## Predicting Environmental Conditions from Biological Observations (PECBO) Appendix

### Area Under the ROC Curve: R Script

The area under the receiver operating characteristic (ROC) curve provides an indication of how accurately a model classifies sites into sites with the taxon present and sites with the taxon absent.

The area under the ROC curve for each model can be computed by first imagining a pair of sites where the species of interest is present at one site but absent at the other. We would expect that the probabilities of occurrence predicted by the regression model would be greater at the site where the species is present than at the site where the species is absent. The area under the ROC is equivalent to the proportion of all such pairwise comparisons in which this condition is satisfied. The following script performs this computation.

```# Define storage vector for ROC
roc <- rep(NA, times = length(taxa.names))

for (i in 1:length(taxa.names)) {
# Compute mean predicted probability of occurrence
predout <- predict(modlist.glm[[i]], type = "response")

# Generate logical vector corresponding to presence/absence
resp <- dfmerge[, taxa.names[i]] > 0

# Divide predicted probabilities into sites where
# species is present ("x") and sites where the species is
# absent ("y").
x <- predout[resp]
y <- predout[! resp]

# Now perform all pairwise comparisons of x vs. y
# and store results in a matrix
rocmat <- matrix(NA, nrow = length(x), ncol = length(y))
for (j in 1:length(x)) {
rocmat[j,] <- as.numeric(x[j] > y)
}

# Summarize all comparisons to compute area under ROC
roc[i] <- sum(rocmat)/(length(x)*length(y))
}
names(roc)<- taxa.names
print(roc)```

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