jointNmix {jointNmix}

Joint N-mixture models

Description

Fits joint N-mixture models for site-associated species

Usage

jointNmix(sp1, sp2, start, method = "BFGS", K, mixture = c("P", "P"), 
          Xp1, Xp2, Xl1, Xl2, Xpsi, includepsi = TRUE)

Arguments

sp1

observation matrix for species 1

sp2

observation matrix for species 2

start

initial values for the optimization process

method

optimization method passed to optim. Defaults to "BFGS"

K

truncation number of the infinite summations in the log-likelihood. Defaults to max(sp1, sp2) + 100

mixture

two-character vector for latent abundance distributions. "P" for Poisson and "NB" for negative binomial. Defaults to c("P","P")

Xp1

model matrix for detection probabilities of species 1

Xp2

model matrix for detection probabilities of species 2

Xl1

model matrix for abundance of species 1

Xl2

model matrix for linking parameter of species 2

Xpsi

model matrix for abundance of species 2

includepsi

logical. If FALSE, psi is not estimated and set to zero

Details

The function fits a bivariate extension to Royle's (2004) N-mixture model to data on the abundance of two species collected at R sites over T time occasions. The model for observation on site i at time t for species 1 can be specified as

Y_{1it}|N_{1i} ~ Bin(N_{1i},p_{1it})

N_{1i} ~ a count distribution with mean \lambda_{1i}.

The model for species 2 is

Y_{2it}|N_{1i},N_{2i} ~ Bin(N_{2i},p_{2it})

N_{2i}|N_{1i} ~ a count distribution with mean \psi+\lambda_{2i}N_{1i}.

Here, users may define a Poisson or negative binomial distribution for the latent abundances N_1i and N_2i.

Value

An object of class jointNmix and Nmix, for which many methods are available (see methods(class = "jointNmix") and methods(class = "Nmix"))

Author(s)

Rafael A. Moral <[e-mail]>, Clarice G. B. Demétrio and John Hinde

References

Moral, R.A., Hinde, J., Demétrio, C.G.B., Reigada, C. and Godoy, W.A.C. (submitted) Models for jointly estimating abundance of two unmarked site-associated species subject to imperfect detection.

See Also

Nmix

Examples

## simulating data with poisson latent abundances
R <- 10 # sites
T <- 10 # time occasions
lambda1 <- 5
psi <- 3
p1 <- .3
p2 <- .6
lambda2 <- .5
set.seed(1234); N1 <- rpois(R, lambda1)
set.seed(1234); N2 <- rpois(R, psi + lambda2*N1)
y1 <- y2 <- matrix(0, ncol=T, nrow=R)
set.seed(1234); for(i in 1:R) y1[,i] <- rbinom(T, N1, p1)
set.seed(1234); for(i in 1:R) y2[,i] <- rbinom(T, N2, p2)

Xp <- cbind(rep(1, R*T))
Xl <- cbind(rep(1, R))

## Not run: 
## fitting the Poisson-Poisson joint N-mixture model
fitpp <- jointNmix(y1, y2, Xp1=Xp, Xp2=Xp, Xl1=Xl, Xl2=Xl, mixture=c("P","P"), K=30)

## fitting the negbin-Poisson joint N-mixture model
fitnbp <- jointNmix(y1, y2, Xp1=Xp, Xp2=Xp, Xl1=Xl, Xl2=Xl, mixture=c("NB","P"), K=30)

## likelihood-ratio test between P-P and NB-P models
anova(fitpp, fitnbp)

## comparing using AIC
lapply(list(fitpp, fitnbp), AIC)

## conditional posterior probability functions for abundances
plot(fitpp, posterior = TRUE)

## estimated abundances vs. true abundances
data.frame(getranef.jointNmix(fitpp), N1, N2)
  
## End(Not run)