VGAM (version 1.0-4)

quasibinomialff: Quasi-Binomial Family Function


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


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



Link function. See Links for more choices.


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.


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.


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.


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.


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


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


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).


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.


Run this code
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)
# }
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)
# }
fit1@misc$dispersion # dispersion parameter

# 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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