# isomLR: (Inverse) Isometric log-ratio transformation for... In complmrob: Robust Linear Regression with Compositional Data as Covariates

## Description

Projects the D-dimensional compositional data on the (D-1)-dimensional simplex isometrically back and forth by transforming the values according to

z_i = √((D - i)/(D - i + 1)) log( x_i / (∏ (j = i + 1 ... D) x_j)^(1/(D - i))

## Usage

 ```1 2 3``` ```isomLR(x, comp = 1) isomLRinv(z, perc = TRUE) ```

## Arguments

 `x` a numeric vector of length `D` or a numeric matrix with `D` columns `comp` the component to use as the first compositional part `z` a numeric vector of length `D-1` or a numeric matrix with `D-1` columns. `perc` should the result be a matrix with percentage shares (default `TRUE`).

## Value

`isomLR`: a numeric matrix with `(D-1)` columns with the transformed values. The name of the first column is the name of the first part (the other names are according to the order of the columns in the given matrix `x`)

`isomLRinv`: a numeric matrix with `D` columns with the transformed values. The values in the matrix are not on the original scale, but the percentage shares are equal.

## Functions

• `isomLRinv`:

## Examples

 ```1 2 3 4 5 6``` ```X <- as.matrix(USArrests[ , -3]) # Get the ilr with relative information of the 1st column to the other cols ilrZ1 <- isomLR(X) # Get the ilr with relative information of the 2nd column to the other cols ilrZ2 <- isomLR(X, 2) isomLRinv(ilrZ1) ```

### Example output

```            [,1]      [,2]      [,3]
[1,] 0.08334000 0.7828109 0.1338491
[2,] 0.08910738 0.5143648 0.3965278
[3,] 0.03923599 0.8106016 0.1501624
[4,] 0.14478842 0.5343736 0.3208380
[5,] 0.03827275 0.7890746 0.1726526
[6,] 0.08403358 0.5043082 0.4116582
[7,] 0.04362153 0.8096515 0.1467270
[8,] 0.10841551 0.6012514 0.2903331
[9,] 0.06739447 0.7930027 0.1396028
[10,] 0.21073367 0.4767992 0.3124672
[11,] 0.06714572 0.6769404 0.2559139
[12,] 0.06696553 0.5672996 0.3657348
[13,] 0.06121030 0.7975352 0.1412545
[14,] 0.13285964 0.4796331 0.3875073
[15,] 0.03819795 0.7656035 0.1961985
[16,] 0.12428424 0.5028630 0.3728527
[17,] 0.09711100 0.7397025 0.1631865
[18,] 0.19929793 0.5134025 0.2872996
[19,] 0.03853176 0.8183503 0.1431180
[20,] 0.12865988 0.5548140 0.3165261
[21,] 0.04108871 0.8066963 0.1522150
[22,] 0.12387328 0.5167918 0.3593349
[23,] 0.03599360 0.7653750 0.1986314
[24,] 0.23431899 0.5168080 0.2488730
[25,] 0.05576541 0.7695030 0.1747316
[26,] 0.13345261 0.5017769 0.3647705
[27,] 0.04638068 0.7756469 0.1779724
[28,] 0.10549205 0.4967510 0.3977569
[29,] 0.04008407 0.7785833 0.1813327
[30,] 0.13363977 0.5268430 0.3395173
[31,] 0.05398761 0.7939946 0.1520178
[32,] 0.13764078 0.5387174 0.3236418
[33,] 0.08216597 0.8160746 0.1017594
[34,] 0.04501739 0.5441990 0.4107837
[35,] 0.06211275 0.7558033 0.1820840
[36,] 0.11802016 0.5243430 0.3576369
[37,] 0.03185074 0.7776948 0.1904544
[38,] 0.14856610 0.5000633 0.3513706
[39,] 0.04341484 0.8506019 0.1059833
[40,] 0.18187348 0.5339492 0.2841773
[41,] 0.05083085 0.7779494 0.1712197
[42,] 0.16913315 0.4861940 0.3446729
[43,] 0.07758399 0.7666371 0.1557789
[44,] 0.05918144 0.5173014 0.4235172
[45,] 0.04070852 0.7520481 0.2072434
[46,] 0.14280613 0.5094190 0.3477749
[47,] 0.02893501 0.7815407 0.1895243
[48,] 0.19227650 0.4940092 0.3137143
[49,] 0.04698436 0.7578498 0.1951658
[50,] 0.13837779 0.5441673 0.3174549
```

complmrob documentation built on May 29, 2017, 7:10 p.m.