MNM_AR: Fit a Multi-Species N-Mixture Model with AR-1 Using Nimble

Description

Fits a multi-species N-mixture (MNM) model with an autoregressive component (AR-1) using Nimble. This model is suitable for time-series data collected over long periods and includes covariates for abundance and detection probability.

Usage

MNM_AR(
  Y = NULL,
  iterations = 60000,
  burnin = 20000,
  thin = 10,
  Xp = NULL,
  Xn = NULL,
  verbose = TRUE,
  ...
)

Value

An MNM object that contains the following components:

summary: Nimble model summary (mean, standard deviation, standard error, quantiles, effective sample size and Rhat value for all monitored values).
n_parameters: Number of parameters in the model (for use in calculating information criteria).
data: Observed abundances.
fitted_Y:Predicted values for Y: posterior predictive checks can be performed by comparing fitted_Y with the observed data.
logLik:Log-likelihood of the observed data (Y) given the model parameters.
n_converged: Number of parameters with successful convergence (Rhat < 1.1).
plot: traceplots and density plots for all monitored variables.

Arguments

Y

Array of observed counts, with dimensions (R, T, S, K), where:

R: Number of sites.
T: Number of repeated counts (replicates).
S: Number of species.
K: Number of time points.

iterations

Integer. Number of MCMC iterations to run. Defaults to 60,000.

burnin

Integer. Number of iterations to discard as burn-in. Defaults to 20,000.

thin

Integer. Thinning interval for saving MCMC samples. Defaults to 10.

Xp

Array of detection covariates with dimensions (R, S, P1), where:

R: Number of sites.
S: Number of species.
P1: Number of detection probability covariates.

Xn

Array of abundance covariates with dimensions (R, S, K, P2), where:

R: Number of sites.
S: Number of species.
K: Number of time points.
P2: Number of abundance covariates.

verbose

Control the level of output displayed during function execution. Default is TRUE.

...

Additional arguments passed for prior distribution specification. Supported distributions include dnorm, dexp, dgamma, dbeta, dunif, dlnorm, dbern, dpois, dbinom, dcat, dmnorm, dwish, dchisq, dinvgamma, dt, dweib, ddirch, dmulti, dmvt. Default prior distributions are:

prior_detection_probability: prior distribution for the detection probability intercept (gamma). Default is 'dnorm(0, 0.001)'.
prior_precision: prior distribution for the precision matrix for the species-level random effect. Default is 'dwish(Omega[1:S,1:S], df)'.
prior_mean: prior distribution for the mean of the species-level random effect (mu). Default is 'dnorm(0,0.001)'.
prior_hurdle: prior distribution for theta, the probability of structural zero in hurdle models. Default is 'dbeta(1,1)'.
prior_mean_AR: prior distribution for the mean of the autoregressive random effect (phi). Default is 'dnorm(0,0.001)'.
prior_sd_AR: prior distribution for the standard deviation of the autoregressive random effect (phi). Default is 'dexp(1)'.

See Nimble (r-nimble.org) documentation for distribution details.

Details

The model incorporates temporal and species-level covariates and accounts for serial correlation in abundance using an AR(1) process. The input data should be structured as an array with dimensions (R,T,S,K). See parameter descriptions for details.

Features include:

Posterior predictive checks via predicted vs observed abundance.
Calculation of log-likelihood for model evaluation.
Automatic monitoring of parameter convergence.

References

Royle, J. A. (2004). N-mixture models for estimating population size from spatially replicated counts. Biometrics, 60(1), 108-115.
Mimnagh, N., Parnell, A., Prado, E., & Moral, R. D. A. (2022). Bayesian multi-species N-mixture models for unmarked animal communities. Environmental and Ecological Statistics, 29(4), 755-778.

Examples

Run this code

# Example 1:
Y <- array(rpois(1000, lambda = 10), dim = c(10, 10, 5, 2))
Xp <- array(runif(500), dim = c(10, 5, 2, 3))
Xn <- array(runif(1000), dim = c(10, 5, 2, 4))

# Fit the AR-1 model
result <- MNM_AR(Y = Y, Xp = Xp, Xn = Xn)
# nimble creates auxiliary functions that may be removed after model run is complete
# using rm(list = ls(pattern = "^str"))
# Check fitted vs observed abundance
plot(result@data, result@fitted_Y)

data(birds)

# Example 2: North American Breeding Bird Data
# Data must first be reformatted to an array of dimension (R,T,S,K)
R <- 15
T <- 10
S <- 10
K <- 4
# Ensure data is ordered consistently
birds <- birds[order(birds$Route, birds$Year, birds$English_Common_Name), ]

# Create a 4D array with proper dimension
Y <- array(NA, dim = c(R, T, S, K))

# Map route, species, and year to indices
route_idx <- as.numeric(factor(birds$Route))
species_idx <- as.numeric(factor(birds$English_Common_Name))
year_idx <- as.numeric(factor(birds$Year))

# Populate the array
stop_data <- as.matrix(birds[, grep("^Stop", colnames(birds))])

for (i in seq_len(nrow(birds))) {
  Y[route_idx[i], , species_idx[i], year_idx[i]] <- stop_data[i, ]
  }

  # Assign dimnames
  dimnames(Y) <- list(
    Route = sort(unique(birds$Route)),
      Stop = paste0("Stop", 1:T),
        Species = sort(unique(birds$English_Common_Name)),
          Year = sort(unique(birds$Year))
          )

# Selecting only 5 bird species  for analysis:
Y<-Y[,,1:5,]

model<-MNM_fit(Y=Y, AR=TRUE, Hurdle=FALSE, iterations=10000, burnin=2000)

Run the code above in your browser using DataLab