Tract NDVI Models
Michael Minn - 30 April 2015
Variables
Landsat Data
NDVI: Median tract residential area NDVI
Census Data
SQMLAND: Tract area in square meters
MEDIANAGE: Median age
MEDHHINC: Median household income
MEANHHSIZE: Mean number of members in each household
PCOWNEROCC: Percent housing units owner-occupied
PCTURNOVER: Percent residents in same house one year ago
PCBORNUSA: Percent of residents born in the USA
PCUNEMPLOYED: Percent 16 years of age or older unemployed (mean?)
Parcel Data
Data from 2013 Maricopa County Assessor's Office ST 42030 File
SQMLAWN: Total square meters of PLA (lot_size - (home_size / floors) - pool_size)
MEDCONSTYR: Median construction year
Climate Data
P_MINUS_PET: Precipitation - potential evapotranspiration
RAINFALL60: Running sum of rainfall for the past 60 days
A temporally-lagged running sum of rainfall has the highest correlation with tract NDVI.
A five-day lag between P_MINUS_PET and NDVI gives best correlation r = 0.18
A nine-day lag between 60-day Rainfall sum and NDVI gives best correlation r = 0.423
Linear Model
Call:
lm(formula = NDVI ~ ., data = regression_data)
Residuals:
Min 1Q Median 3Q Max
-4.2980 -0.5458 -0.1283 0.3942 13.0695
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.009428 0.001658 5.687 1.3e-08 ***
SQMLAND -0.017284 0.001708 -10.117 < 2e-16 ***
MEDIANAGE -0.334194 0.002522 -132.535 < 2e-16 ***
MEDHHINC 0.320085 0.002271 140.941 < 2e-16 ***
MEANHHSIZE -0.246225 0.002517 -97.832 < 2e-16 ***
PCOWNEROCC 0.018373 0.002167 8.479 < 2e-16 ***
PCTURNOVER 0.113816 0.002150 52.944 < 2e-16 ***
PCBORNUSA 0.095260 0.002555 37.286 < 2e-16 ***
PCUNEMPLOYED -0.070619 0.002257 -31.295 < 2e-16 ***
SQMLAWN 0.081585 0.001991 40.984 < 2e-16 ***
MEDCONSTYR -0.479292 0.002037 -235.245 < 2e-16 ***
RAINFALL60 0.136666 0.001585 86.234 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.8769 on 293032 degrees of freedom
(160337 observations deleted due to missingness)
Multiple R-squared: 0.2538, Adjusted R-squared: 0.2538
F-statistic: 9060 on 11 and 293032 DF, p-value: < 2.2e-16
Random Forest Model
> model
Call:
randomForest(formula = NDVI ~ ., data = database[, rfields], na.action = na.omit)
Type of random forest: regression
Number of trees: 500
No. of variables tried at each split: 4
Mean of squared residuals: 0.2130862
% Var explained: 78.88
> summary(model)
Length Class Mode
call 4 -none- call
type 1 -none- character
predicted 301211 -none- numeric
mse 500 -none- numeric
rsq 500 -none- numeric
oob.times 301211 -none- numeric
importance 12 -none- numeric
importanceSD 0 -none- NULL
localImportance 0 -none- NULL
proximity 0 -none- NULL
ntree 1 -none- numeric
mtry 1 -none- numeric
forest 11 -none- list
coefs 0 -none- NULL
y 301211 -none- numeric
test 0 -none- NULL
inbag 0 -none- NULL
terms 3 terms call
na.action 152170 omit numeric
> importance(model)
IncNodePurity
SQMLAND 22156.939
SQMWATER 8838.317
MEDIANAGE 24688.405
MEDHHINC 26790.211
MEANHHSIZE 23293.283
PCOWNEROCC 13776.804
PCTURNOVER 13744.089
PCBORNUSA 13494.287
PCUNEMPLOYED 9865.677
SQMLAWN 31388.236
MEDCONSTYR 54570.323
PMINPET 12390.099
Generalized Additive Model
summary(gamodel)
Family: gaussian
Link function: identity
Formula:
NDVI ~ s(SQMLAND) + s(MEDIANAGE) + s(MEDHHINC) + s(MEANHHSIZE) +
s(PCOWNEROCC) + s(PCTURNOVER) + s(PCBORNUSA) + s(PCUNEMPLOYED) +
s(SQMLAWN) + s(MEDCONSTYR) + s(RAINFALL60)
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.004502 0.001493 3.016 0.00256 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Approximate significance of smooth terms:
edf Ref.df F p-value
s(SQMLAND) 8.952 8.999 337.97 <2e-16 ***
s(MEDIANAGE) 8.999 9.000 1375.92 <2e-16 ***
s(MEDHHINC) 8.995 9.000 2272.24 <2e-16 ***
s(MEANHHSIZE) 8.975 9.000 1308.43 <2e-16 ***
s(PCOWNEROCC) 8.990 9.000 473.22 <2e-16 ***
s(PCTURNOVER) 8.911 8.998 246.44 <2e-16 ***
s(PCBORNUSA) 8.982 9.000 334.18 <2e-16 ***
s(PCUNEMPLOYED) 8.958 8.999 97.41 <2e-16 ***
s(SQMLAWN) 8.985 9.000 1296.71 <2e-16 ***
s(MEDCONSTYR) 8.932 8.998 5495.54 <2e-16 ***
s(RAINFALL60) 8.976 9.000 1098.06 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
R-sq.(adj) = 0.366 Deviance explained = 36.7%
GCV = 0.65316 Scale est. = 0.65294 n = 293044
