I'm involved with a creel survey. We have reason to believe that anglers are keeping the larger fish they catch, or at least that a relationship exists between the size of caught fish and the probability of retention.
We have the potential for two datasets:
- A creel sample consisting of the lengths of angler-kept fish (obtained by interviewing anglers)
- A "control" sample consisting of the lengths of fish that our crew catches using similar methods.
Let's make a couple of assumptions:
- The creel sample is unbiased and representative of the fish that anglers keep
- The control sample is unbiased and representative of the fish that are subject to capture by anglers.
It seems to me that a logistic relationship "should" exist between fish size and retention probability. Instead of breaking lengths into bins and treating this as a categorical problem, I'd love to be able to use something like logistic regression as a simple way of modeling the relationship. The obvious problem is that we only have kept=TRUE fish in the creel sample.
Is there a way of incorporating the control sample data that will end up with a valid (and interpretable) logistic regression? If I treat the control sample as having an associated response variable kept=FALSE, will the slope coefficient at least be meaningful?