stan_occuTTD function

Fit Time-to-detection Occupancy Models

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.

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

Returns

ubmsFitOccuTTD object describing the model fit.

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))

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