occuPEN.RdThis function fits the occupancy model of MacKenzie et al (2002) with the penalized methods of Hutchinson et al (2015).
occuPEN(formula, data, knownOcc=numeric(0), starts, method="BFGS", engine=c("C", "R"), lambda=0, pen.type = c("Bayes","Ridge","MPLE"), ...)
| formula | Double right-hand side formula describing covariates of detection and occupancy in that order. |
|---|---|
| data | An |
| 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 |
| 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 |
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).
unmarkedFitOccuPEN object describing the model fit.
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.
Rebecca A. Hutchinson
# 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)#> Data frame representation of unmarkedFrame object. #> y.1 y.2 veght habitat veght.1 veght.2 habitat.1 habitat.2 #> 1 0 0 1.0733096 A 1.0733096 3.3024986 A A #> 2 0 0 3.3024986 A -0.7308712 1.1855582 A A #> 3 0 0 -0.7308712 A 0.3037686 0.3758026 A A #> 4 0 0 1.1855582 A -1.0129665 -1.6261948 A A #> 5 0 1 0.3037686 A -0.7386708 -0.4478443 A A #> 6 1 0 0.3758026 A 0.2905940 0.8757997 A A #> 7 0 0 -1.0129665 A -0.1934656 1.0933781 A A #> 8 0 0 -1.6261948 A 0.6177908 -0.4148051 A A #> 9 0 0 -0.7386708 A -0.7710753 -1.3117284 A A #> 10 0 0 -0.4478443 A 0.4820107 -0.9793715 A A#> unmarkedFrame Object #> #> 100 sites #> Maximum number of observations per site: 2 #> Mean number of observations per site: 2 #> Sites with at least one detection: 22 #> #> Tabulation of y observations: #> 0 1 #> 167 33 #> #> Site-level covariates: #> veght habitat #> Min. :-1.80746 A:50 #> 1st Qu.:-0.75747 B:50 #> Median :-0.05057 #> Mean : 0.07205 #> 3rd Qu.: 0.62237 #> Max. : 3.32295 #> #> Observation-level covariates: #> veght habitat #> Min. :-1.80746 A:50 #> 1st Qu.:-0.75747 B:50 #> Median :-0.05057 #> Mean : 0.07205 #> 3rd Qu.: 0.62237 #> Max. : 3.32295# 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")#> Warning: Supplied lambda does not match the computed value. Proceeding with the supplied lambda.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#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 50 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 50 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 50 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 50 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 49 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 60 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 49 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 53 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 47 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 46 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 38 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 46 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 44 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 55 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 47 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 51 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 46 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 48 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 62 sites have been discarded because of missing data.#> Warning: Some observations have been discarded because corresponding covariates were missing.#> Warning: 46 sites have been discarded because of missing data.#> psi(Int) psi(veght) psi(habitatB) p(Int) p(veght) #> psi(Int) 0.54191131 0.8086550 0 -0.3296919 0.11124043 #> psi(veght) 0.80865501 1.4055070 0 -0.6409539 0.23168191 #> psi(habitatB) 0.00000000 0.0000000 0 0.0000000 0.00000000 #> p(Int) -0.32969191 -0.6409539 0 0.4352372 -0.10749050 #> p(veght) 0.11124043 0.2316819 0 -0.1074905 0.11454844 #> p(habitatB) -0.04670788 0.0337051 0 -0.1864737 0.01056793 #> p(habitatB) #> psi(Int) -0.04670788 #> psi(veght) 0.03370510 #> psi(habitatB) 0.00000000 #> p(Int) -0.18647374 #> p(veght) 0.01056793 #> p(habitatB) 0.37218475