# Univariate N-mixture models Fits univariate N-mixture models UTF-8 ```r 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 `optim`. Defaults to `"BFGS"` - `K`: truncation number of the infinite summations in the log-likelihood. Defaults to `max(sp1, sp2) + 100` - `mixture`: latent abundance distribution specification. `"P"` for Poisson, `"NB"` for negative binomial and `"NeymanA"` for Neyman-A distributions are available. Defaults to `"P"` - `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. ## Returns An object of class `uniNmix` and `Nmix`, for which many methods are available (see `methods(class = "uniNmix")` and `methods(class = "Nmix")`) ## References Royle, J.A. (2004) Models for estimating population size from spatially replicated counts. Biometrics 60:108-105. ## Author(s) Rafael A. Moral , Clarice G. B. and John Hinde## See Also `jointNmix` ## Examples ```r ## 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) ```

Nmix function