multinomPois {unmarked} | R Documentation

## 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, ...)

### 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.
`...` | 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))

[Package unmarked version 0.12-3 Index]