Descriptive statistics for data in matrices

TODO

• link to matrix, linearAlgebra

Sums and means

age    <- c(19, 19, 31, 19, 24, 17, 43, 28)
weight <- c(95, 76, 94, 76, 76, 68, 81, 65)
height <- c(197, 178, 189, 184, 173, 165, 181, 192)
(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
[6,]  17     68    165
[7,]  43     81    181
[8,]  28     65    192

sum(mat)

[1] 2290

rowSums(mat)

[1] 311 273 314 279 273 250 305 285

mean(mat)

[1] 95.41667

colMeans(mat)

    age  weight  height 
 25.000  78.875 182.375 

Apply any arithmetic function to rows or columns

apply(mat, 2, sum)

   age weight height 
   200    631   1459 

apply(mat, 1, max)

[1] 197 178 189 184 173 165 181 192

apply(mat, 1, range)

     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,]   19   19   31   19   24   17   43   28
[2,]  197  178  189  184  173  165  181  192

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

    age  weight  height 
 25.000  78.875 182.375 

Center and scale a matrix

Using scale()

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

     age  weight  height
[1,]  -6  16.125  14.625
[2,]  -6  -2.875  -4.375
[3,]   6  15.125   6.625
[4,]  -6  -2.875   1.625
[5,]  -1  -2.875  -9.375
[6,]  -8 -10.875 -17.375
[7,]  18   2.125  -1.375
[8,]   3 -13.875   9.625
attr(,"scaled:center")
    age  weight  height 
 25.000  78.875 182.375 

colMeans(ctrMat)

   age weight height 
     0      0      0 

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

            age     weight     height
[1,] -0.6818685  1.4818499  1.4000184
[2,] -0.6818685 -0.2642058 -0.4188089
[3,]  0.6818685  1.3899523  0.6341964
[4,] -0.6818685 -0.2642058  0.1555576
[5,] -0.1136447 -0.2642058 -0.8974477
[6,] -0.9091580 -0.9993872 -1.6632697
[7,]  2.0456055  0.1952825 -0.1316257
[8,]  0.3409342 -1.2750802  0.9213796
attr(,"scaled:center")
    age  weight  height 
 25.000  78.875 182.375 
attr(,"scaled:scale")
      age    weight    height 
 8.799351 10.881669 10.446291 

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
[6,] -66.33333 -15.333333 81.66667
[7,] -58.66667 -20.666667 79.33333
[8,] -67.00000 -30.000000 97.00000

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
[6,] -66.33333 -15.333333 81.66667
[7,] -58.66667 -20.666667 79.33333
[8,] -67.00000 -30.000000 97.00000
attr(,"scaled:center")
[1] 103.66667  91.00000 104.66667  93.00000  91.00000  83.33333 101.66667
[8]  95.00000

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

     age  weight  height
[1,]  -6  16.125  14.625
[2,]  -6  -2.875  -4.375
[3,]   6  15.125   6.625
[4,]  -6  -2.875   1.625
[5,]  -1  -2.875  -9.375
[6,]  -8 -10.875 -17.375
[7,]  18   2.125  -1.375
[8,]   3 -13.875   9.625

Covariance and correlation matrices

Covariance matrix

Corrected

cov(mat)

            age    weight    height
age    77.42857  16.42857  17.28571
weight 16.42857 118.41071  60.48214
height 17.28571  60.48214 109.12500

cor(mat)

             age    weight    height
age    1.0000000 0.1715749 0.1880505
weight 0.1715749 1.0000000 0.5320709
height 0.1880505 0.5320709 1.0000000

Extract the variances from the diagonal

diag(cov(mat))

      age    weight    height 
 77.42857 118.41071 109.12500 

Uncorrected

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

$cov
          age    weight   height
age    67.750  14.37500 15.12500
weight 14.375 103.60938 52.92188
height 15.125  52.92188 95.48438

$center
    age  weight  height 
 25.000  78.875 182.375 

$n.obs
[1] 8

res$cov

          age    weight   height
age    67.750  14.37500 15.12500
weight 14.375 103.60938 52.92188
height 15.125  52.92188 95.48438

Robust covariance estimator

library(robustbase)
covMcd(mat)

Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=6); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = mat)
Log(Det.):  10.38 

Robust Estimate of Location:
   age  weight  height  
 21.50   80.83  181.00  
Robust Estimate of Covariance:
          age  weight  height
age     67.42   79.36   43.78
weight  79.36  302.91  286.58
height  43.78  286.58  327.37

Correlation matrix

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

             [,1]
age     0.6061347
weight -0.5364582
height -0.2328038

cor(vec, mat)

           age     weight     height
[1,] 0.6061347 -0.5364582 -0.2328038

Robust correlation matrix

library(robustbase)
cov_rob <- covMcd(mat, cor=TRUE)
cov_rob$cor

             age    weight    height
age    1.0000000 0.5553181 0.2947135
weight 0.5553181 1.0000000 0.9100397
height 0.2947135 0.9100397 1.0000000

cov_rob$center

      age    weight    height 
 21.50000  80.83333 181.00000 

Detach (automatically) loaded packages (if possible)

try(detach(package:robustbase))

Get the article source from GitHub

R markdown - markdown - R code - all posts