quasibinomialff {VGAM} | R Documentation |
Family function for fitting generalized linear models to binomial responses, where the dispersion parameters are unknown.
quasibinomialff(link = "logit", mv = FALSE, onedpar = !mv, parallel = FALSE, zero = NULL)
link |
Link function. See |
mv |
Multivariate response? If If |
onedpar |
One dispersion parameter? If |
parallel |
A logical or formula. Used only if |
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. |
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).
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as
vglm
,
vgam
,
rrvglm
,
cqo
,
and cao
.
If mv
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 mv
is TRUE
, then the matrix response can only be of
one format: a matrix of 1's and 0's (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.
Thomas W. Yee
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.
binomialff
,
rrvglm
,
cqo
,
cao
,
logit
,
probit
,
cloglog
,
cauchit
,
poissonff
,
quasipoissonff
,
quasibinomial
.
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="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) ## 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