quasibinomialff: 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", mv = FALSE, onedpar = !mv,
                parallel = FALSE, zero = NULL)

Arguments

link

Link function. See Links for more choices.

Multivariate response? 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 FALS

onedpar

One dispersion parameter? If mv, 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 estimat

parallel

A logical or formula. Used only if mv 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

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.

Value

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

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 mv=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).

References

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

Examples

Run this code

quasibinomialff()
quasibinomialff(link="probit")

# Nonparametric logistic regression
data(hunua)
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)
plot(fit2, se=TRUE, llwd=2, lcol="red", scol="red",
     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)
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

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