I have a collection of samples from which I have estimated prevalence on an annual basis using a logistic regression model. The response variable is whether or not the focal species was present in each sample, and there is approximately the same number of samples coming from roughly the same geographic area in each year. In R,
fm <- glm(y ~ -1 + year, dat4, family = "binomial")
where y is 0/1 and year is a factor. The coefficients of that model are logit(prevalence). Is it appropriate to fit an ARIMA (or a state space) model to those logit-transformed estimates? Also are there any conventions to handle zeroes in prevalence data? (Akin to adding a small quantity to a continuous variable prior to log-transformation.)
