alligator {BART}

American alligator Food Choice

Description

In 1985, American alligators were harvested by hunters from August 26 to September 30 in peninsular Florida from lakes Oklawaha (Putnam County), George (Putnam and Volusia counties), Hancock (Polk County) and Trafford (Collier County). Lake, length and sex were recorded for each alligator. Stomachs from a sample of alligators 1.09-3.89m long were frozen prior to analysis. After thawing, stomach contents were removed and separated and food items were identified and tallied. Volumes were determined by water displacement. The stomach contents of 219 alligators were classified into five categories of primary food choice: Fish (the most common primary food choice), Invertebrate (snails, insects, crayfish, etc.), Reptile (turtles, alligators), Bird, and Other (amphibians, plants, household pets, stones, and other debris).

Usage

data(alligator)

Format

A data frame with 80 observations on the following 5 variables.

lake

a factor with levels George Hancock Oklawaha Trafford

sex

a factor with levels female male

size

alligator size, a factor with levels large (>2.3m) small (<=2.3m)

food

primary food choice, a factor with levels bird fish invert other reptile

count

cell frequency, a numeric vector

Details

The table contains a fair number of 0 counts. food is the response variable. fish is the most frequent choice, and often taken as a baseline category in multinomial response models.

Source

Agresti, A. (2002). Categorical Data Analysis, New York: Wiley, 2nd Ed., Table 7.1

References

Delany MF, Linda SB, Moore CT (1999). "Diet and condition of American alligators in 4 Florida lakes." In Proceedings of the Annual Conference of the Southeastern Association of Fish and Wildlife Agencies, 53, 375–389.

Examples

data(alligator)
     
## nnet::multinom Multinomial logit model fit with neural nets
fit <- multinom(food ~ lake+size+sex, data=alligator, weights=count)

summary(fit$fitted.values)
## 1=bird, 2=fish, 3=invert, 4=other, 5=reptile

(L=length(alligator$count))
(N=sum(alligator$count))
y.train=integer(N)
x.train=matrix(nrow=N, ncol=3)
x.test=matrix(nrow=L, ncol=3)
k=1
for(i in 1:L) {
    x.test[i, ]=as.integer(
        c(alligator$lake[i], alligator$size[i], alligator$sex[i]))
    if(alligator$count[i]>0)
        for(j in 1:alligator$count[i]) {
            y.train[k]=as.integer(alligator$food[i])
            x.train[k, ]=as.integer(
                c(alligator$lake[i], alligator$size[i], alligator$sex[i]))
            k=k+1
        }
}
table(y.train)
##test mbart with token run to ensure installation works
set.seed(99)
check = mbart(x.train, y.train, nskip=1, ndpost=1)

## Not run: 
set.seed(99)
check = mbart(x.train, y.train, nskip=1, ndpost=1)
post=mbart(x.train, y.train, x.test)

##post=mc.mbart(x.train, y.train, x.test, mc.cores=8, seed=99)
##check=predict(post, x.test, mc.cores=8)
##print(cor(post$prob.test.mean, check$prob.test.mean)^2)

par(mfrow=c(3, 2))
K=5
for(j in 1:5) {
    h=seq(j, L*K, K)
    print(cor(fit$fitted.values[ , j], post$prob.test.mean[h])^2)
    plot(fit$fitted.values[ , j], post$prob.test.mean[h],
         xlim=0:1, ylim=0:1,
         xlab=paste0('NN: Est. Prob. j=', j),
         ylab=paste0('BART: Est. Prob. j=', j))
    abline(a=0, b=1)
}
par(mfrow=c(1, 1))

L=16
x.test=matrix(nrow=L, ncol=3)
k=1
for(size in 1:2)
    for(sex in 1:2)
        for(lake in 1:4) {
            x.test[k, ]=c(lake, size, sex)
            k=k+1
        }
x.test

## two sizes: 1=large: >2.3m, 2=small: <=2.3m
pred=predict(post, x.test)
##pred=predict(post, x.test, mc.cores=8)
ndpost=nrow(pred$prob.test)

size.test=matrix(nrow=ndpost, ncol=K*2)
for(i in 1:K) {
    j=seq(i, L*K/2, K) ## large
    size.test[ , i]=apply(pred$prob.test[ , j], 1, mean)
    j=j+L*K/2 ## small
    size.test[ , i+K]=apply(pred$prob.test[ , j], 1, mean)
}
size.test.mean=apply(size.test, 2, mean)
size.test.025=apply(size.test, 2, quantile, probs=0.025)
size.test.975=apply(size.test, 2, quantile, probs=0.975)

plot(factor(1:K, labels=c('bird', 'fish', 'invert', 'other', 'reptile')),
     rep(1, K), col=1:K, type='n', lwd=1, lty=0,
             xlim=c(1, K), ylim=c(0, 0.5), ylab='Prob.',
     sub="Multinomial BART\nFriedman's partial dependence function")
points(1:K, size.test.mean[1:K+K], col=1)
lines(1:K, size.test.025[1:K+K], col=1, lty=2)
lines(1:K, size.test.975[1:K+K], col=1, lty=2)
points(1:K, size.test.mean[1:K], col=2)
lines(1:K, size.test.025[1:K], col=2, lty=2)
lines(1:K, size.test.975[1:K], col=2, lty=2)
## legend('topright', legend=c('Small', 'Large'),
##        pch=1, col=1:2)


## End(Not run)