| Type: | Package |
| Title: | Joint N-Mixture Models for Site-Associated Species |
| Version: | 1.0 |
| Date: | 2016-10-04 |
| Author: | Rafael de Andrade Moral [aut, cre], Clarice Garcia Borges Demetrio [aut], John Hinde [aut] |
| Maintainer: | Rafael de Andrade Moral <rafael_moral@yahoo.com.br> |
| Depends: | R (≥ 3.0.0), methods, graphics, stats |
| Description: | Fits univariate and joint N-mixture models for data on two unmarked site-associated species. Includes functions to estimate latent abundances through empirical Bayes methods. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| NeedsCompilation: | no |
| Packaged: | 2016-10-05 13:55:56 UTC; rafael |
| Repository: | CRAN |
| Date/Publication: | 2016-11-12 00:38:21 |
Joint N-Mixture Models for Site-Associated Species
Description
Fits univariate and joint N-mixture models for data on two unmarked site-associated species. Includes functions to estimate latent abundances through empirical Bayes methods.
Details
The DESCRIPTION file:
| Package: | jointNmix |
| Type: | Package |
| Title: | Joint N-Mixture Models for Site-Associated Species |
| Version: | 1.0 |
| Date: | 2016-10-04 |
| Authors@R: | c(person("Rafael", "de Andrade Moral", role = c("aut", "cre"), email = "rafael_moral@yahoo.com.br"), person("Clarice", "Garcia Borges Demetrio", role = "aut"), person("John", "Hinde", role = "aut")) |
| Author: | Rafael de Andrade Moral [aut, cre], Clarice Garcia Borges Demetrio [aut], John Hinde [aut] |
| Maintainer: | Rafael de Andrade Moral <rafael_moral@yahoo.com.br> |
| Depends: | R (>= 3.0.0), methods, graphics, stats |
| Description: | Fits univariate and joint N-mixture models for data on two unmarked site-associated species. Includes functions to estimate latent abundances through empirical Bayes methods. |
| License: | GPL (>=2) |
Index of help topics:
AIC.Nmix Methods for Nmix objects
Nmix Univariate N-mixture models
dneymanA The Neyman-A probability function
fitted.jointNmix Methods for joint Nmix objects
fitted.uniNmix Methods for univariate Nmix objects
getcorr.jointNmix Extract correlations and covariances
getranef.uniNmix Get empirical Bayes predictions of the latent
abundances
jointNmix Joint N-mixture models
jointNmix-package Joint N-Mixture Models for Site-Associated
Species
plot.uniNmix Plot Methods for Nmix objects
Author(s)
Rafael de Andrade Moral [aut, cre], Clarice Garcia Borges Demetrio [aut], John Hinde [aut]
Maintainer: Rafael de Andrade Moral <rafael_moral@yahoo.com.br>
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.
Univariate N-mixture models
Description
Fits univariate N-mixture models
Usage
Nmix(sp1, start, method = "BFGS", K, mixture, Xp, Xl)
Arguments
sp1 |
observation matrix for the species |
start |
initial values for the optimization process |
method |
optimization method passed to |
K |
truncation number of the infinite summations in the log-likelihood. Defaults to |
mixture |
latent abundance distribution specification. |
Xp |
model matrix for detection probabilities |
Xl |
model matrix for abundance parameter |
Details
The function fits Royle's (2004) N-mixture model to data on species abundance collected at R sites over T time occasions. The model for observation on site i at time t can be specified as
Y_{it}|N_i ~ Bin(N_i,p_{it})
N_i ~ a count distribution with mean \lambda_i.
Here, users may define a Poisson, negative binomial or Neyman-A distributions for the latent abundances N_i.
Value
An object of class uniNmix and Nmix, for which many methods are available (see methods(class = "uniNmix") and methods(class = "Nmix"))
Author(s)
Rafael A. Moral <rafael_moral@yahoo.com.br>, Clarice G. B. Demétrio and John Hinde
References
Royle, J.A. (2004) Models for estimating population size from spatially replicated counts. Biometrics 60:108-105.
See Also
Examples
## simulating data with negative binomial latent abundances
R <- 10 # sites
T <- 10 # time occasions
lambda <- 5 # abundance parameter
p <- .3 # probability of detection
phi <- 1 # dispersion parameter
set.seed(1234); Ni <- rnbinom(R, mu=lambda, size=phi) # latent abundances
y <- matrix(0, ncol=T, nrow=R)
set.seed(1234); for(i in 1:R) y[,i] <- rbinom(T, Ni, p) # observed abundances
## fitting the Poisson N-mixture model
fitp <- Nmix(y, Xp=cbind(rep(1, R*T)), Xl=cbind(rep(1, R)), mixture="P", K=25)
## fitting the negative binomial N-mixture model
fitnb <- Nmix(y, Xp=cbind(rep(1, R*T)), Xl=cbind(rep(1, R)), mixture="NB", K=25)
## fitting the Neyman-A N-mixture model
fitna <- Nmix(y, Xp=cbind(rep(1, R*T)), Xl=cbind(rep(1, R)), mixture="NeymanA", K=25)
## likelihood-ratio test between Poisson and negbin models
anova(fitp, fitnb)
## comparing using AIC
lapply(list(fitp, fitnb, fitna), AIC)
## conditional posterior probability functions for abundances
plot(fitnb, posterior = TRUE)
## estimated abundances vs. true abundances
data.frame(getranef.uniNmix(fitnb), Ni)
Methods for Nmix objects
Description
AIC, anova, coef, and logLik methods for univariate and joint N-mixture models
Usage
## S3 method for class 'Nmix'
AIC(object, ...)
## S3 method for class 'Nmix'
anova(object, object2, ...)
## S3 method for class 'Nmix'
coef(object, ...)
## S3 method for class 'Nmix'
logLik(object, ...)
Arguments
object |
fitted model object |
object2 |
second model object for the |
... |
not used |
Details
AIC.Nmix provides the Akaike Information Criterion for the model fit; anova.Nmix performs a likelihood-ratio test between two nested model fits; coef.Nmix prints the estimates of the model fit; logLik.Nmix prints the log-likelihood of the model fit.
Author(s)
Rafael A. Moral <rafael_moral@yahoo.com.br>, Clarice G. B. Demétrio and John Hinde
See Also
Get empirical Bayes predictions of the latent abundances
Description
Computes the conditional abundance distribution given the data and model estimates
Usage
getranef.uniNmix(obj, distr = FALSE)
getranef.jointNmix(obj, distr = FALSE)
Arguments
obj |
fitted model object |
distr |
logical. If TRUE, returns the matrix of conditional probabilities. If FALSE, returns the expected values of the conditional distributions, i.e. the abundance estimates |
Details
These functions returnt the empirical Bayes estimates of the latent abundances from univariate and joint N-mixture models, as described by Royle (2004) and Moral et al. (submitted), respectively.
Author(s)
Rafael A. Moral <rafael_moral@yahoo.com.br>, Clarice G. B. Demétrio and John Hinde
References
Royle, J.A. (2004) Models for estimating population size from spatially replicated counts. Biometrics 60:108-105.
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
Extract correlations and covariances
Description
Extract estimated correlations and covariances between observed abundances for joint N-mixture models
Usage
getcorr.jointNmix(obj)
getcov.jointNmix(obj)
Arguments
obj |
fitted model object |
Details
The correlations under each specification of the latent abundance distributions are displayed in Moral et al. (submitted)'s Table 1. The covariances are derived as Supplementary information.
Author(s)
Rafael A. Moral <rafael_moral@yahoo.com.br>, 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
The Neyman-A probability function
Description
Computes the probability function of the Neyman-A distribution
Usage
dneymanA(x, lambda1, lambda2, K, log = FALSE)
Arguments
x |
vector of values |
lambda1, lambda2 |
parameters of the distribution |
K |
truncation value for the infinite summation |
log |
logical. If TRUE, the logarithm of the probabilities is returned |
Details
The Neyman-A distribution has probability function
\frac{e^{-\lambda_1}\lambda_2^{x}}{x!}\sum_{k=0}^\infty\frac{(\lambda_1e^{-\lambda_2})^kk^x}{k!}
and is an overdispersion model. The summation is truncated to K.
Author(s)
Rafael A. Moral <rafael_moral@yahoo.com.br>, Clarice G. B. Demétrio and John Hinde
Examples
x <- 0:10
dneymanA(x, lambda1 = 2, lambda2 = 1.5, K = 50)
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 |
K |
truncation number of the infinite summations in the log-likelihood. Defaults to |
mixture |
two-character vector for latent abundance distributions. |
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 <rafael_moral@yahoo.com.br>, 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
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)
Methods for joint Nmix objects
Description
Fitted values, residual extraction, simulation and print method for joint N-mixture models
Usage
## S3 method for class 'jointNmix'
fitted(object, ...)
## S3 method for class 'jointNmix'
print(x, round = TRUE, ...)
## S3 method for class 'jointNmix'
residuals(object, type = c("ordinary", "standardized"), ...)
## S3 method for class 'jointNmix'
simulate(object, ...)
Arguments
object, x |
fitted model object |
round |
logical. Round the estimates? |
type |
type of residuals to be returned. May be ordinary or standardized |
... |
not used |
Details
fitted.uniNmix prints the fitted values for the model fit; residuals.uniNmix returns the ordinary (
r_i^o=y_i-\hat{\mu}_i
) or standardized (
r_i^s=\frac{y_i-\hat{\mu}_i}{\mbox{Var}(Y_i)}
) residuals; simulate.uniNmix simulates one sample from the fitted model.
Author(s)
Rafael A. Moral <rafael_moral@yahoo.com.br>, 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
Plot Methods for Nmix objects
Description
Plots residuals vs. fitted values or the conditional distributions of the abundances for each site
Usage
## S3 method for class 'uniNmix'
plot(x, posterior = FALSE, layout, sites, restype, ...)
## S3 method for class 'jointNmix'
plot(x, posterior = FALSE, layout, sites, restype, ...)
Arguments
x |
fitted model object |
posterior |
logical. If TRUE, plots the conditional distributions of the abundances. If FALSE, plots residuals vs. fitted values |
layout |
two-number vector indicating the partition of the graphical window in rows and columns, respectively |
sites |
index of sites to plot the conditional distribution of the abundances. If left unspecified, all sites are plotted |
restype |
type of residuals to be plotted. Defaults to "ordinary" |
... |
not used |
Author(s)
Rafael A. Moral <rafael_moral@yahoo.com.br>, 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
Methods for univariate Nmix objects
Description
Fitted values, residual extraction, simulation and print method for univariate N-mixture models
Usage
## S3 method for class 'uniNmix'
fitted(object, ...)
## S3 method for class 'uniNmix'
print(x, round = TRUE, ...)
## S3 method for class 'uniNmix'
residuals(object, type = c("ordinary", "standardized"), ...)
## S3 method for class 'uniNmix'
simulate(object, ...)
Arguments
object, x |
fitted model object |
round |
logical. Round the estimates? |
type |
type of residuals to be returned. May be ordinary or standardized |
... |
not used |
Details
fitted.uniNmix prints the fitted values for the model fit; residuals.uniNmix returns the ordinary (
r_i^o=y_i-\hat{\mu}_i
) or standardized (
r_i^s=\frac{y_i-\hat{\mu}_i}{\mbox{Var}(Y_i)}
) residuals; simulate.uniNmix simulates one sample from the fitted model.
Author(s)
Rafael A. Moral <rafael_moral@yahoo.com.br>, Clarice G. B. Demétrio and John Hinde