multinomPois {unmarked}

Multinomial-Poisson Mixtures Model

Description

Fit the multinomial-Poisson mixture model to data collected using survey methods such as removal sampling or double observer sampling.

Usage

multinomPois(formula, data, starts, method = "BFGS",
   se = TRUE, engine=c("C","R","TMB"), ...)

Arguments

formula

double right-hand side formula for detection and abundance covariates, in that order.

data

unmarkedFrame supplying data.

starts

vector of starting values.

method

Optimization method used by optim.

se

logical specifying whether or not to compute standard errors.

engine

Either "C" to use fast C++ code or "R" to use native R code during the optimization.

...

Additional arguments to optim, such as lower and upper bounds

Details

This function takes advantage of the closed form of the integrated likelihood when a latent Poisson distribution is assumed for abundance at each site and a multinomial distribution is taken for the observation state. Many common sampling methods can be framed in this context. For example, double-observer point counts and removal sampling can be analyzed with this function by specifying the proper multinomial cell probablilities. This is done with by supplying the appropriate function (piFun) argument. removalPiFun and doublePiFun are supplied as example cell probability functions.

Value

unmarkedFit object describing the model fit.

Author(s)

Ian Fiske

References

Royle, J. A. (2004). Generalized estimators of avian abundance from count survey data. Animal Biodiversity and Conservation, 27(1), 375-386.

Royle, J. A., & Dorazio, R. M. (2006). Hierarchical Models of Animal Abundance and Occurrence. Journal Of Agricultural Biological And Environmental Statistics, 11(3), 249.

See Also

piFuns, unmarkedFrameMPois

Examples

# Simulate independent double observer data
nSites <- 50
lambda <- 10
p1 <- 0.5
p2 <- 0.3
cp <- c(p1*(1-p2), p2*(1-p1), p1*p2)
set.seed(9023)
N <- rpois(nSites, lambda)
y <- matrix(NA, nSites, 3)
for(i in 1:nSites) {
  y[i,] <- rmultinom(1, N[i], c(cp, 1-sum(cp)))[1:3]
}

# Fit model
observer <- matrix(c('A','B'), nSites, 2, byrow=TRUE)
umf <- unmarkedFrameMPois(y=y, obsCovs=list(observer=observer),
    type="double")
fm <- multinomPois(~observer-1 ~1, umf)

# Estimates of fixed effects
e <- coef(fm)
exp(e[1])
plogis(e[2:3])

# Estimates of random effects
re <- ranef(fm, K=20)
#ltheme <- canonical.theme(color = FALSE)
#lattice.options(default.theme = ltheme)
plot(re, layout=c(10,5))



## Real data
data(ovendata)
ovenFrame <- unmarkedFrameMPois(ovendata.list$data,
    siteCovs=as.data.frame(scale(ovendata.list$covariates[,-1])),
    type = "removal")
(fm1 <- multinomPois(~ 1 ~ ufc + trba, ovenFrame))

# Detection probability for a single pass
backTransform(fm1, type="det")

# Detection probability after 4 removal passes
rowSums(getP(fm1))

# Empirical Bayes estimates of abundance at first 25 sites
# Very low uncertainty because p is very high
plot(ranef(fm1, K=10), layout=c(10,7), xlim=c(-1, 10))