1. 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

2. Page 2 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).

3. Page 3 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.

4. Page 4 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.

5. Page 5 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.

6. Page 6 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.

7. Page 7 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.

8. Page 8 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).

9. Page 9 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 surveys carried out by INSEE.Face to face interview are still used in most of the 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.

10. Page 10 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).

11. Page 11 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.

12. Page 12 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.

13. Page 13 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Theoretical scheme.

14. Page 14 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.

15. Page 15 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Ste Gauburge PU Municipalities 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-Gauburge 7.3 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 Verrerie Moulins La Marche Le ménil Bérard 7.9 Km 6.4 Km 4.7 Km 9 Km Municipalities surveyed in 2013

16. Page 16 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 STE GAUBURGE

17. Page 17 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 ».

18. Page 18 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Heterogeneous IAA considering the size : IAA Z17434

19. Page 19 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Built Primary Units in Brittany.

20. European Conference on Quality Roma, July 2008

21. Page 21 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 IAA of la Tour du Pin near the French Alpes

22. Page 22 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 IAA of Plounérin in Northern Brittany

23. Page 23 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Situation of the IAA of Plounerin (blue) and Callac

24. Page 24 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.

25. Page 25 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).

26. Page 26 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).

27. Page 27 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Municipalities belonging to the IAA of Surgères. CommuneRotation Groupe Number of dwellings (census of 1999) Surgères (Center)12 569 St-Germain-de-Marencennes2387 St-Georges-des-Bois3575 St-Mard4342 Chambon5268 Vouhé5149

28. Page 28 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 IAA Z17434

29. Page 29 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).

30. Page 30 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Extent of the IAA of Surgères in the Master Sample 1999. MunicipalityDistance by road to Surgères Part of the PU’s dwellings Surgères0 km60% St-Germain4,1 km9% St-Georges4,6 km13% St-Mard5,2 km8% Chambon9,9 km6% Vouhe6,2 km3%

31. Page 31 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.

32. Page 32 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. GroupeMunicipalityNumber of dwellings Proportion of interviews 1Surgères2 56920% 2St-Germain38720% 3St-Georges-57520% 4St-Mard34220% 5 Chambon268 20% Vouhé149

33. Page 33 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. MunicipalitiesGRProportion of interviews in the MS 1999 Proportion of interviews in the NMS 2009 Distance to the center Surgères160%20%0 km St-Germain29%20%4,1 km St-Georges313%20%4,6 km St-Mard48%20%5,2 km Chambon56%13%9,9 km Vouhé53%7%6,2 km

34. Page 34 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.

35. Page 35 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).

36. Page 36 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. Threshold10 km15 km20 km30 kmTotal IAA NMS 2009 1 6332 5332 8142 8842 893 56%88%97%99,6%100% PU MS 1999 2 2682 9143 1163 1803 202 71%91%97%99,3%100%

37. Page 37 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.

38. Page 38 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.

39. Page 39 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.

40. Page 40 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.

41. Page 41 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).

42. Page 42 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…).

43. Page 43 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Provence IAA – 1st sample

44. Page 44 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Provence IAA – 2nd sample

45. Page 45 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.

46. Page 46 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 General scheme of different phases of sampling of dwellings :

47. Page 47 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).

48. Page 48 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.

49. Page 49 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 rotationErreur relative (estimateur en expansion) GR 1+3,4% GR 2-3,3% GR 3-7,9% GR 4-8,1% GR 5-9,4%

50. Page 50 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 One solution to face this problem : calibration of IAA. Theoretical background for calibration.  Ensure each year a calibration in order to obtain a yearly « representative » sampling frame.

51. Page 51 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.

52. Page 52 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).

53. Page 53 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.

54. Page 54 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.

55. Page 55 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).

56. Page 56 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.

57. Page 57 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).

58. Page 58 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…

59. Page 59 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Thank you for your attention ! marc.christine@insee.fr sebastien.faivre@insee.fr

60. Page 60 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 ANNEXES sur le calage

61. Page 61 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.

62. Page 62 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

63. Page 63 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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68. Page 68 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 ANNEXES

69. Page 69 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Répartition des ZAE par type d’espace (urbain, périurbain et rural)

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71. Page 71 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.

72. Page 72 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Biais relatif observé sur les tirages 1 et 2 (agrégation nationale).

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75. Page 75 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

76. Page 76 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 ZAE de Paray-le-Monial (Z71342)

77. Page 77 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 ZAE de Paray-le-Monial et commune de Vitry-en-Charollais

78. Page 78 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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81. Page 81 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.

82. Page 82 European Conference on Quality in Official Statistics - Roma, 8 – 11 July 2008 Formalisation mathématique :

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