NTTS 2009 Brussels, 18-20 February 2009 The French New Master Sample 2009 : building fresh annual sampling frames for household surveys based on the new.

NTTS 2009

Brussels, 18-20 February 2009

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

Bruno BERLEMONT,Marc CHRISTINE, Sébastien FAIVRE

INSEE

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New Techniques and Technologies for Statistics - Brussels, 18 – 20 February 2009

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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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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CONTENTS :

I. Introduction : framework of the new Census. II. New orientations for future samples.III. Building PUs of Master Sample (IAA).IV. Allocation and drawing of IAA.V. Drawing of dwellings within IAA.VI. Drawing IAA : quality, calibration and weighting.VII. Conclusion and future work.

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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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The main new characteristics of Census :

• each year

• but only on a part of the territory.

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

space)– White = urban space.

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II. New orientations for future samples.

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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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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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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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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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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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 (if the distance to the « center municipality » does not exceed the fixed threshold).

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Simulations carried out in order to find out the « optimal » IAA partition

› Automatic process of building of IAA developped

› Several values of the threshold tested

› Criteria: number of unaffected municipalities + extent of the IAA

› Chosen threshold value: 20 km (363 remaining municipalities)

› All 363 remaining municipalities are affected to an IAA

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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


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


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STE GAUBURGE

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III.3 Results of building PUs (IAA).

• 2893 IAA small municipalities.

• 892 IAA big municipalities

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

• TOTAL = 3785 IAA.

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

=> IAA are « random objects ».

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Built Primary Units in Brittany.

NTTS 2009

Brussels, 18-20 February 2009

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Heterogeneous IAA considering the size : IAA Z17434

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IV. Allocation and drawing IAA.

IV. 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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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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IV. 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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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.

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Provence IAA – 1st sample

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Provence IAA – 2nd sample

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V. 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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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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VI. 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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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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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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The initial weights are given by the « expanded » estimator :

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

=> several sets of calibrated weights.

sk k

tkte

TT

,

, 5ˆ

kIAAintgrouprotationinerestofiableaoftotalT

kIAAofselectionofyprobabilit

tk

k

intvar,

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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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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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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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Consequences and conclusion about calibrating process of IAA.

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..

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).

An innovating methodology of calibrating at the level of Primary Units, with empirical validation on the basis of drawn IAA sample.

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VII. 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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Thank you for your attention !

[email protected]

[email protected]

NTTS 2009 Brussels, 18-20 February 2009 The French New Master Sample 2009 : building fresh annual sampling frames for household surveys based on the new.

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