Weighting sample surveys with Bascula Harm Jan Boonstra Statistics Netherlands Outline • General overview – Calibration/weighting – Estimation and variance estimation • Demonstration with example data from the Dutch Labour Force Survey (LFS) • Other applications at Statistics Netherlands Bascula • Part of Blaise (current version 4.7), a general system for computer-assisted survey processing developed at Statistics Netherlands • History: predecessor LINWEIGHT developed by Jelke Bethlehem in the 1980’s Main features • Calibration: computation of weights using auxiliary information encoded in a weighting model • Estimation of (sub)population totals, means, proportions and ratios • Variance estimation: Taylor linearisation and balanced repeated replication (BRR) for several sampling designs Weighting • Reduction of MSE – Reduction of (non-resonse) bias – Reduction of sampling variance • Calibration to auxiliary totals for consistency with known population totals • A single set of weights – Easy tabulation – Mutual consistency between estimated tables ‘Small sample’ problems • Full consistency with register data or data from related surveys can usually not be achieved (overfitting). Not all information can be used at the same time. • Weighting can be ineffective for (small) domain estimates For sufficiently large samples weighting is an effective and convenient way to improve estimates! Weighting/calibration methods in Bascula Based on the general regression (GREG) estimator: • Poststratification, e.g. Region x AgeClass • Ratio estimator, e.g. AgeClass x Income • Linear weighting, e.g. Region + AgeClass x Income Based on Iterative Proportional Fitting (IPF): • Multiplicative weighting, e.g. Region + AgeClass Further weighting options • Bounding of weights for linear weighting, Huang and Fuller algorithm • Consistent linear weighting, e.g. for equal weights within households, Lemaître and Dufour Estimation of totals • Based on the calibration weights: Ycal wi yi ˆ is • General regression estimator: wi d i g i Yregr YHT B t ( X X HT ) wi yi ˆ ˆ ˆ ˆ is 1 g i 1 ( x / i ) d j x j x j / j ( X X HT ) t i t ˆ js • Also ratios of totals, means, proportions, subclasses Variance estimation • Direct/Taylor method (HT and GREG only) • Balanced Repeated Replication (BRR) Sampling designs supported: • Stratified two-stage element or cluster design with simple random sampling without replacement in both stages • Stratified multistage cluster designs with replacement in the first stage and unequal propabilities Taylor variance • Taylor linearisation: ˆ ˆ ˆ ˆ Yregr YHT Bt ( X X HT ) ˆ yi B t xi ei ˆ ) var v(Yregr var is i is i • Modified variance estimator (default in Bascula): gi ei v(Yregr ) var wi ei var ˆ is is i BRR variance ˆ vBRR Yregr 1 R ˆ ( ) 2 (Yregr, Yregr ) 2 R 1 ˆ • R balanced half samples (partially balanced if R < #strata) • Fay factor • Grouped BRR (more than 2 PSUs per stratum allowed) – Artificial strata – Repeated grouping Input • Sample data file: Ascii (fixed column or separated), Blaise, other OleDB compatible • Blaise meta information; Blaise Textfile Wizard helps in making data model for Ascii files • Tables of population totals • Selection of weighting scheme and other parameters that influence the weighting • Some additional input required for estimation and variance estimation: target tables and sampling design details Data integrity checks • Consistency of set of population tables • Sample counts per cell do not exceed population counts • Enough sample observations for each cell in weighting model • Inclusion weights/sampling fractions compatible with sampling design specified Output • Set of final and correction weights (written to the sample file and to a separate weights file) • Optionally: fitted values y ˆ ˆi Bt xi • Tables of estimates (including estimates of standard errors) in export file; format compatible with population data file Example: Dutch Labour Force Survey • Rotating panel design with five waves; CAPI in first wave, CATI in subsequent waves • CATI data first calibrated on the most important target variable (employment in several categories) to initial CAPI panel to reduce panel attrition bias • Weighted CATI data is combined with CAPI data and together calibrated to population totals of weighting scheme Region44 x Age4 x Sex2 + Age21 x Sex2 + Age5 x MarStat2 + Sex2 x Age5 x Ethnicity8 + CWI3 Dacseis software evaluation report on Bascula: ‘Bascula is a part of Blaise (an integrated system for survey processing), and it might not be reasonable to purchase Blaise only for the use of Bascula. When having Blaise available, Bascula provides an advanced weighting tool (linear or multiplicative weighting) with abilities for proper variance estimation based on Taylor’s linearisation. When the basic order of the weight and estimate calculations of Bascula is understood, the operations can be carried out quite easily.’ Usage • menu-based interactive version • from Blaise’s script language Manipula • from most modern programming languages, e.g. VB, VBA, Delphi, C++, C# • from other software able to act as automation client, e.g. S-Plus Automation Bascula component (dll) can be used to automate weighting/estimation processes For recurring weighting/estimation processes, batch processing, integration into production systems Build custom tools utilizing Bascula’s functionality Tools that use Bascula component • Tool that integrates imputation/outlier detection and handling/weighting for the Production Statistics • Tool for analysing results of experiments • Tool for repeated weighting • Simple simulation tools – Variance estimation (Dacseis) – GREG as input for small area estimators Repeated weighting • Practical sequential approach to make tables of estimates consistent between data sources • Two step procedure 1. Start with GREG estimates 2. Adjust these estimates such that they are consistent with register totals (not used in the weighting scheme of GREG) and possibly with previously estimated marginal tables from a combination of surveys. Estimation 15 Software tool Rectangular Meta Micro datasets database database VRD Dataset, weighting model, population totals StatBase Bascula Estimates Export Source: Systemdocumentation VRD, V.Snijders Use of Bascula at Statistics Netherlands • Labour Force Survey • Repeated weighting for the Social Statistical Database • Survey on Household Incomes • Budget Survey • Survey on Living Conditions • Production Statistics and more Survey on Household Incomes • Calibration on both person totals and household totals, both obtained from municipal registrations • Consistent linear weighting: Region29 x Age8 x Sex2 + Region29 x HouseholdType9 x OneHH OneHH is auxiliary variable that sums to one over each household Production Statistics • Continuous auxiliary variables available from Tax Office; categorical variables from Business Register • Weighting scheme: Activity x SizeClass x Source x Tax + Activity x SizeClass x Source • Variable Source indicates whether tax info can be matched to surveyed businesses Finally, • Priorities for further development have not been very high in the last three years, but that may change • Possible extensions: variance structure, Newton-Raphson for exponential method, two-phase regression estimator, synthetic estimation for subpopulations, small area estimation?
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