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CBS case study

CBS case study. Crime survey Neuchatel, 7-8 July 2011. Introduction. Crime and victimization survey Planned domains: police districts Sample size approx 750 / district 2005-2008: NSM 2008 onwards: ISM. From NSM to ISM. Local oversampling Data collection: sequential mixed-mode

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CBS case study

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  1. CBS case study Crime survey Neuchatel, 7-8 July 2011

  2. Introduction • Crime and victimization survey • Planned domains: police districts • Sample size approx 750 / district • 2005-2008: NSM • 2008 onwards: ISM SAE of crime statistics

  3. From NSM to ISM • Local oversampling • Data collection: sequential mixed-mode • Different questionnaire Discontinuities expected SAE of crime statistics

  4. Quantifying discontinuities • Survey transition from NSM to ISM • Small scale NSM in parallel to new ISM(full scale: approx 18,000; small: 1/3rd) • Discontinuities at national level • Now: police district level discontinuities required • But: NSM sample too small => SAE SAE of crime statistics

  5. Example of discontinuity Bicycle thefts NSM and ISM NSM ISM 2009 Total: 541,000 (NSM) ; 897,000 (ISM) SAE of crime statistics

  6. Coeff of variation, bicycle theft, 2009 NSM: 0.41 ; ISM: 0.24 SAE of crime statistics

  7. SAE to increase precision of NSM • Fay-Herriot model: linear mixed, area level • EBLUP and HB estimators • Bayesian estimation of model variance also in EBLUP (avoiding zero-estimates of model variance) SAE of crime statistics

  8. Bayesian estimation of model variance SAE of crime statistics

  9. Covariates from registers • Police:Reported offences: property crimes, violence, assaults, threats, illicit drugs, weapons, vandalism, traffic offences • Administration:age, ethnicity, urbanisation, house prices, welfare claimants SAE of crime statistics

  10. Covariates from ISM survey • Design based GREG estimates as auxiliary information (Ybarra & Lohr 2008) • Consequences for small area estimates • Model estimate weighted lower in BLUP due to error in covariate • Achieved through higher estimate of model variance in EBLUP (not Y & L adjustment) • Variance of GREGs approx. equal for all areas • (Other idea: multivariate FH model) SAE of crime statistics

  11. Simulating errors in covariates • Bicycle thefts: NSM survey ~ police-reported • No error • post. mean model var = 1.22 • Adding error, mean 0, sd 2, iterate 1,000 x • post. mean model var = 1.32 • To add detail, e.g. estimated beta SAE of crime statistics

  12. Dimension reduction: PCA • Rather than using a small subset of covariates, use small dimension of PC subspace • Not guaranteed to work as correlation with survey variables not used in PCA • Use as a separate set of potential covariates in model selection SAE of crime statistics

  13. PC space of dim 2 SAE of crime statistics

  14. Model selection • Conditional AIC (Vaida & Blanchart 2005)cAIC = - 2 cond_llh + 2 eff_d ( AIC = - 2 llh + 2 d ) • Cross validation (CV)LOO: leave-one-out, predictive accuracy Start from minimal model, and add terms, maximizing improvement wrt cAIC or CV, until no further improvement SAE of crime statistics

  15. Model selection results • For each NSM survey variable: 2 years, 2 criteria • CV-models are larger • cAIC are nested within CV models • Hence: • Use cAIC models • Models differ between years • Alternative: choose single model for both years SAE of crime statistics

  16. Selected models SAE of crime statistics

  17. Selected models excl. ISM SAE of crime statistics

  18. SAE results (hybrid EBLUP), reduction in coeff. of variation SAE of crime statistics

  19. Bicycle theft, cv, 2009 NSM: 0.41, EBLUP: 0.23, ISM:0.24 SAE of crime statistics

  20. SAE results, weight of direct est. in BLUP SAE of crime statistics

  21. EBLUP vs. Hierarchical Bayes HB accounts for uncertainty in estimating the model variance SAE of crime statistics

  22. Conclusions • Considerable increase in precision with SAE • Gain in precision depends on variable • PCA is important for some variables • Using ISM outcomes important for some variables • MSE estimates HB higher (preferable) SAE of crime statistics

  23. To do (maybe) • Sort out errors in input data! And re-run everything. • Calibration to direct estimate of totals (is model diagnostic) • Study residuals • Elaborate on errors in covariates • Use past survey outcomes as covariates • More detailed comparison of HB-NSM estimates with ISM SAE of crime statistics

  24. Future work (post-ESSnet) • Multivariate modelling of NSM and ISM variables • Consider model averaging • Using more detailed areas, with smaller sample sizes: beneficial? SAE of crime statistics

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