stan_occuTTD {ubms}

Fit Time-to-detection Occupancy Models

Description

Fit time-to-detection occupancy models of Garrard et al. (2008, 2013). Time-to-detection can be modeled with either an exponential or Weibull distribution.

Usage

stan_occuTTD(
  psiformula = ~1,
  gammaformula = ~1,
  epsilonformula = ~1,
  detformula = ~1,
  data,
  ttdDist = c("exp", "weibull"),
  linkPsi = c("logit"),
  prior_intercept_state = logistic(0, 1),
  prior_coef_state = logistic(0, 1),
  prior_intercept_det = normal(0, 5),
  prior_coef_det = normal(0, 2.5),
  prior_intercept_shape = normal(0, 2.5),
  prior_sigma = gamma(1, 1),
  log_lik = TRUE,
  ...
)

Arguments

psiformula

Right-hand sided formula for the initial probability of occupancy at each site.

gammaformula

Right-hand sided formula for colonization probability. Currently ignored as dynamic models are not yet supported.

epsilonformula

Right-hand sided formula for extinction probability. Currently ignored as dynamic models are not yet supported.

detformula

Right-hand sided formula for mean time-to-detection.

data

unmarkedFrameOccuTTD object that supplies the data (see unmarkedFrameOccuTTD).

ttdDist

Distribution to use for time-to-detection; either "exp" for the exponential, or "weibull" for the Weibull, which adds an additional shape parameter k.

linkPsi

Link function for the occupancy model. Only option is "logit" for now, in the future "cloglog" will be supported for the complimentary log-log link.

prior_intercept_state

Prior distribution for the intercept of the state (occupancy probability) model; see ?priors for options

prior_coef_state

Prior distribution for the regression coefficients of the state model

prior_intercept_det

Prior distribution for the intercept of the time-to-detection model

prior_coef_det

Prior distribution for the regression coefficients of the time-to-detection model

prior_intercept_shape

Prior distribution for the intercept of the shape parameter (i.e., log(shape)) for Weibull TTD models

prior_sigma

Prior distribution on random effect standard deviations

log_lik

If TRUE, Stan will save pointwise log-likelihood values in the output. This can greatly increase the size of the model. If FALSE, the values are calculated post-hoc from the posteriors

...

Arguments passed to the stan call, such as number of chains chains or iterations iter

Value

ubmsFitOccuTTD object describing the model fit.

References

Garrard, G.E., Bekessy, S.A., McCarthy, M.A. and Wintle, B.A. 2008. When have we looked hard enough? A novel method for setting minimum survey effort protocols for flora surveys. Austral Ecology 33: 986-998.

Garrard, G.E., McCarthy, M.A., Williams, N.S., Bekessy, S.A. and Wintle, B.A. 2013. A general model of detectability using species traits. Methods in Ecology and Evolution 4: 45-52.

Kery, Marc, and J. Andrew Royle. 2016. Applied Hierarchical Modeling in Ecology, Volume 1. Academic Press.

See Also

occuTTD, unmarkedFrameOccuTTD

Examples

#Simulate data
N <- 500; J <- 1
scovs <- data.frame(elev=c(scale(runif(N, 0,100))),
                    forest=runif(N,0,1),
                    wind=runif(N,0,1))
beta_psi <- c(-0.69, 0.71, -0.5)
psi <- plogis(cbind(1, scovs$elev, scovs$forest) %*% beta_psi)
z <- rbinom(N, 1, psi)

Tmax <- 10 #Same survey length for all observations
beta_lam <- c(-2, -0.2, 0.7)
rate <- exp(cbind(1, scovs$elev, scovs$wind) %*% beta_lam)
ttd <- rexp(N, rate)
ttd[z==0] <- Tmax #Censor at unoccupied sites
ttd[ttd>Tmax] <- Tmax #Censor when ttd was greater than survey length

#Build unmarkedFrame
umf <- unmarkedFrameOccuTTD(y=ttd, surveyLength=Tmax, siteCovs=scovs)

#Fit model
(fit <- stan_occuTTD(psiformula=~elev+forest, detformula=~elev+wind,
                     data=umf, chains=3, iter=300))