Application of log-linear models in producing small area estimates of unemployment in Poland

Transcription

1 Application of log-linear models in producing small area estimates of unemployment in Poland Tomasz Klimanek 1, Tomasz Józefowski 1, Marcin Szymkowiak 1,2, Li-Chun Zhang 3,4 1 Statistical Office in Poznan 2 Poznan University of Economics and Business 3 University of Southampton 4 Statistics Norway

2 Outline 1 Information and motivation Challenges in LFS 2 3 of the study 4 Summary Literature

3 Information and motivation Challenges in LFS 1 Information (demand and supply) Different needs User expectations (quality) Role of the methods Data sources 2 Motivation Experiences of the Centre for Small Area Estimation (Statistical Office in Poznan) 1 Calibration 2 Estimation of counts, estimation of disability, unemployment Dynamic development of spree methodology (one number policy)

4 Challenges in LFS Information and motivation Challenges in LFS Respondent burden Nonresponse Calibration Monthly unemployment rate Sample increase/reallocation User expectations

5 Challenges in LFS Information and motivation Challenges in LFS

6 Challenges in LFS Information and motivation Challenges in LFS

7 SPREE in literature Information and motivation Challenges in LFS Deming & Stephan (1940) Purcell and Kish (1980) Noble (2002), Qiao (2006), Isidro (2010) Zhang & Chambers (2004) Berg & Fuller (2014) SPREE modifications (Luna et al. 2014): 1 relaxing the structural equation of SPREE to consider other types of relationship between the two association structures 2 by including cell-specific random effects

8 Information and motivation Challenges in LFS SPREE Structure-preserving estimates Structure-preserving estimates SPREE (Purcell and Kish 1980), update the cells in a contingency table formed from previous census or register data (proxy variables) so that they sum to the updated margins, which may or not be found from new sample survey data. It uses the iterative proportional fitting (IPF) algorithm to fit the new margins. This method will preserve all the higher order interactions that are not affected by IPF.

9 Noble et al (2002) use a simple method based on this idea: log (µ) = X β = [X 1X 2] [β 1 β 2 ] T = X 1β 1 + X 2β 2, (1) where: Y and µ = E (Y ) denote the column vectors of observed and expected small area unemployment counts for the n cells in the contingency table, X is the (nxp) design matrix, β is the (px1) vector of parameters, β 1 denotes the parameters that are estimated by the survey data (e.g. main effects terms), X 1 is the part of the design matrix corresponding to β 1, β 2 denotes those parameters that are estimated by the census data (e.g. high-order interaction terms), X 2 is the part of the design matrix corresponding to β 2.

10 Study of the study Data Census 2011 (as of ) Registered unemployment (31.03 each year) LFS (1 st quater) Domain: regions(16) x sex(2) x age groups(5) Variable: Number of unemployed (ILO definition) Association structure: Census 2011, Registered unemployment (proxy) Allocation structure: marginal totals for domains Methods: IPF (SAS call ipf routine), SPREE - loglinear model (SAS proc genmod Quiao 2006)

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14 Summary Summary Literature Encouraging results There are no obvious differences between including Census association structure or Register association structure using this simple diagnostic. Analysis of the model behaviour for Quality assesment of the estimates (bootstrap approach) Learning application of advanced modern approach to SPREE (cooperation with Li-Chun Zhang) Testing for approaches modifying association structure based on time series, seasonal adjustments, spatial autocorrelation Aplication of SPREE approach to other phenomenon (disability analysis)

15 Literature Summary Literature Berg E.J., Fuller W.A. (2014), Small Area Prediction of Proportions with Applications to the Canadian Labour Force Survey, Journal of Survey Statistics and Methodology, 2 (3), Deming W.E., Stephan F.K. (1940), On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are Known, Ann. Math. Statist. Volume 11, Number 4, Eurostat (2016), Labour force survey in the EU, candidate and EFTA countries, Statistical Working Papers. Isidro C.M. (2010), Intercensal Updating of Small Area Estimates, Unpublished PhD thesis. Massey University. Luna A., Zhang L.C., Whitworth A., Piller K. (2014), Small Area Estimates of the Population Distribution by Ethnic Goup in England: A Proposal Using Structure Preserving Estimators, Statistics in Transition new series and Survey Methodology Joint Issue: Small Area Estimation 2014, Vol. 16, No. 4, pp Nobel A., Haslett S., Arnold G. (2002), Small Area Estimation via Generalized Linear Models, Journal of Offcial Statistics, Vol. 18, No. 1. Purcell N.J., Kish L. (1980), Postcensal Estimates for Local Areas (or Domains), International Statistical Review, 48, Qiao Ch. (2006), Small area estimates produced using loglinear models in SAS discussion and implementation, Prepared for the Centre for Social Research and Evaluation, Working Paper. Zhang L.C., Chambers R. (2004), Small area estimates for crossclassifications, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66(2),

16 Summary Literature Thank you very much for your attention!