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Spatial Data Analysis

Explore the land values per acre, corn yield, grain percentages, and spatial autocorrelation in Iowa counties circa 1926. Regression model highlights associations with land use factors.

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Spatial Data Analysis

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  1. Spatial Data Analysis Iowa County Land Values (1926)

  2. Data Description • County Level Data (Circa 1926, n=99) • Latitude/Longitude Co-Ordinates of County Seat • Land Values per Acre (Federal/State) • Corn Yield per Acre • Percent Corn • Percent Other Grains • Percent Un-plowable Land

  3. Map of Federal Land Values

  4. Summary Statistics

  5. Weight Matrices • We consider 2 weight matrices: • Inverse distance: • Queen’s Case: • Each is scaled to have rows sum to 1 with Wii=0

  6. Test for Autocorrelation • Moran’s I statistic under Randomization:

  7. Moran’s I – Federal Land (Queen’s W) • N = 99 Counties • S0 = 99 (Rows sum to 1) • S1 = 34.82809 • S2 = 400.6013 • k = 2.6268 • e’We = 45395.6967 • e’e = 70033.6566 • I = 0.6482 • E(I) = -0.0102 • V(I) = 0.003373 • Zobs = 11.34

  8. Moran’s I – Federal Land (Inverse Distance) • N = 99 Counties • S0 = 99 (Rows sum to 1) • S1 = 3.2919 • S2 = 397.1385 • k = 2.0925 • e’We= 9772.80233 • e’e = 70033.6566 • I = 0.1395 • E(I) = -0.0102 • V(I) = 0.00012972 • Zobs = 13.15

  9. SemiVariogram Estimates • Counties assigned to 34 distance classes: <0.35,0.40 to 2.00 by 0.05

  10. Several Semivariogram Models

  11. Fitted Semivariograms – (R gstat)

  12. Regression Model • Response: FEDVAL = Federal land value • Predictors: • CORNYLD = Corn yield/acre • PCTCORN = Percent of land planted corn • PCTGRAIN = Percent of land for other grains • PCTUNPLOW = Percent land un-plowable

  13. Regression Output • Federal land values are: • Positively associated with corn yield per acre • Positively associated with percent of land planted corn • Positively associated with percent of land planted other grains • Negatively associated with percent of land un-plowable • No evidence of autocorrelated residuals (see following slides)

  14. Moran’s I – Residuals (Queen’s W) • N = 99 Counties • S0 = 99 (Rows sum to 1) • S1 = 34.82809 • S2 = 400.6013 • k = 4.1487 • e’We = 998.2657 • e’e = 12677.997 • I = 0.07874 • E(I) = -0.0102 • V(I) = 0.00330 • Zobs = 1.548

  15. Moran’s I – Residuals (Inverse Distance) • N = 99 Counties • S0 = 99 (Rows sum to 1) • S1 = 3.2919 • S2 = 397.1385 • k = 4.1487 • e’We = 91.9083 • e’e = 12677.997 • I = 0.00725 • E(I) = -0.0102 • V(I) = 0.00012693 • Zobs = 1.549

  16. Map of OLS Residuals

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