corals <- read.csv('ecol 562/corals.csv', header=T)
corals.sort <- corals[order(corals$CORAL_COVE),]
model2 <- glm(PREV_1~CORAL_COVE*WSSTA+I(WSSTA^2), data=corals.sort, family=poisson)

#fit saturated model
corals.sort$ID<-1:nrow(corals.sort)
model0 <- glm(PREV_1~factor(ID), data=corals.sort, family=poisson)
nrow(corals.sort)
length(coef(model0))

#goodness of fit test
2*logLik(model0)-2*logLik(model2)

anova(model2,test='Chisq')
1-pchisq(4912.3,275)

#check minimum count criterion
#fraction of expected counts less than 5
sum(fitted(model2)<5)/length(fitted(model2))