R: Quasi-Binomial Family Function

quasibinomialff {VGAM} | R Documentation

## Quasi-Binomial Family Function

### Description

Family function for fitting generalized linear models to binomial responses, where the dispersion parameters are unknown.

### Usage

    quasibinomialff(link = "logit", multiple.responses = FALSE,
                    onedpar = !multiple.responses, parallel = FALSE, zero = NULL)

### Arguments

`link` | Link function. See `Links` for more choices.
`multiple.responses` | Multiple responses? If `TRUE`, then the response is interpreted as M binary responses, where M is the number of columns of the response matrix. In this case, the response matrix should have zero/one values only. If `FALSE` and the response is a (2-column) matrix, then the number of successes is given in the first column and the second column is the number of failures.
`onedpar` | One dispersion parameter? If `multiple.responses`, 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 `multiple.responses` is `TRUE`. This argument allows for the parallelism assumption whereby the regression coefficients for a variable is constrained to be equal over the M linear/additive predictors.
`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.

### Details

The final model is not fully estimated by maximum likelihood since the dispersion parameter is unknown (see pp.124–8 of McCullagh and Nelder (1989) for more details).

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

Setting `multiple.responses=TRUE` is necessary when fitting a Quadratic RR-VGLM (see `cqo`) because the response will be a matrix of M columns (e.g., one column per species). Then there will be M dispersion parameters (one per column of the response).

### 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

The log-likelihood pertaining to the ordinary family is used to test for convergence during estimation, and is printed out in the summary.

### Note

If `multiple.responses` is `FALSE` (the default), then the response can be of one of three formats: a factor (first level taken as success), a vector of proportions of success, or a 2-column matrix (first column = successes) of counts. The argument `weights` in the modelling function can also be specified. In particular, for a general vector of proportions, you will need to specify `weights` because the number of trials is needed.

If `multiple.responses` is `TRUE`, then the matrix response can only be of one format: a matrix of 1s and 0s (1=success).

This function is only a front-end to the VGAM family function `binomialff()`; indeed, `quasibinomialff(...)` is equivalent to `binomialff(..., dispersion=0)`. Here, the argument `dispersion=0` signifies that the dispersion parameter is to be estimated.

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

`binomialff`, `rrvglm`, `cqo`, `cao`, `logit`, `probit`, `cloglog`, `cauchit`, `poissonff`, `quasipoissonff`, `quasibinomial`.

### Examples

    quasibinomialff()
    quasibinomialff(link = "probit")

    # Nonparametric logistic regression
    hunua <- transform(hunua, a.5 = sqrt(altitude))  # Transformation of altitude
    fit1 <- vglm(agaaus ~ poly(a.5, 2), quasibinomialff, hunua)
    fit2 <- vgam(agaaus ~ s(a.5, df = 2), quasibinomialff, hunua)
    ## Not run:
    plot(fit2, se = TRUE, llwd = 2, lcol = "orange", scol = "orange",
         xlab = "sqrt(altitude)", ylim = c(-3, 1),
         main = "GAM and quadratic GLM fitted to species data")
    plotvgam(fit1, se = TRUE, lcol = "blue", scol = "blue", add = TRUE, llwd = 2)

    ## End(Not run)
    fit1@misc$dispersion # dispersion parameter
    logLik(fit1)

    # Here, the dispersion parameter defaults to 1
    fit0 <- vglm(agaaus ~ poly(a.5, 2), binomialff, hunua)
    fit0@misc$dispersion # dispersion parameter

[Package VGAM version 1.0-3 Index]