Suppressed tabular data: Inner cell frequencies as decimal numbers

Assume that frequencies to be published, z, can be computed from inner frequencies, y, via z = t(x) %*% y, where x is a dummy matrix. Assuming correct suppression, this function will generate safe inner cell frequencies as decimal numbers.

Usage

SuppressDec(
  x,
  z = NULL,
  y = NULL,
  suppressed = NULL,
  digits = 9,
  nRep = 1,
  yDeduct = NULL,
  resScale = NULL,
  rmse = NULL,
  sparseLimit = 500
)

Arguments

x: Dummy matrix where the dimensions matches z and/or y input. Sparse matrix (Matrix package) is possible.
z: Frequencies to be published. All, only the safe ones or with suppressed as NA.
y: Inner cell frequencies (see details).
suppressed: Logical vector defining the suppressed elements of z.
digits: Output close to whole numbers will be rounded using digits as input to RoundWhole.
nRep: Integer, when >1, several y's will be generated. Extra columns in output.
yDeduct: Values to be subtracted from y and added back after the calculations. Can be used to perform the modulo method described in the paper (see examples).
resScale: Residuals will be scaled by resScale
rmse: Desired root mean square error (residual standard error). Will be used when resScale is NULL or cannot be used.
sparseLimit: Limit for the number of rows of a reduced x-matrix within the algorithm. When exceeded, a sparse algorithm is used (see IpsoExtra).

Value

The inner cell frequencies as decimal numbers

Details

This function makes use of ReduceX and RegSDCipso. It is not required that y consists of cell frequencies. A multivariate y or z is also possible. Then several values are possible as digits, resScale and rmse input.

Note

Capital letters, X, Y and Z, are used in the paper.

Author

Øyvind Langsrud

Examples

# Same data as in the paper
z <- RegSDCdata("sec7z")
x <- RegSDCdata("sec7x")
y <- RegSDCdata("sec7y")  # Now z is t(x) %*% y 
zAll <- RegSDCdata("sec7zAll")
zAllSupp <- RegSDCdata("sec7zAllSupp")
xAll <- RegSDCdata("sec7xAll")

# When no suppression, output is identical to y
SuppressDec(xAll, zAll, y)
#>           freq
#> row1_col1    3
#> row2_col1    1
#> row3_col1   12
#> row4_col1   18
#> row1_col2   11
#> row2_col2    9
#> row3_col2   22
#> row4_col2   19
#> row1_col3   32
#> row2_col3   13
#> row3_col3    2
#> row4_col3   16
#> row1_col4   30
#> row2_col4    8
#> row3_col4    2
#> row4_col4    3
SuppressDec(xAll, zAll)  # y can be seen in z
#>           freq
#> row1_col1    3
#> row2_col1    1
#> row3_col1   12
#> row4_col1   18
#> row1_col2   11
#> row2_col2    9
#> row3_col2   22
#> row4_col2   19
#> row1_col3   32
#> row2_col3   13
#> row3_col3    2
#> row4_col3   16
#> row1_col4   30
#> row2_col4    8
#> row3_col4    2
#> row4_col4    3

# Similar to Y* in paper (but other random values)
SuppressDec(x, z, y)
#>                 freq
#> row1_col1  8.3760459
#> row2_col1 -2.1183476
#> row3_col1 12.0000000
#> row4_col1 15.7423017
#> row1_col2  5.6239541
#> row2_col2 14.3760459
#> row3_col2 22.0000000
#> row4_col2 19.0000000
#> row1_col3 32.0000000
#> row2_col3 10.7423017
#> row3_col3  4.2576983
#> row4_col3 16.0000000
#> row1_col4 30.0000000
#> row2_col4  8.0000000
#> row3_col4 -0.2576983
#> row4_col4  5.2576983

# Residual standard error forced to be 1
SuppressDec(x, z, y, rmse = 1)
#>                freq
#> row1_col1  3.627008
#> row2_col1  4.600348
#> row3_col1 12.000000
#> row4_col1 13.772644
#> row1_col2 10.372992
#> row2_col2  9.627008
#> row3_col2 22.000000
#> row4_col2 19.000000
#> row1_col3 32.000000
#> row2_col3  8.772644
#> row3_col3  6.227356
#> row4_col3 16.000000
#> row1_col4 30.000000
#> row2_col4  8.000000
#> row3_col4 -2.227356
#> row4_col4  7.227356

# Seven ways of obtaining the same output
SuppressDec(x, z, rmse = 1)  # slower, y must be estimated
#>                freq
#> row1_col1  4.070156
#> row2_col1  5.179566
#> row3_col1 12.000000
#> row4_col1 12.750278
#> row1_col2  9.929844
#> row2_col2 10.070156
#> row3_col2 22.000000
#> row4_col2 19.000000
#> row1_col3 32.000000
#> row2_col3  7.750278
#> row3_col3  7.249722
#> row4_col3 16.000000
#> row1_col4 30.000000
#> row2_col4  8.000000
#> row3_col4 -3.249722
#> row4_col4  8.249722
SuppressDec(x, y = y, rmse = 1)
#>                freq
#> row1_col1  4.895203
#> row2_col1  3.951412
#> row3_col1 12.000000
#> row4_col1 13.153385
#> row1_col2  9.104797
#> row2_col2 10.895203
#> row3_col2 22.000000
#> row4_col2 19.000000
#> row1_col3 32.000000
#> row2_col3  8.153385
#> row3_col3  6.846615
#> row4_col3 16.000000
#> row1_col4 30.000000
#> row2_col4  8.000000
#> row3_col4 -2.846615
#> row4_col4  7.846615
SuppressDec(xAll, zAllSupp, y, rmse = 1)
#>                freq
#> row1_col1  4.832868
#> row2_col1  4.209071
#> row3_col1 12.000000
#> row4_col1 12.958061
#> row1_col2  9.167132
#> row2_col2 10.832868
#> row3_col2 22.000000
#> row4_col2 19.000000
#> row1_col3 32.000000
#> row2_col3  7.958061
#> row3_col3  7.041939
#> row4_col3 16.000000
#> row1_col4 30.000000
#> row2_col4  8.000000
#> row3_col4 -3.041939
#> row4_col4  8.041939
SuppressDec(xAll, zAllSupp, rmse = 1)  # slower, y must be estimated
#>                freq
#> row1_col1  4.884392
#> row2_col1  4.033761
#> row3_col1 12.000000
#> row4_col1 13.081846
#> row1_col2  9.115608
#> row2_col2 10.884392
#> row3_col2 22.000000
#> row4_col2 19.000000
#> row1_col3 32.000000
#> row2_col3  8.081846
#> row3_col3  6.918154
#> row4_col3 16.000000
#> row1_col4 30.000000
#> row2_col4  8.000000
#> row3_col4 -2.918154
#> row4_col4  7.918154
SuppressDec(xAll, zAll, y, is.na(zAllSupp), rmse = 1)
#>                freq
#> row1_col1  4.781734
#> row2_col1  3.703295
#> row3_col1 12.000000
#> row4_col1 13.514971
#> row1_col2  9.218266
#> row2_col2 10.781734
#> row3_col2 22.000000
#> row4_col2 19.000000
#> row1_col3 32.000000
#> row2_col3  8.514971
#> row3_col3  6.485029
#> row4_col3 16.000000
#> row1_col4 30.000000
#> row2_col4  8.000000
#> row3_col4 -2.485029
#> row4_col4  7.485029
SuppressDec(xAll, zAll, suppressed = is.na(zAllSupp), rmse = 1)  # y seen in z
#>                freq
#> row1_col1  4.616492
#> row2_col1  3.696645
#> row3_col1 12.000000
#> row4_col1 13.686863
#> row1_col2  9.383508
#> row2_col2 10.616492
#> row3_col2 22.000000
#> row4_col2 19.000000
#> row1_col3 32.000000
#> row2_col3  8.686863
#> row3_col3  6.313137
#> row4_col3 16.000000
#> row1_col4 30.000000
#> row2_col4  8.000000
#> row3_col4 -2.313137
#> row4_col4  7.313137
SuppressDec(xAll, y = y, suppressed = is.na(zAllSupp), rmse = 1)
#>                freq
#> row1_col1  4.729882
#> row2_col1  4.427013
#> row3_col1 12.000000
#> row4_col1 12.843105
#> row1_col2  9.270118
#> row2_col2 10.729882
#> row3_col2 22.000000
#> row4_col2 19.000000
#> row1_col3 32.000000
#> row2_col3  7.843105
#> row3_col3  7.156895
#> row4_col3 16.000000
#> row1_col4 30.000000
#> row2_col4  8.000000
#> row3_col4 -3.156895
#> row4_col4  8.156895

# YhatMod4 and YhatMod10 in Table 2 in paper
SuppressDec(xAll, zAllSupp, y, yDeduct = 4 * (y%/%4), resScale = 0)
#>                 freq
#> row1_col1  2.9565217
#> row2_col1  0.8695652
#> row3_col1 12.0000000
#> row4_col1 18.1739130
#> row1_col2 11.0434783
#> row2_col2  8.9565217
#> row3_col2 22.0000000
#> row4_col2 19.0000000
#> row1_col3 32.0000000
#> row2_col3 13.1739130
#> row3_col3  1.8260870
#> row4_col3 16.0000000
#> row1_col4 30.0000000
#> row2_col4  8.0000000
#> row3_col4  2.1739130
#> row4_col4  2.8260870
SuppressDec(xAll, zAllSupp, y, yDeduct = 10 * (y%/%10), rmse = 0)
#>                 freq
#> row1_col1  0.6956522
#> row2_col1  4.0869565
#> row3_col1 12.0000000
#> row4_col1 17.2173913
#> row1_col2 13.3043478
#> row2_col2  6.6956522
#> row3_col2 22.0000000
#> row4_col2 19.0000000
#> row1_col3 32.0000000
#> row2_col3 12.2173913
#> row3_col3  2.7826087
#> row4_col3 16.0000000
#> row1_col4 30.0000000
#> row2_col4  8.0000000
#> row3_col4  1.2173913
#> row4_col4  3.7826087

# As data in Table 3 in paper (but other random values)
SuppressDec(xAll, zAllSupp, y, yDeduct = 10 * (y%/%10), resScale = 0.1)
#>                 freq
#> row1_col1  0.6512744
#> row2_col1  4.3390612
#> row3_col1 12.0000000
#> row4_col1 17.0096643
#> row1_col2 13.3487256
#> row2_col2  6.6512744
#> row3_col2 22.0000000
#> row4_col2 19.0000000
#> row1_col3 32.0000000
#> row2_col3 12.0096643
#> row3_col3  2.9903357
#> row4_col3 16.0000000
#> row1_col4 30.0000000
#> row2_col4  8.0000000
#> row3_col4  1.0096643
#> row4_col4  3.9903357

# rmse instead of resScale and 5 draws
SuppressDec(xAll, zAllSupp, y, yDeduct = 10 * (y%/%10), rmse = 1, nRep = 5)
#>                 freq      freq      freq      freq       freq
#> row1_col1  0.4336625  1.005745  1.324514  1.416361  0.7262801
#> row2_col1  3.7672470  3.307106  3.278874  3.447879  4.6382642
#> row3_col1 12.0000000 12.000000 12.000000 12.000000 12.0000000
#> row4_col1 17.7990905 17.687149 17.396612 17.135760 16.6354556
#> row1_col2 13.5663375 12.994255 12.675486 12.583639 13.2737199
#> row2_col2  6.4336625  7.005745  7.324514  7.416361  6.7262801
#> row3_col2 22.0000000 22.000000 22.000000 22.000000 22.0000000
#> row4_col2 19.0000000 19.000000 19.000000 19.000000 19.0000000
#> row1_col3 32.0000000 32.000000 32.000000 32.000000 32.0000000
#> row2_col3 12.7990905 12.687149 12.396612 12.135760 11.6354556
#> row3_col3  2.2009095  2.312851  2.603388  2.864240  3.3645444
#> row4_col3 16.0000000 16.000000 16.000000 16.000000 16.0000000
#> row1_col4 30.0000000 30.000000 30.000000 30.000000 30.0000000
#> row2_col4  8.0000000  8.000000  8.000000  8.000000  8.0000000
#> row3_col4  1.7990905  1.687149  1.396612  1.135760  0.6354556
#> row4_col4  3.2009095  3.312851  3.603388  3.864240  4.3645444