Function to perform various methods of microaggregation.

```
microaggregation(
obj,
variables = NULL,
aggr = 3,
strata_variables = NULL,
method = "mdav",
weights = NULL,
nc = 8,
clustermethod = "clara",
measure = "mean",
trim = 0,
varsort = 1,
transf = "log"
)
```

- obj
either an object of class

`sdcMicroObj-class`

or a`data.frame`

- variables
variables to microaggregate. For

`NULL`

: If obj is of class sdcMicroObj, all numerical key variables are chosen per default. For`data.frames`

, all columns are chosen per default.- aggr
aggregation level (default=3)

- strata_variables
for

`data.frames`

, by-variables for applying microaggregation only within strata defined by the variables. For`sdcMicroObj-class`

-objects, the stratification-variable defined in slot`@strataVar`

is used. This slot can be changed any time using`strataVar<-`

.- method
pca, rmd, onedims, single, simple, clustpca, pppca, clustpppca, mdav, clustmcdpca, influence, mcdpca

- weights
sampling weights. If obj is of class sdcMicroObj the vector of sampling weights is chosen automatically. If determined, a weighted version of the aggregation measure is chosen automatically, e.g. weighted median or weighted mean.

- nc
number of cluster, if the chosen method performs cluster analysis

- clustermethod
clustermethod, if necessary

- measure
aggregation statistic, mean, median, trim, onestep (default=mean)

- trim
trimming percentage, if measure=trim

- varsort
variable for sorting, if method=single

- transf
transformation for data x

If ‘obj’ was of class `sdcMicroObj-class`

the corresponding
slots are filled, like manipNumVars, risk and utility. If ‘obj’ was
of class “data.frame”, an object of class “micro” with following entities is returned:

`x`

: original data`mx`

: the microaggregated dataset`method`

: method`aggr`

: aggregation level`measure`

: proximity measure for aggregation

On https://research.cbs.nl/casc/glossary.htm one can found the “official” definition of microaggregation:

Records are grouped based on a proximity measure of variables of interest, and the same small groups of records are used in calculating aggregates for those variables. The aggregates are released instead of the individual record values.

The recommended method is “rmd” which forms the proximity using multivariate distances based on robust methods. It is an extension of the well-known method “mdav”. However, when computational speed is important, method “mdav” is the preferable choice.

While for the proximity measure very different concepts can be used, the aggregation itself is naturally done with the arithmetic mean. Nevertheless, other measures of location can be used for aggregation, especially when the group size for aggregation has been taken higher than 3. Since the median seems to be unsuitable for microaggregation because of being highly robust, other mesures which are included can be chosen. If a complex sample survey is microaggregated, the corresponding sampling weights should be determined to either aggregate the values by the weighted arithmetic mean or the weighted median.

This function contains also a method with which the data can be clustered with a variety of different clustering algorithms. Clustering observations before applying microaggregation might be useful. Note, that the data are automatically standardised before clustering.

The usage of clustering method ‘Mclust’ requires package mclust02, which must be loaded first. The package is not loaded automatically, since the package is not under GPL but comes with a different licence.

The are also some projection methods for microaggregation included. The robust version ‘pppca’ or ‘clustpppca’ (clustering at first) are fast implementations and provide almost everytime the best results.

Univariate statistics are preserved best with the individual ranking method (we called them ‘onedims’, however, often this method is named ‘individual ranking’), but multivariate statistics are strong affected.

With method ‘simple’ one can apply microaggregation directly on the (unsorted) data. It is useful for the comparison with other methods as a benchmark, i.e. replies the question how much better is a sorting of the data before aggregation.

if only one variable is specified, `mafast`

is applied and argument `method`

is ignored.
Parameters `measure`

are ignored for methods `mdav`

and `rmd`

.

Templ, M. and Meindl, B., *Robust Statistics Meets SDC: New Disclosure
Risk Measures for Continuous Microdata Masking*, Lecture Notes in Computer
Science, Privacy in Statistical Databases, vol. 5262, pp. 113-126, 2008.

Templ, M. *Statistical Disclosure Control for Microdata Using the
R-Package sdcMicro*, Transactions on Data Privacy, vol. 1, number 2, pp.
67-85, 2008. http://www.tdp.cat/issues/abs.a004a08.php

Templ, M. *New Developments in Statistical Disclosure Control and
Imputation: Robust Statistics Applied to Official Statistics*,
Suedwestdeutscher Verlag fuer Hochschulschriften, 2009, ISBN: 3838108280,
264 pages.

Templ, M. Statistical Disclosure Control for Microdata: Methods and Applications in R.
*Springer International Publishing*, 287 pages, 2017. ISBN 978-3-319-50272-4. doi:10.1007/978-3-319-50272-4
doi:10.1007/978-3-319-50272-4

Templ, M. and Meindl, B. and Kowarik, A.: *Statistical Disclosure Control for
Micro-Data Using the R Package sdcMicro*, Journal of Statistical Software,
67 (4), 1--36, 2015.

```
data(testdata)
m <- microaggregation(
obj = testdata[1:100, c("expend", "income", "savings")],
method = "mdav",
aggr = 4
)
summary(m)
#> $meansx
#> expend income savings
#> Min. : 1106874 Min. : 2897 Min. : 11751
#> 1st Qu.:25977689 1st Qu.:27750000 1st Qu.:2620342
#> Median :45716872 Median :44850000 Median :4771488
#> Mean :48440371 Mean :49180278 Mean :4798498
#> 3rd Qu.:69426340 3rd Qu.:70650000 3rd Qu.:6940269
#> Max. :98685205 Max. :99600000 Max. :9984098
#>
#> $meansxm
#> expend income savings
#> Min. :14471827 Min. : 4482460 Min. : 872137
#> 1st Qu.:22752145 1st Qu.:24675000 1st Qu.:2353262
#> Median :42916487 Median :46850000 Median :5116959
#> Mean :48440371 Mean :49180278 Mean :4798498
#> 3rd Qu.:71888065 3rd Qu.:65000000 3rd Qu.:7020042
#> Max. :91918606 Max. :93725000 Max. :9407783
#>
#> $amean
#> [1] 0
#>
#> $amedian
#> [1] 0.1782512
#>
#> $aonestep
#> [1] 0
#>
#> $devvar
#> [1] 0.3747106
#>
#> $amad
#> [1] 0.5343033
#>
#> $acov
#> [1] 0.1873553
#>
#> $arcov
#> [1] NA
#>
#> $acor
#> [1] 0.25935
#>
#> $arcor
#> [1] NA
#>
#> $acors
#> [1] 0.6424174
#>
#> $adlm
#> [1] 0.1699611
#>
#> $adlts
#> [1] NA
#>
#> $apcaload
#> [1] 0.6853318
#>
#> $apppcaload
#> [1] 2.27684
#>
#> $totalsOrig
#> expend income savings
#> 4844037117 4918027777 479849813
#>
#> $totalsMicro
#> numeric(0)
#>
#> $atotals
#> [1] 0
#>
#> $pmtotals
#> [1] 0
#>
#> $util1
#> [1] 53.39995
#>
#> $deigenvalues
#> [1] 0.0596172
#>
#> $risk0
#> [1] 0
#>
#> $risk1
#> [1] 0.29
#>
#> $risk2
#> [1] 0
#>
#> $wrisk1
#> [1] 0.7450012
#>
#> $wrisk2
#> [1] 0
#>
## for objects of class sdcMicro:
## no stratification because `@strataVar` is `NULL`
data(testdata2)
sdc <- createSdcObj(
dat = testdata2,
keyVars = c("urbrur", "roof", "walls", "water", "electcon", "sex"),
numVars = c("expend", "income", "savings"),
w = "sampling_weight"
)
sdc <- microaggregation(
obj = sdc,
variables = c("expend", "income")
)
## with stratification using variable `"relat"`
strataVar(sdc) <- "relat"
sdc <- microaggregation(
obj = sdc,
variables = "savings"
)
```