Mike Livermore – CSI 773 – Week 8 Assignment –Maps and Smoothes – November 2010

(1) Plot 4.2 Region centroids smoothed map with Green Violet palette

(2) Model 3 compared with Model 2

model3 = loess(rate ~ a.long*a.lat,

               span=.20,

               degree=2,

               surface='direct',

               normalize=FALSE,

               weights=pop/(10^5*rate))

summary(model3)

Call:

loess(formula = rate ~ a.long * a.lat, weights = pop/(10^5 *

    rate), span = 0.2, degree = 2, normalize = FALSE, surface = "direct")

Number of Observations: 802

Equivalent Number of Parameters: 35.89

Residual Standard Error: 1.485

Trace of smoother matrix: 42.89

Control settings:

  normalize:  FALSE

  span      :  0.2

  degree   :  2

  family   :  gaussian

  surface  :  direct

it = 2

for (i in 1:it){

model3  = loess(rate ~ a.long*a.lat,

               span=.20,

               degree=2,

               surface='direct',

               normalize=FALSE,

               weights=pop/(10^5*fitted(model3)))

}

summary(model3)

Call:

loess(formula = rate ~ a.long * a.lat, weights = pop/(10^5 *

    fitted(model3)), span = 0.2, degree = 2, normalize = FALSE,

    surface = "direct")

Number of Observations: 802

Equivalent Number of Parameters: 35.93

Residual Standard Error: 1.426

Trace of smoother matrix: 42.93

Control settings:

  normalize:  FALSE

  span      :  0.2

  degree   :  2

  family   :  gaussian

  surface  :  direct

anova(model1, model3)

Model 1: loess(formula = rate ~ a.long * a.lat, weights = pop/(10^5 * fitted(model1)), span = 0.15, degree = 2, normalize = FALSE, surface = "direct")

Model 2: loess(formula = rate ~ a.long * a.lat, weights = pop/(10^5 * fitted(model3)), span = 0.2, degree = 2, normalize = FALSE, surface = "direct")

Analysis of Variance:   denominator df 742.87

       ENP    RSS F-value    Pr(>F)   

[1,] 46.49 1444.5                     

[2,] 35.93 1528.4  2.9349 0.0002791 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(3) Smoothed Plot 4.2 fitted with model 3:

hsaSmooth = fitted(model3)

rateClass = classifyRates(hsaSmooth,pop,percents)

polygonClass =classifyPolygons(hsaPolyId,rateId,rateClass$class)

hsaSetup()

polygon(hsaPoly,col=currentPalette[polygonClass],density=-1,border=F)

polygon(hsaPoly,col="#898989",density=0,lwd=1)

polygon(usGrid90States,density=0,lwd=1,col="black") # "#606060"

mtext('White Male Colon Cancer Mortality, 1980-1989',side=3,line=.7,cex=1.4,adj=.5)

mtext('Smoothed Age-Adjusted Rates Per 100,000 Fitted With Model 3', side=3,line=-.8,cex=1.0,adj=.5)

mtext('Population Based Percentiles', side=3,line=-2.1,cex=1.0,adj=.5)

albers.legend(percents,rateClass$breaks,palette=currentPalette,brk.rnd=1)

(4) Show Differences between 4.2 model 2 and model 3

currentPalette[6]=blueRed5[5]

hsaSmooth2 = fitted(model2)

rateClass2 = classifyRates(hsaSmooth2,pop,percents)

polygonClass2 =classifyPolygons(hsaPolyId,rateId,rateClass2$class)

replaceDiff = function(list1, list2, newValue) {

                listRet = list1

for(index in 1:length(list1)) {

                                if (list1[index] != list2[index]) listRet[index] = newValue

                        }

                        return (listRet)

}

polygonClass = replaceDiff(polygonClass, polygonClass2, 6)

hsaSetup()

polygon(hsaPoly,col=currentPalette[polygonClass],density=-1,border=F)

polygon(hsaPoly,col="#898989",density=0,lwd=1)

polygon(usGrid90States,density=0,lwd=1,col="black") # "#606060"

mtext('White Male Colon Cancer Mortality, 1980-1989',side=3,line=.7,cex=1.4,adj=.5)

mtext('Smoothed Age-Adjusted Rates Per 100,000', side=3,line=-.8,cex=1.0,adj=.5)

mtext('Differences between Model2 and Model3 Fits in Red', side=3,line=-2.1,cex=1.0,adj=.5)

mtext('Population Based Percentiles', side=3,line=-3.4,cex=1.0,adj=.5)

albers.legend(percents,rateClass$breaks,palette=currentPalette,brk.rnd=1)