Anco Hundepool Sarah Giessing ProdCom Rounding Anco Hundepool Sarah Giessing

Overview Current situation Cell suppression or rounding ProdCom solution Prototype Further work

Current situation (MS) Member states collect and process the data. MS applies its own conf. rules. (Dom. rule, freq rule, p% rule) MS publishes its own data first. Process done individually by each MS. Then MS sends the data to Eurostat

Current situation (Eurostat) Eurostat receives MS data plus conf. info. Problem: Eurostat cannot publish many EU-aggregates because some countries are blocked. Eurostat should respect/safeguard the national confidential cells. Result: many EU-aggregates are blocked.

ProdCom conf. chapter If one country is conf.: EU-aggregate is conf, If 2 countries are conf. and both are singleton: EU-aggregate is blocked. If 2 countries are conf. and one is a zero-cell then EU-aggregate is blocked If 2 or more countries are conf. and there is dominance then EU-aggregate is blocked If all countries are safe, then EU-aggregate is OK

ProdCom conf. chapter Result: Many ProdCom aggregates are blocked.  The usefulness of this publication is ‘limited’  Is there a way out?

ProdCom rounding project Cell suppression = replacing the conf. cell value by an interval. Minimum size of the interval is determined by the sensitivity rule. (distance to a safe cell). Dom. rule and p% rule give a clear formula. Freq. rule not but we choose a percentage.

ProdCom rounding project Conclusion: Eurostat should respect these protection intervals. Eurostat can publish approximations or intervals of the EU-aggregates. EU-intervals should respect the MS-intervals. So build those intervals.

t-ARGUS Standard solution: Cell suppression. Finding a safe pattern and minimising information loss is a hard problem. Efficient solutions offered by t-ARGUS. Lead to too many suppression on the EU-level (because suppression of additional member state level cells not allowed)

Rounding Rounded value = interval. 37 rounded to 40 base 10 = [35,44] If interval is large enough the rounded value (= interval) can be published.

Simple rounding does not work Intervals often smaller as rounding base because of table relations Sometimes the rounding can be undone Does not always provide upper protection even with large rounding base upper bound may still be sensitive – dominance problem!!!

Simple rounding does not work Intervals often smaller as rounding base Example: Cell value 5800, contributions 5200, 300, 300 sensitive at (1,85)-dominance rule Protection of 400 would be enough (5200 not dominant f.i. in 6200). Still, simple rounding with base 1000 may not provide sufficient protection: Assume table relation Becomes after rounding 6400 | 5800 600 6000 | 6000 1000 So upper bound for 5800 is 6000. But 5200 is still dominant in 6000 !!! < 6500 ≥ 500 < 6000

Simple rounding does not work Sometimes rounding can be undone Example 28 | 7 7 7 7 30 | 5 5 5 5

Simple rounding does not work Does not always provide upper protection Example: Cell value 5400, contributions 4800, 300, 300 sensitive at (1,85)-dominance rule Protection of 300 would be enough (4800 not dominant f.i. in 5700). Still, simple rounding with base 1000 does not provide sufficient protection: Cell value Becomes after rounding 5400 5000 Upper bound 5500 too close: 4800 is still dominant in 5500 !!! < 5500

Countrolled Rounding Controlled rounding preserves additivity and avoids underprotection problems. In higher dimensions very difficult. Bounds are twice as large. In t-ARGUS a rounder solution similar to cell-suppression. Based on optimisation techniques. Originally designed for freq. tables but can also be used to protect magnitude data.

Rounding Use t-ARGUS rounder to compute EU-aggregates Which rounding base? At least larger than largest protection interval. If not enough iterate till enough

Rounding base Two series: Simple (powers of 10) 10,20,…,80, 90,100,200,…,800, 900, 1000, 2000, …, 8000, 9000, 10000 Version 2 less information loss, more difficult to explain. Both have been implemented. Your choice.

Results (rounding base) Rounding base (% EU total) Frequency Proc 1 Proc 2 0-<1 23 70 1-<5 190 277 5-<10 82 109 10-<20 92 58 20-<50 107 15 50+ 39 4

Results (Iterations) Number of iterations Frequency Proc 1 Proc 2 1 448 162 2 84 195 3 111 4 48 5+ 17

Rounding Parameters to be chosen: Prot. interval freq. unsafe (%) Prot. interval secondaries (%) Prot. interval zero-cells (interval) In above examples Freq: 10%, Sec:10%, Zero 100.

Prototype Indicate the data file Indicate the rules file A few parameters And then all will be done automatically

Program

Prototype Output: File with EU-aggregates Orig. values if safe Rounded values + rounding base if unsafe Comma-separated; easily loaded in Excel Report/log file

Future A bit more testing Extend the aggregates

Conclusions Solution based on rounding has been created. Looks satisfactorily for the ProdCom problem Most EU-aggregates rounded moderately only; a few might still be considered suppressed. Much more useful ProdCom publication.