# Fit the MacKenzie et al. (2002) Occupancy Model with the penalized likelihood methods of Hutchinson et al. (2015) This function fits the occupancy model of MacKenzie et al (2002) with the penalized methods of Hutchinson et al (2015). ```r occuPEN(formula, data, knownOcc=numeric(0), starts, method="BFGS", engine=c("C", "R"), lambda=0, pen.type = c("Bayes","Ridge","MPLE"), ...) ``` ## Arguments - `formula`: Double right-hand side formula describing covariates of detection and occupancy in that order. - `data`: An `unmarkedFrameOccu` object - `knownOcc`: Vector of sites that are known to be occupied. These should be supplied as row numbers of the y matrix, eg, c(3,8) if sites 3 and 8 were known to be occupied a priori. - `starts`: Vector of parameter starting values. - `method`: Optimization method used by `optim`. - `engine`: Either "C" or "R" to use fast C++ code or native R code during the optimization. - `lambda`: Penalty weight parameter. - `pen.type`: Which form of penalty to use. - ``...``: Additional arguments to optim, such as lower and upper bounds ## Details See `unmarkedFrame` and `unmarkedFrameOccu` for a description of how to supply data to the `data` argument. `occuPEN` fits the standard occupancy model based on zero-inflated binomial models (MacKenzie et al. 2006, Royle and Dorazio 2008) using the penalized likelihood methods described in Hutchinson et al. (2015). See `occu` for model details. `occuPEN` returns parameter estimates that maximize a penalized likelihood in which the penalty is specified by the `pen.type` argument. The penalty function is weighted by `lambda`. The MPLE method includes an equation for computing `lambda` (Moreno & Lele, 2010). If the value supplied does not equal match the one computed with this equation, the supplied value is used anyway (with a warning). ## Returns unmarkedFitOccuPEN object describing the model fit. ## References Hutchinson, R. A., J. V. Valente, S. C. Emerson, M. G. Betts, and T. G. Dietterich. 2015. Penalized Likelihood Methods Improve Parameter Estimates in Occupancy Models. Methods in Ecology and Evolution. DOI: 10.1111/2041-210X.12368 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. MacKenzie, D. I. et al. 2006. **Occupancy Estimation and Modeling**. Amsterdam: Academic Press. Moreno, M. and S. R. Lele. 2010. Improved estimation of site occupancy using penalized likelihood. Ecology 91: 341-346. Royle, J. A. and R. Dorazio. 2008. **Hierarchical Modeling and Inference in Ecology**. Academic Press. ## Author(s) Rebecca A. Hutchinson ## See Also `unmarked`, `unmarkedFrameOccu`, `occu`, `computeMPLElambda`, `occuPEN_CV`, `nonparboot` ## Examples ```r # Simulate occupancy data set.seed(344) nSites <- 100 nReps <- 2 covariates <- data.frame(veght=rnorm(nSites), habitat=factor(c(rep('A', nSites/2), rep('B', nSites/2)))) psipars <- c(-1, 1, -1) ppars <- c(1, -1, 0) X <- model.matrix(~veght+habitat, covariates) # design matrix psi <- plogis(X %*% psipars) p <- plogis(X %*% ppars) y <- matrix(NA, nSites, nReps) z <- rbinom(nSites, 1, psi) # true occupancy state for(i in 1:nSites) { y[i,] <- rbinom(nReps, 1, z[i]*p[i]) } # Organize data and look at it umf <- unmarkedFrameOccu(y = y, siteCovs = covariates) obsCovs(umf) <- covariates head(umf) summary(umf) # Fit some models fmMLE <- occu(~veght+habitat ~veght+habitat, umf) fm1pen <- occuPEN(~veght+habitat ~veght+habitat, umf,lambda=0.33,pen.type="Ridge") fm2pen <- occuPEN(~veght+habitat ~veght+habitat, umf,lambda=1,pen.type="Bayes") # MPLE: fm3pen <- occuPEN(~veght+habitat ~veght+habitat, umf,lambda=0.5,pen.type="MPLE") MPLElambda = computeMPLElambda(~veght+habitat ~veght+habitat, umf) fm4pen <- occuPEN(~veght+habitat ~veght+habitat, umf,lambda=MPLElambda,pen.type="MPLE") # nonparametric bootstrap for uncertainty analysis: fm1pen <- nonparboot(fm1pen,B=20) # should use more samples vcov(fm1pen,method="nonparboot") ```

occuPEN function