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

A Conditionally Parametric ProbitModel of Micro-Data Land Use in Chicago

Daniel McMillenMaria Soppelsa

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

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.

GMM Probit

• ,

β, ρ to minimize

Linearized GMM Probit

1. Standard probit: 2. 2SLS regression of e on on and , where

3. . Requires inversion of

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)

Spatial AR v. LWR

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)

Explanatory Variables

• Distance from parcel centroid to:1. CBD2. Lake Michigan3. EL line4. EL stop5. Rail line6. Major street7. Park8. Highway

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

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

Probability of Residential Land Use: Standard Probit

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

Difference, CPAR Probability – Standard Probit Probability

Kernel Density Estimates for CPAR Coefficients

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LWR Estimates of CPAR Coefficients

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Marginal Probabilities

Marginal Probabilities

Marginal Probabilities

Marginal Probabilities

Marginal Probabilities

Marginal Probabilities

Marginal Probabilities

Marginal Probabilities

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

Correlations, Predicted Probabilities

Standard GMM CPAR

Standard 1 0.57 0.99

GMM 0.57 1 0.57

CPAR 0.99 0.57 1

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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