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Spatial Smoothing for Categorical Data

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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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