Spatial Data Analysis Iowa County Land Values (1926)
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
Map of Federal Land Values
Summary Statistics StatisticCorn Yield/AcrePercent CornPercent GrainPercent Un-plowFederal ValueState Value q min median max q Mean Std Dev
Weight Matrices We consider 2 weight matrices: Inverse distance: Queen’s Case: Each is scaled to have rows sum to 1 with W ii =0
Test for Autocorrelation Moran’s I statistic under Randomization:
Moran’s I – Federal Land (Queen’s W) N = 99 Counties S 0 = 99 (Rows sum to 1) S 1 = S 2 = k = e’We = e’e = I = E(I) = V(I) = Z obs = 11.34
Moran’s I – Federal Land (Inverse Distance) N = 99 Counties S 0 = 99 (Rows sum to 1) S 1 = S 2 = k = e’We = e’e = I = E(I) = V(I) = Z obs = 13.15
SemiVariogram Estimates Counties assigned to 34 distance classes: <0.35,0.40 to 2.00 by 0.05
Several Semivariogram Models
Fitted Semivariograms – (R gstat)
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
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)
Moran’s I – Residuals (Queen’s W) N = 99 Counties S 0 = 99 (Rows sum to 1) S 1 = S 2 = k = e’We = e’e = I = E(I) = V(I) = Z obs = 1.548
Moran’s I – Residuals (Inverse Distance) N = 99 Counties S 0 = 99 (Rows sum to 1) S 1 = S 2 = k = e’We = e’e = I = E(I) = V(I) = Z obs = 1.549
Map of OLS Residuals