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Spatial Smoothing for Categorical Data

Spatial Smoothing for Categorical Data. Work Session On Statistical Data Editing May 17, 2005 Yves Thibaudeau William E. Winkler. Population Model (Valliant Dorfman Royal 2002). Tract Level (~2000 Housing Units) Superpopulation Model? Loglinear Model All 2 nd Order Interactions.

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Spatial Smoothing for Categorical Data

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  1. Spatial Smoothing for Categorical Data Work Session On Statistical Data Editing May 17, 2005 Yves Thibaudeau William E. Winkler

  2. Population Model (Valliant Dorfman Royal 2002) • Tract Level (~2000 Housing Units) • Superpopulation Model? • Loglinear Model • All 2nd Order Interactions

  3. Spatial Patterns • Vacancy Status (Occupied, Vacant) • New Construction ( < 1 Year ) • 2 x 2 Table • Unit x Neighbor: 2 x 2 x 2 x 2 Table • 10 Degrees of Freedoms

  4. Spatial Transition Probabilities(7 Degrees of Freedom)

  5. Spatial Transition Probabilities • Can Estimate with EM Algorithm (Thibaudeau 2002) • Can Estimate in the Context of A Linear Regression

  6. Imputation through Spatial Modeling • Imputation of Vacancy / Age Conditional on Neighbor • Flip Coin Loaded with Estimated Transition Probabilities • Smooth Over Track-Level Estimates

  7. Conditional Log-Odds

  8. Loglinear Space for the Transition Probabilities

  9. Counts:Unit: Occupied, OldNeighbor: Occupied, Old

  10. Counts:Unit: Vacant, OldNeighbor: Occupied, Old

  11. Observed Log-Odds

  12. Linear Model (log-odds)

  13. Partial Counts

  14. Partial Counts

  15. Spatial Modeling – Discussion • Can Account for More Covariates • Tend to do well over extended areas (state) • Does poorly at the small area level (block)

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