1、Introduction to Emerging Methods for Imputation in Official Statistics,Ventspils 08/2006 Pasi Piela,25.08.2006,2,Pasi Piela,Overview,1. Imputation in the quality framework of official statistics2. Classes of imputation methods3. Requirements for imputation in official statistics4. Past research work
2、5. Statistical clustering6. Best imputation methods7. Processing imputation (and editing)8. New research plans9. Multiple imputation10. Fractional imputation11. Multilevel model based imputation,25.08.2006,3,Pasi Piela,Overview,1. Imputation in the quality framework of official statistics2. Classes
3、of imputation methods3. Requirements for imputation in official statistics4. Past research work5. Statistical clustering6. Best imputation methods7. Processing imputation (and editing)8. New research plans9. Multiple imputation10. Fractional imputation11. Multilevel model based imputation,25.08.2006
4、,4,Pasi Piela,Imputation is defined as the process of statistical replacement of missing valuesEditing and imputation are undertaken as part of a quality improvement strategy to improve accuracy, consistency and completeness.,25.08.2006,5,Pasi Piela,Classes of imputation methods,A1. Deterministic im
5、putation, or A2. Stochastic imputationB1. Logical imputation, B2. Real donor imputation, or B3. Model donor imputationC1. Single imputation, or C2. Multiple imputationD1. Hot-deck D2. Cold-deck,25.08.2006,6,Pasi Piela,Five requirements for imputation in official statistics (Chambers, 2001),Predictiv
6、e Accuracy: The imputation procedure should maximise the preservation of true values. Distributional Accuracy: The preservation of the distribution of the true values is also important. Estimation Accuracy: The imputation procedure should reproduce the lower order moments of the distributions of the
7、 true values. Imputation Plausibility: The imputation procedure should lead to imputed values that are plausible. Ranking Accuracy: The imputation procedure should maximise the preservation of order in the imputed values.,25.08.2006,7,Pasi Piela,Past research work,traditional methods: cell-mean impu
8、tation, regression imputation, random donor, nearest neighbour, etc. advanced imputation techniques based on statistical clustering (e.g. K-means) homogenous imputation classes hierarchical clustering (e.g. classification and regression trees) ”modern” statistical pattern recognition methods,25.08.2
9、006,8,Pasi Piela,Statistical clustering for imputation,imputation classes, cells, clusters, groups,average point locating the cluster,Computational methods?,.or searching appropriate imputation cells by using categorical sorting variables?,25.08.2006,9,Pasi Piela,K-means Clustering,The basic varianc
10、e minimization clustering algorithm. The ”Voronoi region” (as part of the tesselation) for cluster i is given bywhere | refers to the Euclidean norm (distance). At the iteration time t + 1 the weight wi is updated bywhere #Vi refers to the number of units xk in Vi.,25.08.2006,10,Pasi Piela,Classific
11、ation and Regression Trees,WAID - Weighted Automatic Interaction Detection software EU FP4 Project AUTIMP,Node,Y,X15,X1= 5,X27,X2=7,Binary splits,Target variable: categorical or continuous,Predictor variable,The original data,Original data splitted into two separate parts,Only one variable in turn d
12、efines the split.,Neural networks for clustering: Self-Organizing Maps, SOM,The basic SOM defines a mapping from the input data space Rn onto a latent space consisted typically of a two-dimensional array of nodes or neurons.,25.08.2006,12,Pasi Piela,Best methods,Nearest neighbour (hot-deck) by Eucli
13、dean distance metrics The best method is actually a system that includes several competitive imputation methods The development and evaluation of new imputation methods is closely connected to the software development.,25.08.2006,13,Pasi Piela,Processing imputation (and editing),The Banff system of
14、Statistics Canada is a good example about computerized editing and imputation process. It is a collection of specialized SAS procedures “each of which can be used independently or put together in order to satisfy the edit and imputation requirements of a survey“ as stated in the Banff manual (Statis
15、tics Canada, 2006). successor to more well-known GEIScurrently Statistics Finland is evaluating Banff,25.08.2006,14,Pasi Piela,25.08.2006,15,Pasi Piela,Verifying edits, generating implied edits and extremal points,25.08.2006,16,Pasi Piela,(Pre-)view of failure rates, fine-tuning the edits,25.08.2006
16、,17,Pasi Piela,Three basic outlier detection methods,25.08.2006,18,Pasi Piela,Identifying which fields require imputation and how to satisfy edits.,25.08.2006,19,Pasi Piela,Here : logical imputation (one possible value allowing to pass the edits).,25.08.2006,20,Pasi Piela,Nearest neighbour via const
17、ructing a k-dimensional tree.,25.08.2006,21,Pasi Piela,Using user-defined or some of the 20 hard-coded algorithms.,25.08.2006,22,Pasi Piela,Adjusting and rounding the data so that they add to a specific totals.,25.08.2006,23,Pasi Piela,Mass imputation procedure (not handled in this presentation),25.
18、08.2006,24,Pasi Piela,25.08.2006,25,Pasi Piela,Plans for future research - intro,Multiple imputation, MI, was not handled here because of the context of the research. But also detailed research in imputation variance and careful analysis of the datasets with hierarchical, multilevel nature (note the
19、 difference to the previously mentioned hierarchical clustering methods) containing cross-classifications and missingness were also excluded. This will lead us to the forthcoming research that will be next outlined.,25.08.2006,26,Pasi Piela,Multiple imputation,Donald Rubin, 1987 Bayesian framework v
20、ery famous and popular family of the imputation methods rarely used in official statistics several imputed datasets are combined to reach an estimate for the imputation variance assumptions are strict and there also exist some difficulties with MI variance estimation as discussed by Rao (2005) and K
21、im et al. (2004),25.08.2006,27,Pasi Piela,Fractional imputation,a sort of mixed real donor and model donor “hot-deck” imputation method for a population divided into imputation cells involves using more than one donor for a recipient simply: three imputed values might be assigned to each missing val
22、ue, with each entry allocated a weight of 1/3 of the nonrespondents original weight Kim and Fuller (2004): superior to MI designed to reduce the imputation variance while MI gives only a simple way to estimate it,25.08.2006,28,Pasi Piela,Fractional imputation,a sort of mixed real donor and model don
23、or “hot-deck” imputation method for a population divided into imputation cells involves using more than one donor for a recipient simply: three imputed values might be assigned to each missing value, with each entry allocated a weight of 1/3 of the nonrespondents original weight Kim and Fuller (2004
24、): superior to MI designed to reduce the imputation variance while MI gives only a simple way to estimate it,Assume the within-cell uniform response model in which the responses in a cell g are equivalent to a Bernoulli sample sample selected from the elements ng.,25.08.2006,29,Pasi Piela,Fractional
25、 imputation 2,Formulating the fractionally imputed estimator:,AR,AM,A,sample respondents,sample non-respondents,imputation fraction,population quantity of interest,25.08.2006,30,Pasi Piela,Fractional imputation 3,Kim and Fuller (2004) showed also how fractional imputation combined with the proposed
26、replication variance estimator gives a set of replication weights that can be used to construct unbiased variance estimators for estimators based on imputed data (and for estimators based on the completely responding variables). fully efficient fractional imputation, FEFI produces zero imputation va
27、riance,25.08.2006,31,Pasi Piela,Fractional imputation 3,Kim and Fuller (2004) showed also how fractional imputation combined with the proposed replication variance estimator gives a set of replication weights that can be used to construct unbiased variance estimators for estimators based on imputed
28、data (and for estimators based on the completely responding variables). fully efficient fractional imputation, FEFI produces zero imputation variance,Approximations to FEFI by fixed number of donors. - e.g. systematic sampling with probability proportional to the weights to select donors for each re
29、cipient. After the donors are assigned, the initial fractions are adjusted so that the sum of the weights gives the fully efficient fractionally imputed estimator.,25.08.2006,32,Pasi Piela,Multilevel modeling for imputation,Many kinds of data have a hierarchical or clustered nature. We refer to a hi
30、erarchy as consisting of units grouped at different levels. Thus children may be the level 1 units in a 2-level structure where the level 2 units are the families and students may be the level 1 units clustered within schools that are the level 2 units. More recently there has been a growing awarene
31、ss that many data structures are not purely hierarchical but contain cross-classifications of higher level units and multiple membership patterns.,25.08.2006,33,Pasi Piela,Multilevel modeling for imputation 2,Multilevel models (Goldstein, 2003) take advantage of the correlation structure between dif
32、ferent levels of hierarchy. Correlation structures and connections between the study variables can be a challenge in imputation tasks as well. Currently in literature, there are some papers about the use of multiple imputation with multilevel models. Carpenter and Goldstein (2004): if a dataset is m
33、ultilevel then the imputation model should be multilevel too. MLwiN,25.08.2006,34,Pasi Piela,Plans for future research,new imputation methods and the analysis of imputed and missing data when data structures are complex use of multilevel imputation models in which clusters in the cluster sampling de
34、sign can be incorporated in an imputation model as random effects information on the complex sampling design can be incorporated, for example, by using strata indicators as fixed covariates modified fractional and single imputation will be considered,25.08.2006,35,Pasi Piela,Plans for future researc
35、h 2,Another new avenue of research is the use of multilevel models and imputation in the context of small area estimation (Rao, 2003).,25.08.2006,36,Pasi Piela,Paldies,pasi.pielastat.fi,25.08.2006,37,Pasi Piela,References 1/2 Aitkin, M., Anderson, D., and Hinde, J. (1981): Statistical Modelling of D
36、ata on Teaching Styles (with discussion). Journal of the Royal Statistical Society, A 144, 148-1461. Breiman, L., Friedman, J.H., Olsen, R.A., and Stone, C.J. (1984): Classification and Regression Trees. Wadsworth, Belmont, CA. Carpenter, J.R., and Goldstein, H. (2004): Multiple Imputation Using MLw
37、iN, Multilevel Modelling Newsletter, 16, 2. * Charlton, J. (2003): Editing and Imputation Issues. Towards Effective Statistical Editing and Imputation Strategies - Findings of the Euredit project. * Chambers, R. (2001): Evaluation Criteria for Statistical Editing and Imputation. National Statistics
38、Methodological Series, United Kingdom, 28, 1-41. * Eurostat (2002): Quality in the European Statistical System - the Way Forward. European Comission. Goldstein, H. (2003). Multilevel Statistical Models (Third Edition). Edward Arnold, London. Hill, P.W., and Goldstein, H. (1998): Multilevel Modelling
39、 of Educational Data with Cross Classification and Missing Indentification of Units, Journal of Educational and Behavioural Statistics, 23, 117-128. Kalton, G., and Kish, L. (1984): Some Efficient Random Imputation Methods. Communications in Statistics, A13, 1919-1939. Kim, J.K., and Fuller, W.A. (2
40、004): Fractional hot deck imputation, Biometrika, 91, 559-578. Fuller, W.A., and Kim, J.K. (2005): Hot Deck Imputation for the Response Model, Survey Methodology, 31, 2, 139-149. Kim, J.K., Brick, J.M., Fuller, W.A. and Kalton, G. (2004): On the Bias of the Multiple Imputation Variance Estimator in
41、Survey Sampling. Technical Report. Kohonen, T. (1997): Self-Organizing Maps. Springer Verlag, New York. Koikkalainen, P., Horppu, I., and Piela P. (2003): Evaluation of SOM based Editing and Imputation. Towards Effective Statistical Editing and Imputation Strategies - Findings of the Euredit project
42、. * Lehtonen, R., Srndal, C.-E., and Veijanen, A. (2003): The Effect of Model Choice in Estimation for Domains, Including Small Domains, Survey Methodology, 29, 33-44. Lehtonen, R., Srndal, C.-E., and Veijanen, A. (2005): Does the Model Matter? Comparing Model-assisted and Model-dependent Estimators
43、 of Class Frequencies for Domains, Statistics in Transition, 7, 649-673.,25.08.2006,38,Pasi Piela,References 2/2 Piela, P., and Laaksonen, S. (2001): Automatic Interaction Detection for Imputation Tests with the WAID Software Package. In: Proceedings of Federal Committee on Statistical Methodology R
44、esearch Conference, Statistical Policy Working paper, 34, 2, 49-59, Washington, DC. Piela, P. (2002): Introduction to Self-Organizing Maps Modelling for Imputation - Techniques and Technology. Research in Official Statistics, 2, 5-19. Piela, P. (2004): Neuroverkot ja virallinen tilastotoimi, Suomen
45、Tilastoseuran Vuosikirja 2004. Helsinki. Piela, P. (2005): On Emerging Methods for Imputation in Official Statistics. Licentiate Thesis. University of Jyvskyl. Rasbash, J., Steele, F., Browne, W., and Prosser, B. (2004): A Users Guide to MLwiN (version 2.0). London. * Rao, J.N.K. (2003): Small Area
46、Estimation. Wiley, New York. Rao, J.N.K. (2005): Interplay Between Sample Survey Theory and Practice: An Appraisal, Survey Methodology, Statistics Canada, 31, 2, 117-138. Ritter, H., Martinez, T., and Schulten, K. (1992): Neural Computation and Self-Organizing Maps: An Introduction. Addison-Wesley,
47、Reading, MA. Schafer, J.L., and Graham, J.W. (2002): Missing Data: Our View of the State of the Art, Psychological Methods 7, 2, 147-177. Statistics Canada (2003): Statistics Canada Quality Guidelines. Catalogue no. 12-539-XIE. Statistics Canada (2006): Functional Description of the Banff System for Edit and Imputation. Statistics Canada. Rubin, D. (1987): Multiple Imputation in Surveys. John Wiley & Sons, New York.*) The Euredit project: http:/www.cs.york.ac.uk/euredit/ *) Centre for Multilevel Modelling: http:/
