Data integration: an overview on statistical methodologies and applications.

1. Data integration: an overview on statistical methodologies and applications. Mauro Scanu Istat Central Unit on User Needs, Integration and Territorial Statistics scanu@istat.it Poznan 20 October 2010

2. Summary • In what sense methods for integration are “statistical”? • Record linkage: definition, examples, methods, objectives and open problems • Statistical matching: definition, examples, methods, objectives and open problems • Micro integration processing: definition, examples, methods, objectives and open problems • Other statistical integration methods? World Statistics Day

3. Methods for integration 1 Generally speaking, integration of two data sets is understood as a single unit integration: the objective is the detection of those records in the different data sets that belong to the same statistical unit. This action allows the reconstruction of a unique record of data that contains all the unit information collected in the different data sources on that unit. On the contrary: let’s distinguish two different objectives - micro and macro Micro: the objective is the “development” of a complete data set Macro: the objective is the “development” of an aggregate (for example, a contingency table) World Statistics Day

4. Methods for integration 2 Further, the methods of integration can be split in automatic and statistical methods The automatic methods take into account a priori rules for the linkage of the data records The statistical methods include a formal estimation or test procedure that should be applied on the available data: this estimation or test procedure • can be chosen according to optimality criteria, • and are associated with an estimate error. This talk restricts the attention on the (micro and macro) statistical methods of integration World Statistics Day

5. Statistical methods Classical inference • There exists a data generating model 2) The observed sample is an image of the data generating model 3) We estimate the model from the observed sample World Statistics Day

6. Statistical methods of integration If a method of integration is used, it is necessary to include an intermediate phase. The final data set is a blurred image of the data generating model World Statistics Day

7. Statistical methods of integration Statistical methods for integration can be organized according to the available input World Statistics Day

8. Record linkage Input: two data sets on overlapping sets of units. Problem: lack of a unique and correct record identifier Alternative: sets of variables that (jointly) are able to identify units Attention: variables can have “problems”! Objective: the largest number of correct links, the lowest number of wrong links World Statistics Day

9. Book of life Dunn (1946)* describes record linkage in this way: …each person in the world creates a book of life. The book starts with the birth and ends with the death. Its pages are made up of all the principal events of life. Record linkage is the name given to the process of assembling the pages of this book into one volume. The person retains the same identity throughout the book. Except for advancing age, he is the same person… *Dunn (1946) "Record Linkage". American Journal of Public Health 36 (12): 1412–1416. World Statistics Day

10. When there is the lack of a unique identifier If a record identifier is missing or cannot be used, it is necessary to use the common variables in the two files. The problem is that these variables can be “unstable”: • Time changes (age, address, educational level) • Errors in data entry and coding • Correct answers but different codification (e.g. address) • Missing items World Statistics Day

11. Main motivations for record linkage According to Fellegi (1997)*, the development of tools for integration is due to the intersection of these facts: • occasion: construction of big data bases • tool: computer • need: new informative needs *Fellegi (1997) “Record Linkage and Public Policy: A Dynamic Evolution”. In Alvey, Jamerson (eds) Record Linkage Techniques, Proceedings of an international workshop and exposition, Arlington (USA) 20-21 March 1997. World Statistics Day

12. Why record linkage? Some examples • To have joint information on two or more variables observed in distinct data sources • To “enumerate” a population • To substitute (parts of) surveys with archives • To create a “list” of a population • Other official statistics objectives (imputation and editing / to enhance micro data quality; to study the risk of identification of the released micro data) World Statistics Day

13. Example 1 – analysis of mortality Problem: to analyze jointly the “risk factors” with the event “death”. • The risk factors are observed on ad hoc surveys (e.g. those on nutrition habits, work conditions, etc.) • The event “death” (after some months the survey is conducted) can be taken from administrative archives These two sources (survey on the risk factors and death archive) should be “fused” so that each unit observed in the risk factor survey can be associated with a new dichotomous variable (equal to 1 if the person is dead and zero otherwise). World Statistics Day

14. Example 2 – to enumerate a population Problem: what is the number of residents in Italy? Often the number of residents is found in two steps, by means of a procedure known as “capture-recapture”. This method is usually applied to determine the size of animal populations. • Population census • Post enumeration survey (some months after the census) to evaluate Census quality and give an accurate estimate of the population size USA - in 1990 Post Enumeration Survey, in 2000 Accuracy and Coverage Evaluation Italy - in 2001 “Indagine di Copertura del Censimento” World Statistics Day

15. Example 2 – to enumerate a population The result of the comparison between Census and post enumeration survey is a 22 table: World Statistics Day

16. Example 2 - to enumerate a population For short, for any distinct unit it is necessary to understand if it was observed 1) both in the census and in the PES 2) only in the census 3) only in the PES These three values allow to estimate (with an appropriate model) the fourth value. World Statistics Day

17. Example 3 – surveys and archives Problem: is it possible to use jointly administrative archives and sample surveys? At the micro level this means: to modify the questionnaire of a survey dropping those questions that are already available on some administrative archives (reduction of the response burden) E.g., for enterprises: Social security archives, chambers of commerce, … World Statistics Day

18. Example 4 – Creation of a list Problem: what is the set of the active enterprises in Italy? In Istat, ASIA (Archivio Statistico delle Imprese Attive) is the most important example of a creation of a list of units (the active enterprises in a time instant) “fusing” different archives. It is necessary to pay attention to: • Enterprises which are present in more than one archives (deduplication) • Non active enterprises • New born enterprises • transformations (that can lead to a new enterprise or to a continuation of the previous one) World Statistics Day

19. Example 5 – Imputation and editing Problem: to enhance microdata quality Micro Integration in the Netherlands (virtual census, social statistical data base) It will be seen later, when dealing with micro integration processing World Statistics Day

20. Example 6 - Privacy Problem: does it exist a “measure” of the degree of identification of the released microdata? In order to evaluate if a method for the protection of data disclosure is good, it is possible to compare two datasets (the true and the protected ones) and detect how many modified records are “easily” linked to the true ones. World Statistics Day

21. Record linkage steps The record linkage techniques are a multidisciplinary set of methods and practices • DECISION MODEL CHOICE • Fellegi & Sunter • exact • Knowledge – based • Mixed • … • SEARCH SPACE REDUCTION • Sorted Neighbourhood Method • Blocking • Hierarchical Grouping • … ...... RECORD LINKAGE ...... ...... • PRE-PROCESSING • Conversion of upper/lower cases • Replacement of null strings • Standardization • Parsing • … • COMPARISON FUNCTION CHOICE • Edit distance • Smith-Waterman • Q-grams • Jaro string comparator • Soundex code • TF-IDF • … World Statistics Day Tiziana Tuoto, FCSM 2007, Arlington, November 6 2007

22. Example (Fortini, 2008)* Census is sometimes associated with a post enumeration surveys, in order to detect the actual census coverage. To this purpose, a “capture-recapture” approach is generally considered. It is necessary to find out how many individuals have been observed: • in both the census and the PES • Only in the census • Only in the PES These figures allow to estimate how many individuals have NOT been observed in both the census and the PES * In ESSnet Statistical Methodology Project on Integration of Survey and Administrative Data “Report of WP2. Recommendations on the use of methodologies for the integration of surveys and administrative data”, 2008 World Statistics Day

23. CENSUS PES Matched households Unmatched people Unmatched people Unmatched people Unmatched households Unmatched people Unmatched households Matched households Matched people Matched people Matched people Matched people Matched people Unmatched people Record linkage workflow for Census - PES Step 1 Step 2 Step 3.a Step 3.b Step 4.b Step 4.a Step 5 World Statistics Day

24. Problem: Lack of identifiers Difference between step 1 and step 2 is that: Step 1 identifies all those households that coincide for all these variables: • Name, surname and date of birth of the household head • Address • Number of male and female components Step 2 uses the same keys, but admits the possibility of differences of the variable states for modifications of errors World Statistics Day

25. Probabilistic record linkage For every pairs of records from the two data sets, it is necessary to estimate • The probability that the differences between what observed on the two records is due to chance, because the two records belong to the same unit • The probability that the two records belong to different units These probabilities are compared: this comparison is the basis for the decision whether a pair of records is a match or not Estimate of this probability is the “statistical step” in the probabilistic record linkage method World Statistics Day

26. Statistical step Data set A with na units. Data set B with nb units. K key variables (they jointly make an identifier) World Statistics Day

27. Statistical procedure The key variables of the two records in a pair (a,b) is compared: yab=f(xAa,xBb) The function f(.) should register how much the key variables observed in the two units are different. For instance, y can be a vector with k components, composed of 0s (inequalities) or 1s (equalities) The final result is a data set of na x nb comparisons World Statistics Day

28. Statistical procedure The na x nb pairs are split in two sets: M: the pairs that are a match U: the unmatched pairs Likely, the comparisons y will follow this situation: • Low levels of diversity for the pairs that are match, (a,b)M • High levels of diversity for the pairs that are non-match, (a,b)U For instance: if y=(sum of the equalities for the k key variables), y tends to assume large values for the pairs in M with respect to those in U World Statistics Day

29. Statistical procedure If y=(sum of the equalities), the distribution of y is a mixture of the distribution of y in M (right) and that in u (left) World Statistics Day

30. Statistical procedure Inclusion of a pair (a,b) in M or U is a missing value (latent variable). Let C denote the status of a pair (C=1 if (a,b) in M; C=0 if (a,b) in U) Likelihood is the product on the na x nb pairs of P(Y=y, C=c) = [p m(y)]c [(1-p) u(y)](1-c) Estimation method: maximum likelihood on a partially observed data set (EM algorithm – Expectation Maximization) World Statistics Day

31. Statistical procedure A pair is assigned to M or U in the following way 1) For every comparison y assign a “weight”: t(y)=m(y)/u(y) where m and u are estimated; 2) Assign the pairs with a large weight to M and the pairs with a small weight to U. 3) There can be a class of weights t where it is better to avoid definitive decisions (m and u are similar) World Statistics Day

32. Statistical procedure The procedure is the following. Note that, generally, probabilities of mismatching are still not considered World Statistics Day

33. Open problems Different probabilistic record linkage aspects should still be better investigated. Two of them are related to record linkage quality • What model should be considered • a1) on the pairs relationship (Copas and Hilton, 1990) • a2) on the key variables relationship (Thibaudeau, 1993) b) How probabilities of mismatching can be used for a statistical analysis of a linked data file? (Scheuren and Winkler, 1993, 1997) Copas J.R., Hilton F.J. (1990). “Record linkage: statistical models for matching computer records”. Journal of the Royal Statistical Society, Series A, 153, 287-320. Thibaudeau Y. (1993). “The discrimination power of dependency structures in record linkage”. Survey Methodology, 19, 31-38. Scheuren F., Winkler W.E. (1993). “Regression analysis of data files that are computer matched”. Survey Methodology, 19, 39-58 Scheuren F., Winkler W.E. (1997). “Regression analysis of data files that are computer matched - part II”. Survey Methodology, 23, 157-165. World Statistics Day

34. Statistical matching What kind of integration should be considered if the analysis involves two variables observed in two independent sample surveys? • Let A and B be two samples of size nA and nB respectively, drawn from the same population. • Some variables X are observed in both samples • Variables Y are observed only in A • Variables Z are observed only in B. Statistical matching aims at determining information on (X;Y;Z), or at least on the pairs of variables which are not observed jointly (Y;Z) World Statistics Day

35. Statistical matching It is very improbable that the two samples observe the same units, hence record linkage is useless. World Statistics Day

36. Some statistical matching applications 1 The objective of the integration of the Time Use Survey (TUS) and of the Labour Force Survey (LFS) is to create at a micro level, a synthetic file of both surveys that allows the study of the relationships between variables measured in each specific survey. By using together the data relative to the specific variables of both surveys, one would be able to analyse the characteristics of employment and the time balances at the same time. Information on labour force units and the organisation of her/his life times will help enhance the analyses of the labour market The analyses of the working condition characteristics that result from the labour force survey will integrate the TUS more general analysis of the quality of life World Statistics Day

37. Some statistical matching applications 1 The possibilities for a reciprocal enrichment have been largely recognised (see the 17th International Conference of Labour Statistics in 2003 and the 2003 and 2004 works of the Paris group). The emphasis was indeed put on how the integration of the two surveys could contribute to analysing the different participation modalities in the labour market determined by hour and contract flexibility. Among the issues raised by researchers on time use, we list the following two: the usefulness and limitations involved in using and combining various sources, such as labour force and time-use surveys, for improving data quality Time-use surveys are useful, especially for measuring hours worked of workers in the informal economy, in home-based work, and by the hidden or undeclared workforce, as well as to measure absence from work World Statistics Day

38. Some statistical matching applications 1 Specific variables in the TUS (Y ): it enables to estimate the time dedicated to daily work and to study its level of "fragmentation" (number of intervals/interruptions), flexibility (exact start and end of working hours) and intra-relations with the other life times Specific variables in the LFS (Z): The vastness of the information gathered allow us to examine the peculiar aspects of the Italian participation in the labour market: professional condition, economic activity sector, type of working hours, job duration, profession carried out, etc. Moreover, it is also possible to investigate dimensions relative to the quality of the job World Statistics Day

39. Some statistical matching applications 2 The Social Policy Simulation Database and Model (SPSD/M) is a micro computer-based product designed to assist those interested in analyzing the financial interactions of governments and individuals in Canada (see http://www.statcan.ca/english/spsd/spsdm.htm). It can help one to assess the cost implications or income redistributive effects of changes in the personal taxation and cash transfer system. The SPSD is a non-confidential, statistically representative database of individuals in their family context, with enough information on each individual to compute taxes paid to and cash transfers received from government. World Statistics Day

40. Some statistical matching applications 2 The SPSM is a static accounting model which processes each individual and family on the SPSD, calculates taxes and transfers using legislated or proposed programs and algorithms, and reports on the results. It gives the user a high degree of control over the inputs and outputs to the model and can allow the user to modify existing tax/transfer programs or test proposals for entirely new programs. The model can be run using a visual interface and it comes with full documentation. World Statistics Day

41. Some statistical matching applications 2 In order to apply the algorithms for microsimulation of tax–transfer benefits policies, it is necessary to have a data set representative of the Canadian population. This data set should contain information on structural (age, sex,...), economic (income, house ownership, car ownership, ...), health–related (permanent illnesses, child care,...) social (elder assistance, cultural–educational benefits,...) variables (among the others). • It does not exist a unique data set that contains all the variables that can influence the fiscal policy of a state • In Canada 4 samples are integrated (Survey of consumers finances, Tax return data, Unemployment insurance claim histories, Family expenditure survey) • Common variables: some socio-demographic variables • Interest is on the relation between the distinct variables in the different samples World Statistics Day

42. Example (Coli et al, 2006*) The new European System of the Accounts (ESA95) is a detailed source of information on all the economic agents, as households and enterprises. The social accounting matrix (SAM) has a relevant role. Module on households: it includes the amount of expenditures and income, per typology of household Coli A., Tartamella F., Sacco G., Faiella I., D’Orazio M., Di Zio M., Scanu M., Siciliani I., Colombini S., Masi A. (2006). “La costruzione di un Archivio di microdati sulle famiglie italiane ottenuto integrando l’indagine ISTAT sui consumi delle famiglie italiane e l’Indagine Banca d’Italia sui bilanci delle famiglie italiane”, Documenti ISTAT, n.12/2006. World Statistics Day

43. Example Problem: • Income are observed on a Bank of Italy survey • Expenditures are observed on an Istat survey • The two samples are composed of different households, hence record linkage is useless World Statistics Day

44. Adopted solutions 1 The first statistical matching solution was imputation of missing data. Usually, “distance hot deck” was used. In pratice, this method “mimics” record linkage: instead of matching records of the same unit, this approach “matches” records of similar units, where similarity is in terms of the common variables in the two files. The procedure is 1) Compute the distances between the matching variables for every pair of records 2) Every record in A is associated to that record in B with minimum distance World Statistics Day

45. Adopted solutions 1 The inferential path is the following World Statistics Day

46. Adopted solutions 2 It is applied an estimate procedure under specific models that considers the presence of missing items. The easiest model is: conditional independence of the never jointly observed variables (e.g., income and expenditures) given the matching variables. Example: Y = income, Z = expenditures, X = house surface (X,Y,Z) is distributed as a multivariate normal with parameters: Mean vector =  Variance matrix =  World Statistics Day

47. Adopted solutions 2 • Estimate the regression equation on A: Y=+X • Impute Y in B: Yb=+Xb , b=1,…,nB • Estimate the regression equation in B: Z=+X • Impute Z in A: Za= +Xa , a=1,…,nA World Statistics Day

48. Adopted solutions 2 The inferential mechanism assumes that Y and Z are independent given X (there is not the regression coefficient of Z on Y given X) World Statistics Day

49. Adopted solutions 2 This method can be applied also with this inferential scheme: the problem is what hypotheses are before the analysis phase World Statistics Day

50. Adopted solutions 3 We do not hypothesize any model. It is estimated a set of values, one for every plausible model given the observed data Example When matching two sample surveys on farms (Rica-Rea - FADN and SPA - FSS), it was asked the following contingency table for farms Y = presence of cattle (FSS) Z = class of intermediate consumption (from FADN) Using the common variables X1 = Utilized Agricultural Area (UAA) , X2 = Livestock Size Unit (LSU) X3 = geographical characteristics World Statistics Day