R: Additional Information-Loss measures

IL_correl {sdcMicro} | R Documentation

## Additional Information-Loss measures

### Description

Measures `IL_correl()` and `IL_variables()` were proposed by Andrzej Mlodak and are (theoretically) bounded between `0` and `1`.

### Usage

    IL_correl(x, xm)

    ## S3 method for class 'il_correl'
    print(x, digits = 3, ...)

    IL_variables(x, xm)

    ## S3 method for class 'il_variables'
    print(x, digits = 3, ...)

### Arguments

`x` | an object coercible to a `data.frame` representing the original dataset
`xm` | an object coercible to a `data.frame` representing the perturbed, modified dataset
`digits` | number digits used for rounding when displaying results
`...` | additional parameter for print-methods; currently ignored

### Details

- `IL_correl()`: is a information-loss measure that can be applied to common numerically scaled variables in `x` and `xm`. It is based on diagonal entries of inverse correlation matrices in the original and perturbed data.

- `IL_variables()`: for common-variables in `x` and `xm` the individual distance-functions depend on the class of the variable; specifically these functions are different for numeric variables, ordered-factors and character/factor variables. The individual distances are summed up and scaled by `n * m` with `n` being the number of records and `m` being the number of (common) variables.

Details can be found in the references below

The implementation of `IL_correl()` differs slightly with the original proposition from Mlodak, A. (2020) as the constant multiplier was changed to `1 / sqrt(2)` instead of `1/2` for better efficiency and interpretability of the measure.

### Value

the corresponding information-loss measure

### Author(s)

Bernhard Meindl bernhard.meindl@statistik.gv.at

### References

Mlodak, A. (2020). Information loss resulting from statistical disclosure control of output data, Wiadomosci Statystyczne. The Polish Statistician, 2020, 65(9), 7-27, DOI: 10.5604/01.3001.0014.4121

Mlodak, A. (2019). Using the Complex Measure in an Assessment of the Information Loss Due to the Microdata Disclosure Control, Przegląd Statystyczny, 2019, 66(1), 7-26, DOI: 10.5604/01.3001.0013.8285

### Examples

    data("Tarragona", package = "sdcMicro")
    res1 <- addNoise(obj = Tarragona, variables = colnames(Tarragona), noise = 100)
    IL_correl(x = as.data.frame(res1$x), xm = as.data.frame(res1$xm))

    res2 <- addNoise(obj = Tarragona, variables = colnames(Tarragona), noise = 25)
    IL_correl(x = as.data.frame(res2$x), xm = as.data.frame(res2$xm))

    # creating test-inputs
    n <- 150
    x <- xm <- data.frame(
      v1 = factor(sample(letters[1:5], n, replace = TRUE), levels = letters[1:5]),
      v2 = rnorm(n),
      v3 = runif(3),
      v4 = ordered(sample(LETTERS[1:3], n, replace = TRUE), levels = c("A", "B", "C"))
    )
    xm$v1[1:5] <- "a"
    xm$v2 <- rnorm(n, mean = 5)
    xm$v4[1:5] <- "A"
    IL_variables(x, xm)

[Package sdcMicro version 5.6.1 Index]