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A Conditionally Parametric Probit Model of Micro-Data Land Use in Chicago

A Conditionally Parametric Probit Model of Micro-Data Land Use in Chicago. Daniel McMillen Maria Soppelsa. Overview. Residential v. Commercial/Industrial Land Use in Chicago, 2010 A conditionally parametric (CPAR) approach produces smooth estimates over space

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A Conditionally Parametric Probit Model of Micro-Data Land Use in Chicago

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  1. A Conditionally Parametric ProbitModel of Micro-Data Land Use in Chicago Daniel McMillen Maria Soppelsa

  2. Overview • Residential v. Commercial/Industrial Land Use in Chicago, 2010 • A conditionally parametric (CPAR) approach produces smooth estimates over space • Target points chosen using an adaptive decision tree approach (Loader, 1999) • Interpolation from 182 target points to all 583,063 individual parcels in the data set

  3. Estimation Procedures • Case (1992). Special From for W • McMillen (1992). EM Algorithm • Pinkse and Slade (1998). GMM for spatial error model. • LeSage (2000). Bayesian approach • Klier and McMillen (2007). Linearized version of GMM probit/logit for spatial AR model.

  4. GMM Probit • , β, ρ to minimize

  5. Linearized GMM Probit 1. Standard probit: 2. 2SLS regression of e on on and , where • . Requires inversion of

  6. CPAR Probit • = kernel weight function, distance between observation j and target point. • Straightforward extension of “GWR” – a special case of locally weighted or locally linear regression. • Applications: • McMillen and McDonald (2004) • Wang, Kockelman, and Wang (2011) • Wren and Sam (2012)

  7. Spatial AR v. LWR

  8. Data • Individual parcels in Chicago, 2010 • Major Classes: • Vacant Land (33,139) • Residential, 6 units or fewer (728,541, 539,975 after geocoding) • Multi-Family Residential (11,529) • Non-Profit (316) • Commercial and Industrial (50,508, 43,088 after geocoding) • “Incentive Classes” (1,487)

  9. Explanatory Variables • Distance from parcel centroid to: • CBD • Lake Michigan • EL line • EL stop • Rail line • Major street • Park • Highway

  10. Rogers Park

  11. Descriptive Statistics

  12. Probit Models, Probability Residential

  13. Probability of Residential Land Use: Standard Probit

  14. Probability of Residential Land Use: CPAR Probit, 10% Window Size

  15. Difference, CPAR Probability – Standard Probit Probability

  16. Kernel Density Estimates for CPAR Coefficients

  17. LWR Estimates of CPAR Coefficients

  18. Marginal Probabilities

  19. Marginal Probabilities

  20. Marginal Probabilities

  21. Marginal Probabilities

  22. Marginal Probabilities

  23. Marginal Probabilities

  24. Marginal Probabilities

  25. Marginal Probabilities

  26. Rogers Park

  27. Rogers Park, n = 3,193

  28. Correlations, Predicted Probabilities

  29. Standard Probit Probabilities

  30. CPAR Probit Probabilities

  31. Standard Probit: Southwest

  32. CPAR – Standard: Southwest

  33. Standard Probit: Southeast

  34. CPAR – Standard: Southeast

  35. Standard Probit: Northwest

  36. CPAR – Standard: Northwest

  37. Standard Probit: Northeast

  38. CPAR – Standard: Southeast

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