Marc CHRISTINE, Sébastien FAIVRE Insee, Statistical Methods Unit

1. 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. This presentation is based on a collective work with contributions of : Vincent LOONIS, Edouard MAUGENDRE, Bruno BERLEMONT, Emmanuel GROS, Fabien GUGGEMOS (Insee).

3. 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. CONTENTS : • Introduction : framework of the new Census. • New orientations for future samples. • Building PUs of Master Sample (IAA). • Consequences of the New Master Sample 2009 for interviewers. • Allocation and drawing of IAA. • Drawing of dwellings within IAA. • Drawing IAA : quality, calibration and weighting. • Conclusion and future work.

5. 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 than10 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. The main new characteristics of Census : • each year • but only on a part of the territory.

7. Example : the case of Brittany • The municipalities according to the 5 rotation groups (rural space) • White = urban space.

8. 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. 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. => 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. 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. 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. 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. Theoretical scheme.

14. 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. Municipalities surveyed in 2009 Municipalities surveyed in 2010 Municipalities surveyed in 2011 Sainte-Gauburge Sainte-Hilaire-sur-Risle 4.9 Km 5.1 Km Echauffour Brethel 7.2 Km Sainte-Gauburge 7.3 Km 5.5 Km Sainte-Gauburge Auguaise Foy 11.1 Km 8.1 Km 9.1 Km Les Genettes Saint-Aquilin-de-Corbion Saint-Martin-des-Pezerits Municipalities surveyed in 2012 Municipalities surveyed in 2013 Le ménil Bérard 5.7 Km Sainte-Gauburge 4.7 Km Planches 7.9 Km 9 Km Mahéru 6.4 Km Bonnefoi 4.6 Km 11.4 Km Ferrières La Verrerie Moulins La Marche Courtomer Ste Gauburge PU Municipalities surveyed 2009-2013

16. STE GAUBURGE

17. 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. Heterogeneous IAA considering the size : IAA Z17434

19. Built Primary Units in Brittany.

21. vague 1 2 3 4 5 IAA of la Tour du Pin near the French Alpes

22. vague 1 2 3 4 5 IAA of Plounérin in Northern Brittany

23. Situation of the IAA of Plounerin (blue) and Callac

24. 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. 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. 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. Municipalities belonging to the IAA of Surgères.

28. IAA Z17434

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

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

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

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

37. 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. 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. Results : • Threshold of take-all stratum : 40.000 main dwellings. • 37big municipalitiesassigned to several interviewers. • 488 drawn IAA, among which : • 286 IAA-small municipalities • 202 IAA-big municipalities.

40. 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. 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. 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. Provence IAA – 1st sample

44. Provence IAA – 2nd sample

45. 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. General scheme of different phases of sampling of dwellings :

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

50. 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.