# Fit occupancy models when false positive detections occur (e.g., Royle and Link [2006] and Miller et al. [2011]) This function fits the single season occupancy model while allowing for false positive detections. ```r occuFP(detformula = ~ 1, FPformula = ~ 1, Bformula = ~ 1, stateformula = ~ 1, data, starts, method="BFGS", se = TRUE, engine = "R", ...) ``` ## Arguments - `detformula`: formula describing covariates of detection. - `FPformula`: formula describing covariates of false positive detection probability. - `Bformula`: formula describing covariates of probability detections are certain. - `stateformula`: formula describing covariates of occupancy. - `data`: An `unmarkedFrameOccuFP` object - `starts`: Vector of parameter starting values. - `method`: Optimization method used by `optim`. - `se`: Logical specifying whether or not to compute standard errors. - `engine`: Currently only choice is R. - ``...``: Additional arguments to optim, such as lower and upper bounds ## Details See `unmarkedFrame` and `unmarkedFrameOccuFP` for a description of how to supply data to the `data` argument. `occuFP` fits an extension of the standard single-season occupancy model (MacKenzie et al. 2002), which allows false positive detections. The occupancy status of a site is the same way as with the `occu` function, where stateformula is used to specify factors that lead to differences in occupancy probabilities among sites. The observation process differs in that both false negative and false positive errors are modeled for observations. The function allows data to be of 3 types. These types are specified using in `unmarkedFrameOccuFP` as type. Occassions are specified to belong to 1 of the 3 data types and all or a subset of the data types can be combined in the same model. For type 1 data, the detection process is assumed to fit the assumptions of the standard MacKenzie model where false negative probabilities are estimated but false positive detections are assumed not to occur. If all of your data is of this type you should use `occu` to analyze data. The detection parameter p, which is modeled using the detformula is the only observation parameter for these data. For type 2 data, both false negative and false positive detection probabilities are estimated. If all data is of this type the likelihood follows Royle and Link (2006). Both p (the true positive detection probability) and fp (the false positive detection probability described by fpformula) are estimated for occassions when this data type occurs For type 3 data, observations are assumed to include both certain detections (false positives assumed not to occur) and uncertain detections that may include false positive detections. When only this data type occurs, the estimator is the same as the multiple detection state model described in Miller et al. (2011). Three observation parameters occur for this data type: p - true positive detection probability, fp - false positive detection probability, and b - the probability a true positive detection was designated as certain. When both type 1 and type 2 data occur, the estimator is equivalent to the multiple detection method model described in Miller et al. (2011). The frog data example in the same paper uses an analysis where type 1 (dipnet surveys) and type 3 (call surveys) data were used. Data in the y matrix of the unmarked frame should be all 0s and 1s for type 1 and type 2 data. For type 3 data, uncertain detections are given a value of 1 and certain detections a value of 2. ## Returns unmarkedFitOccuFP object describing the model fit. ## References MacKenzie, D. I., J. D. Nichols, G. B. Lachman, S. Droege, J. Andrew Royle, and C. A. Langtimm. 2002. Estimating Site Occupancy Rates When Detection Probabilities Are Less Than One. Ecology 83: 2248-2255. Miller, D.A., J.D. Nichols, B.T. McClintock, E.H.C. Grant, L.L. Bailey, and L.A. Weir. 2011. Improving occupancy estimation when two types of observational error occur: non-detection and species misidentification. Ecology 92:1422-1428. Royle, J.A., and W.A. Link. 2006. Generalized site occupancy models allowing for false positive and false negative errors. Ecology 87:835-841. ## Author(s) David Miller ## See Also `unmarked`, `unmarkedFrameOccuFP`, `modSel`, `parboot` ## Examples ```r n = 100 o = 10 o1 = 5 y = matrix(0,n,o) p = .7 r = .5 fp = 0.05 y[1:(n*.5),(o-o1+1):o] <- rbinom((n*o1*.5),1,p) y[1:(n*.5),1:(o-o1)] <- rbinom((o-o1)*n*.5,1,r) y[(n*.5+1):n,(o-o1+1):o] <- rbinom((n*o1*.5),1,fp) type <- c((o-o1),o1,0) ### vector with the number of each data type site <- c(rep(1,n*.5*.8),rep(0,n*.5*.2),rep(1,n*.5*.2),rep(0,n*.8*.5)) occ <- matrix(c(rep(0,n*(o-o1)),rep(1,n*o1)),n,o) site <- data.frame(habitat = site) occ <- list(METH = occ) umf1 <- unmarkedFrameOccuFP(y,site,occ, type = type) m1 <- occuFP(detformula = ~ METH, FPformula = ~1, stateformula = ~ habitat, data = umf1) predict(m1, type = 'fp') coef(m1) confint(m1, type = 'det') ```

occuFP function