The sample frequencies are assumed to be independent and following a Poisson distribution. The parameters of the corresponding parameters are estimated by a log-linear model including the main effects and possible interactions.

modRisk(obj, method = "default", weights, formulaM, bound = Inf, ...)

## Arguments

obj

An sdcMicroObj-class-object or a numeric matrix or data.frame containing all variables required in the specified model.

method

chose method for model-based risk-estimation. Currently, the following methods can be selected:

• "default": the standard log-linear model.

• "CE": the Clogg Eliason method, additionally, considers survey weights by using an offset term.

• "PML": the pseudo maximum likelihood method.

• "weightedLLM": the weighted maximum likelihood method, considers survey weights by including them as one of the predictors.

• "IPF": iterative proportional fitting as used in deprecated method 'LLmodGlobalRisk'.

weights

a variable name specifying sampling weights

formulaM

A formula specifying the model.

bound

a number specifying a threshold for 'risky' observations in the sample.

...

additional parameters passed through, currently ignored.

## Value

Two global risk measures and some model output given the specified model. If this method is applied to an sdcMicroObj-class-object, the slot 'risk' in the object ist updated with the result of the model-based risk-calculation.

## Details

This measure aims to (1) calculate the number of sample uniques that are population uniques with a probabilistic Poisson model and (2) to estimate the expected number of correct matches for sample uniques.

ad 1) this risk measure is defined over all sample uniques as $$\tau_1 = \sum\limits_{j:f_j=1} P(F_j=1 | f_j=1) \quad ,$$ i.e. the expected number of sample uniques that are population uniques.

ad 2) this risk measure is defined over all sample uniques as $$\tau_2 = \sum\limits_{j:f_j=1} P(1 / F_j | f_j=1) \quad .$$

Since population frequencies $$F_k$$ are unknown, they need to be estimated.

The iterative proportional fitting method is used to fit the parameters of the Poisson distributed frequency counts related to the model specified to fit the frequency counts. The obtained parameters are used to estimate a global risk, defined in Skinner and Holmes (1998).

## References

Skinner, C.J. and Holmes, D.J. (1998) Estimating the re-identification risk per record in microdata. Journal of Official Statistics, 14:361-372, 1998.

Rinott, Y. and Shlomo, N. (1998). A Generalized Negative Binomial Smoothing Model for Sample Disclosure Risk Estimation. Privacy in Statistical Databases. Lecture Notes in Computer Science. Springer-Verlag, 82--93.

Clogg, C.C. and Eliasson, S.R. (1987). Some Common Problems in Log-Linear Analysis. Sociological Methods and Research, 8-44.

loglm, measure_risk

## Author

Matthias Templ, Marius Totter, Bernhard Meindl

## Examples

## data.frame method
data(testdata2)
form <- ~sex+water+roof
w <- "sampling_weight"
(modRisk(testdata2, method = "default", formulaM = form, weights = w))
#> The estimated model (using method 'default') was:
#> 	~ sex + water + roof
#> global risk-measures:
#> 	Risk-Measure 1: 0.244 (24.436 %)
#> 	Risk-Measure 2: 0.384 (38.400 %)
(modRisk(testdata2, method = "CE", formulaM = form, weights = w))
#> The estimated model (using method 'CE') was:
#> 	~ sex + water + roof
#> global risk-measures:
#> 	Risk-Measure 1: 0.237 (23.740 %)
#> 	Risk-Measure 2: 0.379 (37.936 %)
(modRisk(testdata2, method = "PML", formulaM = form, weights = w))
#> The estimated model (using method 'PML') was:
#> 	~ sex + water + roof
#> global risk-measures:
#> 	Risk-Measure 1: 0.244 (24.436 %)
#> 	Risk-Measure 2: 0.384 (38.400 %)
(modRisk(testdata2, method = "weightedLLM", formulaM = form, weights = w))
#> The estimated model (using method 'weightedLLM') was:
#> 	~ sex + water + roof
#> global risk-measures:
#> 	Risk-Measure 1: 0.314 (31.424 %)
#> 	Risk-Measure 2: 0.442 (44.249 %)
(modRisk(testdata2, method = "IPF", formulaM = form, weights = w))
#> The estimated model (using method 'IPF') was:
#> 	~ sex + water + roof
#> global risk-measures:
#> 	Risk-Measure 1: 0.274 (27.354 %)
#> 	Risk-Measure 2: 0.410 (41.038 %)

## application to a sdcMicroObj
data(testdata2)
sdc <- createSdcObj(testdata2,
keyVars = c("urbrur", "roof", "walls", "electcon", "relat", "sex"),
numVars = c("expend", "income", "savings"),
w = "sampling_weight")
sdc <- modRisk(sdc, form = ~sex+water+roof)
slot(sdc, "risk")\$model
#> The estimated model (using method 'default') was:
#> 	~ sex + water + roof
#> global risk-measures:
#> 	Risk-Measure 1: 0.244 (24.436 %)
#> 	Risk-Measure 2: 0.384 (38.400 %)

# \donttest{
# an example using data from the laeken-pkg
library(laeken)
data(eusilc)
f <- as.formula(paste(" ~ ", "db040 + hsize + rb090 +
age + pb220a + age:rb090 + age:hsize +
hsize:rb090"))
w <- "rb050"
(modRisk(eusilc, method = "default", weights = w, formulaM = f, bound = 5))
#> The estimated model (using method 'default') was:
#> 	~ db040 + hsize + rb090 + age + pb220a + age:rb090 + age:hsize + hsize:rb090
#> global risk-measures:
#> 	Risk-Measure 1: 0.296 (29.641 %)
#> 	Risk-Measure 2: 0.360 (36.043 %)
(modRisk(eusilc, method = "CE", weights =  w, formulaM = f, bound = 5))
#> The estimated model (using method 'CE') was:
#> 	~ db040 + hsize + rb090 + age + pb220a + age:rb090 + age:hsize + hsize:rb090
#> global risk-measures:
#> 	Risk-Measure 1: 0.295 (29.526 %)
#> 	Risk-Measure 2: 0.360 (35.966 %)
(modRisk(eusilc, method = "PML", weights = w, formulaM = f, bound = 5))
#> The estimated model (using method 'PML') was:
#> 	~ db040 + hsize + rb090 + age + pb220a + age:rb090 + age:hsize + hsize:rb090
#> global risk-measures:
#> 	Risk-Measure 1: 0.296 (29.609 %)
#> 	Risk-Measure 2: 0.360 (35.963 %)
(modRisk(eusilc, method = "weightedLLM", weights = w, formulaM = f, bound = 5))
#> The estimated model (using method 'weightedLLM') was:
#> 	~ db040 + hsize + rb090 + age + pb220a + age:rb090 + age:hsize + hsize:rb090
#> global risk-measures:
#> 	Risk-Measure 1: 0.324 (32.411 %)
#> 	Risk-Measure 2: 0.383 (38.300 %)
# }