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European Conference on Quality Roma, July 2008 The French New Master Sample 2009 : building fresh annual sampling frames for household surveys based on the new annual Census. Marc CHRISTINE, Sébastien FAIVRE Insee, Statistical Methods Unit

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European Conference on Quality

Roma, July 2008

The French New Master Sample 2009 : building fresh annual sampling frames for household surveys based on the new annual Census.

Marc CHRISTINE, Sébastien FAIVRE

Insee, Statistical Methods Unit

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

This presentation is based on a collective work with contributions of :

Vincent LOONIS, Edouard MAUGENDRE, Bruno BERLEMONT, Emmanuel GROS, Fabien GUGGEMOS (Insee).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

O C T O P U S S E

Organisation

Coordonnée

de Tirages

Optimisés

Pour une Utilisation

StatiStique

des Echantillons.

Coordinated Household Sampling System.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

CONTENTS :

I. Introduction : framework of the new Census. II. New orientations for future samples.III. Building PUs of Master Sample (IAA).IV. Consequences of the New Master Sample 2009 for

interviewers.V. Allocation and drawing of IAA.VI. Drawing of dwellings within IAA.VII. Drawing IAA : quality, calibration and weighting.VIII. Conclusion and future work.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

I. Introduction : framework of the new Census.

Since the 60’s, Insee organizes sample drawing systems based on the Census of population and dwellings and updated with « new » dwellings (identified from building permit records).

Since January 2004 : a new methodology of rotating Censuses, very different from the past :

Small municipalities (less than 10 000 inhabitants) : building 5 random samples of municipalities (« rotation groups »), with equal probabilities whole Census each year of all municipalities belonging to one of the rotation groups.

Big municipalities (over 10 000 inhabitants) : Building in each of them 5 samples of addresses (« rotation groups ») from a file updated each year (RIL, register of located blocks).

Drawing each year a sample of dwellings (clusters of addresses) ; the average sample rate is about 40 % of all dwellings belonging to the current rotation group.

Census of this sample of dwellings.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

The main new characteristics of Census :

• each year

• but only on a part of the territory.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Example : the case of Brittany – The municipalities according to the 5 rotation groups (rural

space)– White = urban space.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

II. New orientations for future samples.

The New Census has led to a new definition of the INSEE sampling system.

A new project has started in 2003 and will end in 2009 (first sample

drawn in the New French Master Sample 2009 in May 2009).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

II.1 Persistence in some methodological choices or in organization.

• Face to face interview are still used in most of the Face to face interview are still used in most of the surveys carried out by INSEE.surveys carried out by INSEE.

=> A Master Sample system is still useful • … with fixed IAA (Interviewer Action Area) (built in 2007)• … and a sample of which being drawn and validated in June 2008,

building the Master Sample IAA.

• The dwellings of main INSEE survey samples will be drawn in the Master Sample IAA.

=> This ensures a geographical concentration of the surveyed dwellings in order to reduce survey costs.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

II.2 Changes and innovation.

To take profit from the « freshness » brought by the new Census :

Using as a frame of a given year n + 1 all the dwellings covered by the Census at year n.

The yearly sampling frame covers only a part of the territory.

=> Advantages :

‐ To limit the wastes due to the changes in buildings (demolition, main homes becoming secondary homes and V.V….), which create unwished costs.

‐ To draw in a more efficient way samples on particular sub-populations (whose recent characteristics are known).

‐ To get rid of a specific system to cover new dwellings.

‐ To ensure that dwellings surveyed one given year will not be surveyed again before 5 years (except particular cases).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

III. Building PUs of Master Sample (IAA).

Issue : how to conciliate the principle of drawing « rotating » samples from the most recent Census and building fixed Primary Units (IAA = Interviewers Action Area).

III. 1 Constraints and objectives.

Build Primary Units within each region, in order to create a division of the territory :

– … composed with municipalities belonging to the 5 rotation groups …– … with a minimum number of dwellings (300) in each of them.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

III.2 The actual building.

A) Big municipalities.

– Each of them constitutes one single PU (the 5 rotation groups of addresses remain in it).

B) Small municipalities.

The aim is to build an optimal partition from the territory :

Under constraints of minimum size (number of dwellings in each group) and with respect to regional boundaries.

With IAA being as less extended as possible.

=> For that purpose, considering the great number of constraints and the complexity of the problem, a specific algorithm has been implemented.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Theoretical scheme.

1

1

5

5

43

2

11

5

4

2

3

Survey carried outduring year n, using

municipalitiesbelonging to group 1

Survey carried outduring year n+1, using

municipalitiesbelonging to group 2

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Algorithm to build PUs with small municipalities.

• In each region, it begins with the largest municipality (number of main dwellings) among the small ones : it is tried to build a PU around this municipality.

• Building of the PU around the largest municipality not yet allocated (that will be the « center » or « pivot » of the PU).

• A PU is achieved if, among municipalities of the same region (not yet allocated), whose distance to the pivot is less than a given threshold, it is possible to find enough municipalities in order to reach 300 main dwellings in each rotation group. If not, the PU is not constituted.

• At each step, the biggest municipality not yet allocated to one PU is tested as a possible pivot.

• At the end, all remaining communities are allocated to the closest PU.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Ste Gauburge PUMunicipalities surveyed 2009-2013

Echauffour

Sainte-Gauburge

Saint-Aquilin-de-Corbion

5.1 Km

8.1 Km

Municipalities surveyed in 2009 Municipalities surveyed in 2010

Sainte-Gauburge

Foy

5.5 Km

Municipalities surveyed in 2011

Saint-Martin-des-Pezerits

9.1 Km

Les Genettes

11.1 Km

Auguaise

Brethel

Sainte-Hilaire-sur-Risle

Sainte-Gauburge7.3 Km

7.2 Km

4.9 Km

Municipalities surveyed in 2012

Courtomer

Planches

Mahéru

Sainte-Gauburge

11.4 Km

4.6 Km

5.7 Km

Bonnefoi

Ferrières La VerrerieMoulins La Marche

Le ménil Bérard

7.9 Km

6.4 Km

4.7 Km

9 Km

Municipalities surveyed in 2013

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

STE GAUBURGE

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

III.3 Results of building PUs (ZAE).

• 2893 IAA small municipalities.

• 892 IAA big municipalities

• Paris, Lyon and Marseille divided in several « arrondissements ».

• TOTAL = 3785 ZAE.

• The algorithm for building IAA is deterministic but the initial assignment of municipalities to different rotation groups is random.

=> ZAE are « random objects ».

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Heterogeneous IAA considering the size : IAA Z17434

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Built Primary Units in Brittany.

European Conference on Quality

Roma, July 2008

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

IAA of la Tour du Pin near the French Alpes

vague 1 2 3 4 5

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

IAA of Plounérin in Northern Brittany

vague 1 2 3 4 5

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Situation of the IAA of Plounerin (blue) and Callac

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

IV. Consequences of the New Master Sample 2009 for interviewers.

Necessary to study the impact of the new PU on interviewers’ trajects.

Interviewers’ trajects in the New French Master Sample 2009 have to be compared with their trajects in the Master Sample 1999.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

IV.1 Methodology of the study

A try to estimate the extent of the new PU in relation with interviewers’ trajects.

Example of the IAA of Surgères (near the French Atlantic Coast).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

a. Definition of a PU’s extent.

Extent : average distance covered by the interviewer to reach a selected dwelling.

Hypothesis : the interviewer lives in the center of the PU (convention : only trajects between two different municipalities are

taken into account, trajects within the same municipality being set to 0).

Center of the PU :- Center (pivot) of the IAA for New Master Sample 2009 (NMS

2009)- Biggest municipality of the PU for the Master Sample 1999 (MS

1999).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Municipalities belonging to the IAA of Surgères.

Commune Rotation

Groupe

Number of dwellings

(census of 1999)

Surgères (Center) 1 2 569

St-Germain-de-Marencennes 2 387

St-Georges-des-Bois 3 575

St-Mard 4 342

Chambon 5 268

Vouhé 5 149

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

IAA Z17434

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

b. Extent of a PU in the Master Sample 1999.

In the Master Sample 1999 :

- All municipalites being covered by Census

- Equal sample of dwellings within the primary units whatever the year the survey is drawn.

=> Average traject of an interviewer is calculated as the average distance of a PU’s dwelling to the center municipality (weighted by the part of PU’s dwellings located in the municipality).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Extent of the IAA of Surgères in the Master Sample 1999.

Municipality Distance by road to Surgères

Part of the PU’s dwellings

Surgères 0 km 60%

St-Germain 4,1 km 9%

St-Georges 4,6 km 13%

St-Mard 5,2 km 8%

Chambon 9,9 km 6%

Vouhe 6,2 km 3%

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

c. Extent of a IAA in the New Master Sample 2009.

Each year, the interviewer has to go to the municipalities belonging to the last rotation group covered by Census.

Hypothesis : same number of interviews carried out each year.

Within municipalities belonging to the same rotation group, selection of dwellings with equal probability sampling.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Number of interviews carried out in the IAA of Surgères over a five years cycle.

Groupe Municipality Number of dwellings

Proportion of interviews

1 Surgères 2 569 20%

2 St-Germain 387 20%

3 St-Georges- 575 20%

4 St-Mard 342 20%

5

Chambon 268

20%Vouhé 149

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Conclusion: comparison of the number of interviews carried out in the IAA of Surgères in the two Master Samples.

Municipalities GR Proportion of interviews in the MS 1999

Proportion of interviews in

the NMS 2009

Distance to the center

Surgères 1 60% 20% 0 km

St-Germain 2 9% 20% 4,1 km

St-Georges 3 13% 20% 4,6 km

St-Mard 4 8% 20% 5,2 km

Chambon 5 6% 13% 9,9 km

Vouhé 5 3% 7% 6,2 km

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Extent of the IAA in the New Master Sample 2009.

IAA of Surgères:

extent of 4,5 km for the new Master Sample 2009 2,3 km for the Master Sample 1999.

Importance of the center municipality : 60% of interviews carried in Surgères in the MS 1999 (distance zero) and only 20% in the NMS 2009.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

IV.2 Generalisation of this study to the Primary Units built for both systems.

Field of comparison :

- 2 893 IAA of NMS 2009 composed with small municipalities

(11,4 millions of dwellings)

- 3 202 PUs of MS 1999 composed with municipalities in rural areas or small urban areas

(12,3 millions of dwellings).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Global results of the comparison of extent of PUs between MS 1999 and NMS 2009.

Threshold 10 km 15 km 20 km 30 km Total

IAA

NMS 2009

1 633 2 533 2 814 2 884 2 893

56% 88% 97% 99,6% 100%

PU

MS 1999

2 268 2 914 3 116 3 180 3 202

71% 91% 97% 99,3% 100%

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Global results of the comparison of the extent of the IAA of NMS 2009 and the PUs

of MS 1999. On the field of comparison, the extent of the IAA NMS 2009 is 2

km higher than the spread of the PUs MS 1999.

An increasing extent is mainly seen on Primary Units with a very low extent.

Two main reasons :

– No IAA made of one municipality (as it happened for MS 1999)

– Fewer interviews carried out in the municipality center.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

V. Allocation and drawing IAA.

V. 1 Computation of allocation.

Basic hypotheses :

– IAA are drawn proportionnally to their sizes (number of main dwellings)

– Some of them are systematically kept (« take-all strata »).

Chosen parameters :

• For a common sample size with sampling rate TAU = 1/ 2000 (a little less than 12.000 main dwellings)….

• Average allocation : e = 20 sampled units for each IAA (except take–all stratum) : 1 IAA = 1 interviewer.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Results :

Threshold of take-all stratum : 40.000 main dwellings.

37 big municipalities assigned to several interviewers. 488 drawn IAA, among which :

286 IAA-small municipalities 202 IAA-big municipalities.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

V. 2. Drawing IAAs.

• Stratified according to the regions (particular case : « Ile de France » – Paris region - splitted in two « crowns »).

• Balanced on regional totals :

It is necessary to balance not only on the level of whole IAA but also for each rotation group… … in order to benefit each year from a « representative » sampling frame.

It increases the number of balancing constraints and reduces the number of allowed independant variables.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Moreover…

• The yearly sampling frame is balanced on the total of

municipalities belonging to the considered rotation group….

• … but not on the total of whole France (in practice, rotation groups are not equivalent).

It may be a source of bias for estimation (use of yearly « incomplete » sampling frame).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Used balancing variables.

• Number of main dwellings of municipalities belonging to the IAA, for each of the five rotation groups.

• Total income (from tax sources) of municipalities belonging to the IAA, for each of the five rotation groups.

• Total number of dwellings in the whole IAA in peri-urban areas, rural areas and urban areas.

• Additional balancing variables in « Ile de France » (Paris region) : age, type of household, individual house / collective block, council flat, owner / tenant, number of immigrated peoples…).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Provence IAA – 1st sample

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Provence IAA – 2nd sample

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

VI. Drawing of dwellings within IAA.

Within each drawn IAA, secondary units (dwellings) are drawn with simple random sample, in the given yearly rotation group.

Particular difficulty in big municipalities :

– 1st phase of Census : addresses have not been completely randomly assigned to rotation groups

=> It is difficult to compute the actual likelihood.

– 2nd phase RP : new and big addresses are over sampled in the selection of addresses to be covered by Census (take-all strata within each rotation group).

=> Necessity of resampling dwellings in the sampling frame to have a frame of dwellings with equal weights.

 

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

General scheme of different phases of sampling of dwellings :

Small Municipalities Big Municipalities

Sampling 5 rotation groups of municipalities (each small municipality being randomly assigned to a rotation group)

Sampling 5 rotation groups of addresses in each municipality.

First phase of sampling for Census Sampling each year addresses

creating clusters of dwellings within one rotation group (average rate = 8% of dwellings of the municipality)

Great and new addresses builld a take-all stratum

Geographical stratification (region)

Building PUs aggregating municipalities, conditionnally to the result of the first phase.

Building Primary Units (IAA) Each big municipality builds a

single PU.

Thresholds used to define the take-all strata (biggest cities)

1er degree : drawing PUs in each stratum (fixed for 5 or 10 years). Calibration of drawn PUs on different known totals.

Yearly sample frame = intersection of drawn PUs and dwellings belonging to the random Rotation Group of the year

Resampling of dwellings belonging to great addresses, in order to ensure equal probabilities for any dwelling belonging to the sample frame

Second phase : sampling of dwellings.

2nd degree : drawing dwellings in each PU (for each survey)

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

VII. Drawing IAA : quality, calibration and weighting.

One looks at the quality of the sample of IAA, comparing :

– the estimate (from the sample of IAA) of totals of different

auxiliary variables (the values of which are supposed known on whole IAA)

– with the true total in France (known through Census 1999 or other comprehensive data, such as tax sources).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

It shows relative gaps : – more or less important – variable from one rotation group to the other, – whatever the type of estimator,– especially for breakdown according to :

‐ the type of space (rural / urban)‐ activity sector for employed people

(variables not taken into account as balancing conditions at the time of drawing IAA).

=> It may creates problems, particularly for yearly surveys, measuring evolutions.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Relative error of yearly sampling frames on the variable « number of main dwellings in rural space ».

Groupe de rotation Erreur relative

(estimateur en expansion)

GR 1 +3,4%

GR 2 -3,3%

GR 3 -7,9%

GR 4 -8,1%

GR 5 -9,4%

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

One solution to face this problem : calibration of IAA.

)()(:5...,,1 , ZTZTtsk

tkk

Theoretical background for calibration.

Ensure each year a calibration in order to obtain a yearly « representative » sampling frame.

)(,ZTtk = total of the calibration variable Z on municipalities belonging to rotation group t in IAA k. )(ZT = true total of variable Z in whole population.

k = new weight of IAA k after calibration process

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

The initial weights are given by the choice of estimators :

• « expanded » :

• ratio :

Calibration is implemented at the national level and for each rotation group separately

=> several sets of calibrated weights.

sk k

tkte

TT

,

, 5ˆ

sk k

tk

tk

ktc

T

N

NT

,

,,

ˆ

kIAAintgrouprotationinerestofiableaoftotalT

kIAAofselectionofyprobabilit

kIAAintgrouprotationindwellingsofnumberN

kIAAindwellingsofnumberN

tk

k

tk

k

intvar,

,

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Used calibration variables :

- the same as used as balancing variables

- number of employed people, according to the sector of activity

- number of dwellings according to the size of urban units (built-up areas).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Results of calibration in terms of relative errors.

• Relative error equals zero for all calibration variables…

• … and does not increase for other variables of interest.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Example : impact of calibration on the variable « number of registered people at the National Employment Agency (ANPE) » at the end of the month.

VariableRotation

group

Estimate ("expanded estimator")

without calibration

Relative error

without calibration

Relative error with calibration

DEFM 1 2 105 629,5 0,2 -0,530/09/207 2 2 085 597,4 -0,7 -0,2

3 2 101 086,9 0,0 0,84 2 074 397,7 -1,2 -0,65 2 111 643,7 0,5 0,0

True value 2 100 415,0

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Consequences of calibration process.

New weights of IAA (computed each year for the different rotation groups) are used to settle the number of dwellings to be drawn in each IAA.

Theoretically, calibration allows to increase allocations of dwellings in under-represented areas and V.V..

Actually, there are minimum / maximum numbers of secondary units to draw in each IAA (constraints of working conditions for the interviewers).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Different impacts to be analysed :

On the number of dwellings to be drawn in each IAA and the structure of final samples.

On the distribution of weights.

On the statistical quality of estimators.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Conclusion about calibrating IAA

An innovating methodology of calibrating at the level of Primary Units.

Empirical validation of the method on the basis of drawn IAA sample.

It allows to solve the problem of choosing among two types of estimators (« expanded » or « ratio »).

It will allow to incorporate fresh information by using calibrating variables derived from the new Census, available after 2009 (until now, use of 1999 Census for building, drawing and calibrating IAA).

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

VIII. Conclusion and future work.

Using yearly Census allows substantial profit concerning the quality of the sampling frame (in particular : selection of sub-populations whose recent characteristics are well known).

But important complication of sampling process.

Some issues to be solved :

– Impact of the choice of estimators on allocations and estimations.– Implementation of a calibration procedure for big municipalities.– Possible change in status of municipalities (small becoming big and

v.v.) after 2011.– Computation of variance…

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Thank you for your attention !

[email protected]

[email protected]

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

ANNEXES sur le calage

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Impact du calage sur les poids des ZAE

› Les travaux menés sur la base de l’EM provisoire montrent que le calage des ZAE n’accroît pas la dispersion des poids pour l’estimateur en expansion.

› Les résultats sont très similaires dans les cinq bases de sondage annuelles.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Fonction de répartition des poids des logements pour un tirage dans le groupe 1

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Impact du calage sur la pondération des logements (exemple du groupe 1)

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

ANNEXES

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Répartition des ZAE par type d’espace(urbain, périurbain et rural)

ZAEGC ZAEPC Total

urbain 808 43 851 periurbain 29 356 385 ZAE sur un type d'espace ZAUER

rural 13 445 458 urbain/periurbain 0 609 609 periurbain/rural 0 1119 1119 ZAE sur deux types d'espace ZAUER

urbain/rural 0 18 18 ZAE sur les trois types d'espace 0 303 303 Total 850 2893 3743

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Région Nombre de

ZAE construites

Nombre de ZAE

exhaustives

Nombre de ZAE non

exhaustives à tirer

Ile-de-France 363 2 84 Champagne-Ardenne 115 1 12 Picardie 183 1 17 Haute-Normandie 141 2 14 Centre 194 2 22 Basse-Normandie 148 1 13 Bourgogne 144 1 15 Nord Pas-De-Calais 235 1 35 Lorraine 181 2 21 Alsace 123 2 13 Franche-Comté 114 1 10 Pays de la Loire 198 3 25 Bretagne 188 2 26 Poitou-Charentes 138 1 16 Aquitaine 221 1 27 Midi-Pyrénées 213 1 22 Limousin 57 1 6 Rhône-Alpes 363 4 47 Auvergne 115 1 12 Languedoc-Roussillon 140 3 18 Provence Alpes Côte d'Azur 150 4 30

Corse 19 0 3

Total France 3743 37 488

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

OCTOPUSSE 2007 :

–Variables d’équilibrage (nombre de logements principaux, revenu fiscal…).

– Emploi au lieu de résidence par grand secteur.

– Structure par âge.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Biais relatif observé sur les tirages 1 et 2 (agrégation nationale).

Variable Biais relatif T1 Biais relatif T2

resprinc GR1 0,9% 0,7% resprinc GR2 0,5% 0,0% resprinc GR3 -0,6% -0,3% resprinc GR4 -0,6% -0,6% resprinc GR5 -0,1% 0,3% resprinc total 0,0% 0,0%

revenufiscal04 GR1 0,7% 0,3% revenufiscal04 GR2 1,0% 0,3% revenufiscal04 GR3 -0,8% -1,0% revenufiscal04 GR4 -0,9% -1,2% revenufiscal04 GR5 -0,6% -0,3% revenufisc04 total -0,1% -0,4%

emploi GR1 2,3% 0,7% emploi GR2 -0,7% 2,1% emploi GR3 -0,3% 1,4% emploi GR4 0,4% 0,2% emploi GR5 -0,3% 0,8% emploi total 0,3% 1,0%

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

emploi agricole GR1 3,9% -3,7% emploi agricole GR2 6,5% -2,0% emploi agricole GR3 -1,0% -11,7% emploi agricole GR4 2,1% -2,1% emploi agricole GR5 2,9% 2,8% emploi agricole total 2,9% -3,3% emploi industrie GR1 5,1% -1,5% emploi industrie GR2 -1,9% 4,6% emploi industrie GR3 0,5% -0,4% emploi industrie GR4 -0,4% -2,6% emploi industrie GR5 0,0% 4,5% emploi industrie total 0,7% 0,9% emploi construction GR1 2,2% -0,6% emploi construction GR2 1,2% -1,2% emploi construction GR3 0,8% -0,1% emploi construction GR4 2,3% -1,8% emploi construction GR5 -0,5% 2,1% emploi construction total 1,2% -0,3% emploi services GR1 1,5% 1,6% emploi services GR2 -1,0% 1,9% emploi services GR3 -0,5% 2,8% emploi services GR4 0,4% 1,2% emploi services GR5 -0,5% -0,3% emploi services total 0,0% 1,4%

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

nb0à19ans GR1 1,3% 0,2% nb0à19ans GR2 0,9% 0,1% nb0à19ans GR3 -1,6% -1,1% nb0à19ans GR4 -1,0% -1,6% nb0à19ans GR5 -0,6% 0,3% nb0à19ans total -0,2% -0,4% nb20à59ans GR1 1,6% 0,3% nb20à59ans GR2 1,1% -0,1% nb20à59ans GR3 -0,8% -0,7% nb20à59ans GR4 -0,4% -1,1% nb20à59ans GR5 -0,1% 0,4% nb20à59ans total 0,3% -0,3% nb60ansetplus GR1 -0,1% 1,1% nb60ansetplus GR2 -0,1% -0,4% nb60ansetplus GR3 -0,7% 0,0% nb60ansetplus GR4 -1,0% 0,1% nb60ansetplus GR5 0,1% -0,1%

nb60ansetplus total -0,3% 0,1%

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Impact du tirage des groupes de rotation sur la constitution des ZAE

› Exemple: cas des communes de Paray-le-Monial et Vitry en Charollais

› Paray-le-Monial:plus grande petite commune de la région Bourgogne (4111 résidences principales)

› => testée en premier en tant que commune pivot dans l’algorithme

› ZAE constituée avec 9209 résidences principales

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

ZAE de Paray-le-Monial (Z71342)

vague 1 2 3 4 5

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

ZAE de Paray-le-Monial et commune de Vitry-en-Charollais

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Impact du tirage des groupes de rotation sur les ZAE

› Vitry-en-Charollais (349 résidences principales): petite commune la plus proche de Paray-le-Monial

› Appartient comme Paray-le-Monial au groupe 2, donc ne fait pas partie de la même ZAE

› Aurait fait partie de la ZAE de Paray-le-Monial si elle avait été dans un autre groupe de rotation (donc d’une ZAE contenant au moins 5360 résidences principales)

› Appartient à une ZAE de taille plus réduite (1770 résidences principales), donc ayant une probabilité de tirage plus faible

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Jugement sur la qualité des tirages.

• Certaines variables souhaitées mais non retenues pour l’équilibrage : classes d’âge, emploi au lieu de résidence par grand secteur d’activité, dispersion géographique (respect du centre de gravité et de l’inertie de la population régionale)…

• MAIS :– On a vérifié ex-post que les tirages de ZAE étaient

admissibles au vu de certaines de ces variables (calcul de biais relatifs).

– variibles not kept as balancing ones can be reintroduced at the time of final calibration.

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Formalisation mathématique :

CiN = nombre de logements principaux de la commune Ci.

Ggi, = 1 la commune iC est affectée au groupe de rotation g,

Une ZAE potentielle construite autour d’une commune-pivot pC est l’ensemble des communes iC

solution du problème : jC

Min P

j

C

j

CC 1

,

sous les contraintes :

C

i

Cigi NGg

1, 300:5...,,1

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European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008

Nombre de ZAE à tirer : k = e

NNexh)(.

Taille de la strate exhaustive : Nexh = SNiii

N/

Taille de l’échantillon : ekNNn exh

Probabilité de tirage d’une ZAE : i = k e

N

NN

N iexhi

Seuil d’exhaustivité : S = e.