First some data to be rounded.
| col1 | col2 | col3 | col4 | col5 | Total | |
|---|---|---|---|---|---|---|
| row1 | 6 | 0 | 1 | 3 | 4 | 14 |
| row2 | 1 | 2 | 3 | 1 | 2 | 9 |
| row3 | 0 | 1 | 1 | 0 | 2 | 4 |
| Total | 7 | 3 | 5 | 4 | 8 | 27 |
Some of the inner cells are rounded. Thereafter new totals are
computed. The underlying algorithm tries to keep the values of these
totals close to the original ones.
| col1 | col2 | col3 | col4 | col5 | Total | |
|---|---|---|---|---|---|---|
| row1 | 6 | 0 | 0 | 5 | 5 | 16 |
| row2 | 0 | 0 | 5 | 0 | 0 | 5 |
| row3 | 0 | 0 | 0 | 0 | 5 | 5 |
| Total | 6 | 0 | 5 | 5 | 10 | 26 |
When the inner cells are not going to be published, the number
of cells to be rounded can be limited.
| col1 | col2 | col3 | col4 | col5 | Total | |
|---|---|---|---|---|---|---|
| row1 | 6 | 0 | 0 | 5 | 4 | 15 |
| row2 | 1 | 0 | 5 | 0 | 2 | 8 |
| row3 | 0 | 5 | 0 | 0 | 0 | 5 |
| Total | 7 | 5 | 5 | 5 | 6 | 28 |
library(SmallCountRounding)
z <- SmallCountData("exPSD")
z rows cols freq
1 row1 col1 6
2 row2 col1 1
3 row3 col1 0
4 row1 col2 0
5 row2 col2 2
6 row3 col2 1
7 row1 col3 1
8 row2 col3 3
9 row3 col3 1
10 row1 col4 3
11 row2 col4 1
12 row3 col4 0
13 row1 col5 4
14 row2 col5 2
15 row3 col5 2To avoid any small values in the range 1-4 we can use 5 as rounding base.
a <- PLSrounding(z, freqVar = "freq", roundBase = 5)The result is given in Table 2 and can bee seen in the output elements below.
a$inner rows cols original rounded difference
1 row1 col1 6 6 0
2 row2 col1 1 0 -1
3 row3 col1 0 0 0
4 row1 col2 0 0 0
5 row2 col2 2 0 -2
6 row3 col2 1 0 -1
7 row1 col3 1 0 -1
8 row2 col3 3 5 2
9 row3 col3 1 0 -1
10 row1 col4 3 5 2
11 row2 col4 1 0 -1
12 row3 col4 0 0 0
13 row1 col5 4 5 1
14 row2 col5 2 0 -2
15 row3 col5 2 5 3a$publish rows cols original rounded difference
1 Total Total 27 26 -1
2 Total col1 7 6 -1
3 Total col2 3 0 -3
4 Total col3 5 5 0
5 Total col4 4 5 1
6 Total col5 8 10 2
7 row1 Total 14 16 2
8 row1 col1 6 6 0
9 row1 col2 0 0 0
10 row1 col3 1 0 -1
11 row1 col4 3 5 2
12 row1 col5 4 5 1
13 row2 Total 9 5 -4
14 row2 col1 1 0 -1
15 row2 col2 2 0 -2
16 row2 col3 3 5 2
17 row2 col4 1 0 -1
18 row2 col5 2 0 -2
19 row3 Total 4 5 1
20 row3 col1 0 0 0
21 row3 col2 1 0 -1
22 row3 col3 1 0 -1
23 row3 col4 0 0 0
24 row3 col5 2 5 3The output element publish contains the original and
rounded versions of the all the 24 values in Table 2. The corresponding
element inner contains only the 15 inner cells and is
similar to the input data. The values in publish are
additive. That is, marginal cells (Totals) can be computed
straightforwardly from inner for both original and rounded
counts.
Assuming only row and column totals to be published, the publishable
cells can be defined by the formula ~rows+cols. Rounding
can now be performed by:
b <- PLSrounding(z, "freq", 5, formula = ~rows + cols)The result is given in Table 3 and can bee seen in the output elements below.
b$inner rows cols original rounded difference
1 row1 col1 6 6 0
2 row2 col1 1 1 0
3 row3 col1 0 0 0
4 row1 col2 0 0 0
5 row2 col2 2 0 -2
6 row3 col2 1 5 4
7 row1 col3 1 0 -1
8 row2 col3 3 5 2
9 row3 col3 1 0 -1
10 row1 col4 3 5 2
11 row2 col4 1 0 -1
12 row3 col4 0 0 0
13 row1 col5 4 4 0
14 row2 col5 2 2 0
15 row3 col5 2 0 -2b$publish rows cols original rounded difference
1 Total Total 27 28 1
2 row1 Total 14 15 1
3 row2 Total 9 8 -1
4 row3 Total 4 5 1
5 Total col1 7 7 0
6 Total col2 3 5 2
7 Total col3 5 5 0
8 Total col4 4 5 1
9 Total col5 8 6 -2The underlying algorithm is sequential. Within a loop, the next cell
to be given the rounding base value is selected according to a
criterion. Random draw is used when draw criterion. To ensure unique
output, a fixed random generator seed is used locally within the
function without affecting the random value stream in R. See the
documentation of rndSeed, a parameter to
RoundViaDummy.
The result of printing the output from PLSrounding is
(a and b as above):
a
PLSrounding summary:
maxdiff HDutility meanAbsDiff rootMeanSquare
4 0.744 1.3333 1.6833
Frequencies of cell frequencies and absolute differences:
inn.0 inn.1-4 inn.5 inn.6+ inn.all pub.0 pub.1-4 pub.5 pub.6+ pub.all
original 3 11 . 1 15 3 14 1 6 24
rounded 10 . 4 1 15 11 . 8 5 24
absDiff 4 11 . . 15 5 19 . . 24b
PLSrounding summary:
maxdiff HDutility meanAbsDiff rootMeanSquare
2 0.941 1 1.2019
Frequencies of cell frequencies and absolute differences:
inn.0 inn.1-4 inn.5 inn.6+ inn.all pub.0 pub.1-4 pub.5 pub.6+ pub.all
original 3 11 . 1 15 . 3 1 5 9
rounded 8 3 3 1 15 . . 4 5 9
absDiff 7 8 . . 15 2 7 . . 9First some utility measures are printet. For example
maxdiff is the maximum difference between an original and
rounded cells within publish. Thereafter a table of
frequencies of cell frequencies and absolute differences are printed.
Summary of inner and publish are shown in the
left and right parts of the table, respectively. For example, row
rounded and column inn.6+ is the number of
rounded inner cell frequencies greater than or equal to 6. The last row
(absDiff) is based on the differences without signs.
It is possible to compute manually the printed utility measures by:
f <- b$publish$original
g <- b$publish$rounded
print(c(
maxdiff = max(abs(g - f)),
HDutility = HDutility(f, g),
meanAbsDiff = mean(abs(g - f)),
rootMeanSquare = sqrt(mean((g - f)^2))
)) maxdiff HDutility meanAbsDiff rootMeanSquare
2.000000 0.940951 1.000000 1.201850 These measures are also found in the output element
metrics together with the same measures based on
inner. See ?HDutility for more information
about the utility measure based on the Hellinger distance.
Apart from printing, output is a usual list and summary
works as usual.
summary(b) Length Class Mode
inner 5 data.frame list
publish 5 data.frame list
metrics 9 -none- numeric
freqTable 30 -none- numericThe output element freqTable is the table seen when the
output object is printed (frequencies of cell frequencies and absolute
differences).
Below is a small data set to be used as input.
| geo | eu | year | freq |
|---|---|---|---|
| Iceland | nonEU | 2018 | 2 |
| Portugal | EU | 2018 | 3 |
| Spain | EU | 2018 | 7 |
| Iceland | nonEU | 2019 | 1 |
| Portugal | EU | 2019 | 5 |
| Spain | EU | 2019 | 6 |
The variables geo and eu is hierarchical
related. This data set can be processed in several ways. In some cases,
the entire table will be input and in other cases the eu
column can be omitted. Then, the hierarchical information is sent as
input in another way. One possibility is the table below, where the
hierarchy is coded as in the r package sdcTable.
| levels | codes |
|---|---|
| @ | Total |
| @@ | EU |
| @@@ | Portugal |
| @@@ | Spain |
| @@ | nonEU |
| @@@ | Iceland |
Another possibility is TauArgus coding. More general coding is also
possible. See ?AutoHierarchies for more information.
Below is output in the case were all possible combinations (including the inner cells) are to be published. Also in this example we use 5 as a rounding base. As can be seen below, this output can be generated in several ways. The inner cells are colored according to the rounding.
| geo | year | original | rounded | difference |
|---|---|---|---|---|
| Total | Total | 24 | 23 | -1 |
| Total | 2018 | 12 | 12 | 0 |
| Total | 2019 | 12 | 11 | -1 |
| EU | Total | 21 | 23 | 2 |
| EU | 2018 | 10 | 12 | 2 |
| EU | 2019 | 11 | 11 | 0 |
| nonEU | Total | 3 | 0 | -3 |
| nonEU | 2018 | 2 | 0 | -2 |
| nonEU | 2019 | 1 | 0 | -1 |
| Iceland | Total | 3 | 0 | -3 |
| Iceland | 2018 | 2 | 0 | -2 |
| Iceland | 2019 | 1 | 0 | -1 |
| Portugal | Total | 8 | 10 | 2 |
| Portugal | 2018 | 3 | 5 | 2 |
| Portugal | 2019 | 5 | 5 | 0 |
| Spain | Total | 13 | 13 | 0 |
| Spain | 2018 | 7 | 7 | 0 |
| Spain | 2019 | 6 | 6 | 0 |
e6 <- SmallCountData("e6") # As Table 4
eDimList <- SmallCountData("eDimList")
eDimList$geo
levels codes
1 @ Total
2 @@ EU
3 @@@ Portugal
4 @@@ Spain
5 @@ nonEU
6 @@@ Iceland
$year
levels codes
1 @ Total
2 @@ 2018
3 @@ 2019As seen above, a hierarchy is specified for both variables.
eDimList$geo is given in Table 5 and
eDimList$year is a plain hierarchy with total code.
The five lines below produce the same results with element
publish as in Table 6. Ordering of rows can be
different.
PLSrounding(e6, "freq", 5) # a)
PLSrounding(e6, "freq", 5, dimVar = c("geo", "eu", "year")) # b)
PLSrounding(e6, "freq", 5, formula = ~eu * year + geo * year) # c)
PLSrounding(e6[, -2], "freq", 5, hierarchies = eDimList) # d)
PLSrounding(e6[, -2], "freq", 5, hierarchies = eDimList, formula = ~geo * year) # e)dimVar is assumed to be all
variables except freq.geo and eu are combined into the same output
column.A difference occur when all combinations are not contained in input
data. Then c) above will limit output to combinations available in
input. In the other cases zeroes will be added. The extra zeroes can be
avoided by using removeEmpty=TRUE. Note also the parameter
inputInOutput which can be used to specify whether to
include codes from input. Below is an example with incomplete input data
using both these parameters.
out <- PLSrounding(e6[-1, ], "freq", 5, removeEmpty = TRUE, inputInOutput = c(FALSE,TRUE))
out
PLSrounding summary:
maxdiff HDutility meanAbsDiff rootMeanSquare
1 0.8925 0.5 0.7071
Frequencies of cell frequencies and absolute differences:
inn.0 inn.1-4 inn.5 inn.6+ inn.all pub.0 pub.1-4 pub.5 pub.6+ pub.all
original . 2 1 2 5 . 2 . 6 8
rounded 1 1 1 2 5 2 . . 6 8
absDiff 4 1 . . 5 4 4 . . 8out$inner geo year original rounded difference
2 Portugal 2018 3 3 0
3 Spain 2018 7 7 0
4 Iceland 2019 1 0 -1
5 Portugal 2019 5 5 0
6 Spain 2019 6 6 0out$publish geo year original rounded difference
1 Total Total 22 21 -1
2 Total 2018 10 10 0
3 Total 2019 12 11 -1
4 EU Total 21 21 0
5 EU 2018 10 10 0
6 EU 2019 11 11 0
7 nonEU Total 1 0 -1
8 nonEU 2019 1 0 -1In this case only a single inner cell needed to be rounded (Iceland, 2019). The original small value of (Portugal, 2018) could be retained.