

apply(mat, 2, sum)

   age weight height 
   112    417    921 

apply(mat, 1, max)

[1] 197 178 189 184 173

apply(mat, 1, range)

     [,1] [,2] [,3] [,4] [,5]
[1,]   19   19   31   19   24
[2,]  197  178  189  184  173

apply(mat, 2, mean, trim=0.1)

   age weight height 
  22.4   83.4  184.2 

Center and scale a matrix

Using scale()

(ctrMat <- scale(mat, center=TRUE, scale=FALSE))

      age weight height
[1,] -3.4   11.6   12.8
[2,] -3.4   -7.4   -6.2
[3,]  8.6   10.6    4.8
[4,] -3.4   -7.4   -0.2
[5,]  1.6   -7.4  -11.2
attr(,"scaled:center")
   age weight height 
  22.4   83.4  184.2 

colMeans(ctrMat)

          age        weight        height 
 1.421085e-15 -5.684342e-15  1.136868e-14 

(sclMat <- scale(mat, center=TRUE, scale=TRUE))

            age     weight      height
[1,] -0.6448468  1.1440933  1.36681637
[2,] -0.6448468 -0.7298526 -0.66205168
[3,]  1.6310830  1.0454645  0.51255614
[4,] -0.6448468 -0.7298526 -0.02135651
[5,]  0.3034573 -0.7298526 -1.19596433
attr(,"scaled:center")
   age weight height 
  22.4   83.4  184.2 
attr(,"scaled:scale")
      age    weight    height 
 5.272571 10.139033  9.364828 

apply(sclMat, 2, sd)

   age weight height 
     1      1      1 

Using sweep()

Mj <- rowMeans(mat)
Mk <- colMeans(mat)
sweep(mat, 1, Mj, "-")

           age     weight   height
[1,] -84.66667  -8.666667 93.33333
[2,] -72.00000 -15.000000 87.00000
[3,] -73.66667 -10.666667 84.33333
[4,] -74.00000 -17.000000 91.00000
[5,] -67.00000 -15.000000 82.00000

t(scale(t(mat), center=TRUE, scale=FALSE))

           age     weight   height
[1,] -84.66667  -8.666667 93.33333
[2,] -72.00000 -15.000000 87.00000
[3,] -73.66667 -10.666667 84.33333
[4,] -74.00000 -17.000000 91.00000
[5,] -67.00000 -15.000000 82.00000
attr(,"scaled:center")
[1] 103.6667  91.0000 104.6667  93.0000  91.0000

sweep(mat, 2, Mk, "-")

      age weight height
[1,] -3.4   11.6   12.8
[2,] -3.4   -7.4   -6.2
[3,]  8.6   10.6    4.8
[4,] -3.4   -7.4   -0.2
[5,]  1.6   -7.4  -11.2

Covariance and correlation matrices

Covariance matrix

Corrected

cov(mat)

         age weight height
age    27.80  22.55    0.4
weight 22.55 102.80   82.4
height  0.40  82.40   87.7

cor(mat)

               age    weight      height
age    1.000000000 0.4218204 0.008100984
weight 0.421820411 1.0000000 0.867822404
height 0.008100984 0.8678224 1.000000000

Extract the variances from the diagonal

diag(cov(mat))

   age weight height 
  27.8  102.8   87.7 

Uncorrected

(res <- cov.wt(mat, method="ML"))

$cov
         age weight height
age    22.24  18.04   0.32
weight 18.04  82.24  65.92
height  0.32  65.92  70.16

$center
   age weight height 
  22.4   83.4  184.2 

$n.obs
[1] 5

res$cov

         age weight height
age    22.24  18.04   0.32
weight 18.04  82.24  65.92
height  0.32  65.92  70.16

Correlation matrix

vec <- rnorm(nrow(mat))
cor(mat, vec)

            [,1]
age    0.2861200
weight 0.4984884
height 0.6549815

cor(vec, mat)

         age    weight    height
[1,] 0.28612 0.4984884 0.6549815

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