R: Poisson Family Function

poissonff {VGAM} | R Documentation

## Poisson Family Function

### Description

Family function for a generalized linear model fitted to Poisson responses. The dispersion parameters may be known or unknown.

### Usage

    poissonff(link = "loge", dispersion = 1, onedpar = FALSE, imu = NULL,
              imethod = 1, parallel = FALSE, zero = NULL, bred = FALSE,
              earg.link = FALSE, type.fitted = c("mean", "quantiles"),
                           percentiles = c(25, 50, 75))

### Arguments

`link` | Link function applied to the mean or means. See `Links` for more choices and information.
`dispersion` | Dispersion parameter. By default, maximum likelihood is used to estimate the model because it is known. However, the user can specify `dispersion = 0` to have it estimated, or else specify a known positive value (or values if the response is a matrix—one value per column).
`onedpar` | One dispersion parameter? If the response is a matrix, then a separate dispersion parameter will be computed for each response (column), by default. Setting `onedpar=TRUE` will pool them so that there is only one dispersion parameter to be estimated.
`parallel` | A logical or formula. Used only if the response is a matrix.
`imu, imethod` | See `CommonVGAMffArguments` for more information.
`zero` | Can be an integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The values must be from the set {1,2,...,M}, where M is the number of columns of the matrix response. See `CommonVGAMffArguments` for more information.
`bred, earg.link` | Details at `CommonVGAMffArguments`. Setting `bred = TRUE` should work for multiple responses and all VGAM link functions; it has been tested for `loge`, `identity` but further testing is required.
`type.fitted, percentiles` | Details at `CommonVGAMffArguments`.

### Details

M defined above is the number of linear/additive predictors.

If the dispersion parameter is unknown, then the resulting estimate is not fully a maximum likelihood estimate.

A dispersion parameter that is less/greater than unity corresponds to under-/over-dispersion relative to the Poisson model. Over-dispersion is more common in practice.

When fitting a Quadratic RR-VGLM (see `cqo`), the response is a matrix of M, say, columns (e.g., one column per species). Then there will be M dispersion parameters (one per column of the response matrix) if `dispersion = 0` and `onedpar = FALSE`.

### Value

An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm`, `vgam`, `rrvglm`, `cqo`, and `cao`.

### Warning

With multiple responses, assigning a known dispersion parameter for each response is not handled well yet. Currently, only a single known dispersion parameter is handled well.

### Note

This function will handle a matrix response automatically.

The call `poissonff(dispersion=0, ...)` is equivalent to `quasipoissonff(...)`. The latter was written so that R users of `quasipoisson()` would only need to add a “`ff`” to the end of the family function name.

Regardless of whether the dispersion parameter is to be estimated or not, its value can be seen from the output from the `summary()` of the object.

### Author(s)

Thomas W. Yee

### References

McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.

### See Also

`Links`, `quasipoissonff`, `genpoisson`, `zipoisson`, `pospoisson`, `oipospoisson`, `otpospoisson`, `skellam`, `mix2poisson`, `cens.poisson`, `ordpoisson`, `amlpoisson`, `inv.binomial`, `simulate.vlm`, `loge`, `polf`, `rrvglm`, `cqo`, `cao`, `binomialff`, `quasibinomialff`, `poisson`, `poisson.points`, `ruge`, `V1`.

### Examples

    poissonff()

    set.seed(123)
    pdata <- data.frame(x2 = rnorm(nn <- 100))
    pdata <- transform(pdata, y1 = rpois(nn, exp(1 + x2)),
                              y2 = rpois(nn, exp(1 + x2)))
    (fit1 <- vglm(cbind(y1, y2) ~ x2, poissonff, data = pdata))
    (fit2 <- vglm(y1 ~ x2, poissonff(bred = TRUE), data = pdata))
    coef(fit1, matrix = TRUE)
    coef(fit2, matrix = TRUE)

    nn <- 200
    cdata <- data.frame(x2 = rnorm(nn), x3 = rnorm(nn), x4 = rnorm(nn))
    cdata <- transform(cdata, lv1 = 0 + x3 - 2*x4)
    cdata <- transform(cdata, lambda1 = exp(3 - 0.5 *  (lv1-0)^2),
                              lambda2 = exp(2 - 0.5 *  (lv1-1)^2),
                              lambda3 = exp(2 - 0.5 * ((lv1+4)/2)^2))
    cdata <- transform(cdata, y1 = rpois(nn, lambda1),
                              y2 = rpois(nn, lambda2),
                              y3 = rpois(nn, lambda3))
    ## Not run:  lvplot(p1, y = TRUE, lcol = 2:4, pch = 2:4, pcol = 2:4, rug = FALSE)

[Package VGAM version 1.0-3 Index]