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A Conditionally Parametric ProbitModel of Micro-Data Land Use in Chicago
Daniel McMillenMaria Soppelsa
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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
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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.
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GMM Probit
• ,
β, ρ to minimize
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Linearized GMM Probit
1. Standard probit: 2. 2SLS regression of e on on and , where
3. . Requires inversion of
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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)
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Spatial AR v. LWR
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Data
• Individual parcels in Chicago, 2010• Major Classes:1. Vacant Land (33,139)2. Residential, 6 units or fewer (728,541, 539,975 after
geocoding)3. Multi-Family Residential (11,529)4. Non-Profit (316)5. Commercial and Industrial (50,508, 43,088 after
geocoding)6. “Incentive Classes” (1,487)
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Explanatory Variables
• Distance from parcel centroid to:1. CBD2. Lake Michigan3. EL line4. EL stop5. Rail line6. Major street7. Park8. Highway
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Rogers Park
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Descriptive StatisticsVariable Mean Std. Dev. Min Max
Residential Lot 0.926 0.262 0.000 1.000
Distance from CBD 7.518 3.433 0.022 17.006
Distance from Lake Michigan 4.116 2.716 0.005 12.321
Distance from EL Line 1.358 1.277 0.001 6.265
Distance from EL Stop 1.214 1.081 0.001 6.265
Distance from Rail Line 0.428 0.294 0.001 1.997
Distance from Major Street 0.080 0.057 0.000 0.508
Distance from Park 0.233 0.153 0.000 2.999
Distance from Highway 1.476 1.027 0.011 4.809
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Probit Models, Probability Residential Standard Probit CPAR Probit
Variable Coef. Std. Error Mean Std. Dev.Intercept 0.061 0.046 0.351 1.008Distance from CBD 0.132 0.007 0.101 0.266Distance from Lake Michigan -0.095 0.007 -0.086 0.308Distance from EL Line 0.002 0.013 -0.423 1.168Distance from EL Stop -0.091 0.013 0.511 1.263Distance from Rail Line 0.626 0.014 0.649 0.686Distance from Major Street 8.748 0.070 11.570 6.427Distance from Park -1.099 0.020 -0.881 0.994Distance from Highway 0.212 0.007 0.048 0.351Log-likelihood -131518.9 -120714.1Pseudo-R2 0.144 0.215
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Probability of Residential Land Use: Standard Probit
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Probability of Residential Land Use: CPAR Probit, 10% Window Size
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Difference, CPAR Probability – Standard Probit Probability
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Kernel Density Estimates for CPAR Coefficients
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LWR Estimates of CPAR Coefficients
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Marginal Probabilities
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Marginal Probabilities
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Marginal Probabilities
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Marginal Probabilities
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Marginal Probabilities
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Marginal Probabilities
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Marginal Probabilities
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Marginal Probabilities
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Rogers Park
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Rogers Park, n = 3,193 Standard GMM CPAR
Coef Std. Err. Coef Std. Err. Mean Std. dev.Intercept 49.979 11.999 42.977 12.592 0.025 2.445CBD -1.804 0.462 -1.549 0.480
Lake Michigan -7.621 1.672 -6.555 1.814 -0.726 5.314
EL Line -3.324 0.651 -2.901 0.723 -4.449 9.934
EL Stop 3.127 0.654 2.698 0.739 6.593 9.706
Rail Line 1.906 0.395 1.659 0.428 1.675 4.059
Major Street 7.123 0.837 5.992 1.346 15.900 9.561
Park -1.797 0.514 -1.594 0.525
Highway -7.207 1.743 -6.197 1.809
Metra Stop 0.038 0.216 0.024 0.178ρ 0.155 0.167pseudo-R2 0.084 0.084 0.343
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Correlations, Predicted Probabilities
Standard GMM CPAR
Standard 1 0.57 0.99
GMM 0.57 1 0.57
CPAR 0.99 0.57 1
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Standard Probit Probabilities
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CPAR Probit Probabilities
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Standard Probit: Southwest
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CPAR – Standard: Southwest
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Standard Probit: Southeast
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CPAR – Standard: Southeast
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Standard Probit: Northwest
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CPAR – Standard: Northwest
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Standard Probit: Northeast
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CPAR – Standard: Southeast
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