inla.nmix.lambda.fitted {INLA} | R Documentation

## Estimate posterior distributions of fitted lambda values

### Description

For use with `'nmix'` and `'nmixnb'` models. This function takes the information contained in an object returned by `inla()` and uses the contents to create fitted lambda values using the linear predictor for log(lambda), the input covariate values, and samples from the posteriors of the model hyperparameters. Fitted values from the linear predictor are exponentiated, by default, before being returned.

### Usage

    inla.nmix.lambda.fitted(
      result,
      sample.size = 1000,
      return.posteriors = FALSE,
      scale = "exp"
    )

### Arguments

`result` | The output object from a call to `inla()`, where the family argument has been set to `'nmix'` or `'nmixnb'`. For the function to work, the call to `inla()` should also include the argument `⁠control.compute=list(config = TRUE))⁠`.
`sample.size` | The size of the sample from the posteriors of the model hyperparameters. This sample size ends up being the size of the estimated posterior for a fitted lambda value. Default is 1000. Larger values are recommended.
`return.posteriors` | A logical value for whether or not to return the full estimated posteriors for each fitted value (`TRUE`), or just a summary of the posteriors (`FALSE`). Default is `FALSE`.
`scale` | A character string, where the default string, `"exp"`, causes values from the linear predictor to be exponentiated before being returned. The string, `"log"`, causes values to be returned on the `log(lambda)` scale.

### Value

`fitted.summary` | A data frame with summaries of estimated posteriors of fitted lambda values. The number of rows equals the number of rows in the data used to create the `'nmix'` or `'nmixnb'` model. There are six columns of summary statistics for each estimated posterior. Columns include an `index`, `mean.lambda`, `sd.lambda`, `quant025.lambda`, `median.lambda`, `quant975.lambda`, and `mode.lambda`.
`fitted.posteriors` | A data frame containing samples that comprise the full estimated posteriors of fitted values. The number of rows equals the number of rows in the data used to create the `'nmix'` or `'nmixnb'` model. The number of columns equals one plus the number of samples specified by the `sample.size` argument.

### Note

This function is experimental.

### Author(s)

Tim Meehan tmeehan@audubon.org

### References

See documentation for families "nmix" and "nmixmb": `inla.doc("nmix")`

### Examples

    ## an example analysis of an N-mixture model using simulated data
    ## set parameters
    n <- 75                       # number of study sites
    nrep.max <- 5                 # number of surveys per site
    b0 <- 0.5                     # lambda intercept, expected abundance
    b1 <- 2.0                     # effect of x1 on lambda
    a0 <- 1.0                     # p intercept, detection probability
    a2 <- 0.5                     # effect of x2 on p
    size <- 3.0                   # size of theta
    overdispersion <- 1 / size    # for negative binomial distribution

    ## make empty vectors and matrix
    x1 <- c(); x2 <- c()
    lambdas <- c(); Ns <- c()
    y <- matrix(NA, n, nrep.max)

    ## fill vectors and matrix
    for(i in 1:n) {
        x1.i <- runif(1) - 0.5
        lambda <- exp(b0 + b1 * x1.i)
        N <- rnbinom(1, mu = lambda, size = size)
        x2.i <- runif(1) - 0.5
        eta <- a0 + a2 * x2.i
        p <- exp(eta) / (exp(eta) + 1)
        nr <- sample(1:nrep.max, 1)
        y[i, 1:nr] <- rbinom(nr, size = N, prob = p)
        x1 <- c(x1, x1.i); x2 <- c(x2, x2.i)
        lambdas <- c(lambdas, lambda); Ns <- c(Ns, N)
    }

    ## bundle counts, lambda intercept, and lambda covariates
    Y <- inla.mdata(y, 1, x1)

    ## run inla and summarize output
    result <- inla(Y ~ 1 + x2,
      data = list(Y=Y, x2=x2),
      family = "nmixnb",
      control.fixed = list(mean = 0, mean.intercept = 0, prec = 0.01,
                          prec.intercept = 0.01),
      control.family = list(hyper = list(theta1 = list(param = c(0, 0.01)),
                                        theta2 = list(param = c(0, 0.01)),
                                        theta3 = list(prior = "flat",
                                                     param = numeric()))),
      control.compute=list(config = TRUE)) # important argument
    summary(result)

    ## get and evaluate fitted values
    lam.fits <- inla.nmix.lambda.fitted(result, 5000)$fitted.summary
    plot(lam.fits$median.lambda, lambdas)
    round(sum(lam.fits$median.lambda), 0); sum(Ns)

[Package INLA version 26.02.05 Index]