binomialff {VGAM} | R Documentation |
Family function for fitting generalized linear models to binomial responses, where the dispersion parameter may be known or unknown.
binomialff(link = "logit", earg = list(), dispersion = 1, mv = FALSE, onedpar = !mv, parallel = FALSE, zero = NULL)
The notation M is used to denote the number of linear/additive predictors.
link |
Link function. See Links for more choices.
|
earg |
Extra argument optionally used by the link function.
See Links for more 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 mv is TRUE ).
|
mv |
Multivariate response? If TRUE , then the response is interpreted
as M independent 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 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 estimated.
|
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.
|
If the dispersion parameter is unknown, then the resulting estimate is not fully a maximum likelihood estimate (see pp.124–8 of McCullagh and Nelder, 1989).
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 is a matrix of M
columns (e.g., one column per species). Then there will be M
dispersion parameters (one per column of the response matrix).
When used with cqo
and cao
, it may be
preferable to use the cloglog
link.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as
vglm
,
vgam
,
rrvglm
,
cqo
,
and cao
.
With a multivariate response, assigning a known dispersion parameter for each response is not handled well yet. Currently, only a single known dispersion parameter is handled well.
If mv
is FALSE
(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).
The call binomialff(dispersion=0, ...)
is equivalent to
quasibinomialff(...)
. The latter was written so that R users
of quasibinomial()
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.
Thomas W. Yee
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.
quasibinomialff
,
Links
,
rrvglm
,
cqo
,
cao
,
zibinomial
,
dexpbinomial
,
mbinomial
,
seq2binomial
,
amlbinomial
,
binomial
.
quasibinomialff() quasibinomialff(link="probit") data(hunua) fit = vgam(agaaus ~ poly(altitude, 2), binomialff(link=cloglog), hunua) ## Not run: attach(hunua) plot(altitude, agaaus, col="blue", ylab="P(agaaus=1)", main="Presence/absence of Agathis australis", las=1) o = order(altitude) lines(altitude[o], fitted(fit)[o], col="red", lwd=2) detach(hunua) ## End(Not run)