poissonff {VGAM} | R Documentation |
Family function for a generalized linear model fitted to Poisson responses. The dispersion parameters may be known or unknown.
poissonff(link = "loge", earg=list(), dispersion = 1, onedpar = FALSE, parallel = FALSE, zero = NULL)
link |
Link function applied to the mean or means.
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 the response
is a matrix—one value per column).
|
onedpar |
One dispersion parameter? If the response is a matrix,
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 the response is a matrix.
|
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.
|
M defined above is the number of linear/additive predictors.
If the dispersion parameter is unknown, then the resulting estimate is not fully a maximum likelihood estimate.
A dispersion parameter that is less/greater than unity corresponds to under-/over-dispersion relative to the Poisson model. Over-dispersion is more common in practice.
When fitting a Quadratic RR-VGLM (see cqo
), the
response is a matrix of M, say, columns (e.g., one column
per species). Then there will be M dispersion parameters
(one per column of the response matrix) if dispersion=0
and
onedpar=FALSE
.
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.
This function will handle a matrix response automatically.
The call poissonff(dispersion=0, ...)
is equivalent to
quasipoissonff(...)
. The latter was written so that R users
of quasipoisson()
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.
Links
,
quasipoissonff
,
genpoisson
,
zipoisson
,
skellam
,
mix2poisson
,
cenpoisson
,
ordpoisson
,
amlpoisson
,
invbinomial
,
loge
,
polf
,
rrvglm
,
cqo
,
cao
,
binomialff
,
quasibinomialff
,
poisson
,
poissonp
.
poissonff() n = 100 x2 = rnorm(n) x3 = rnorm(n) x4 = rnorm(n) lv1 = 0 + x3 - 2*x4 lambda1 = exp(3 - 0.5 * (lv1-0)^2) lambda2 = exp(2 - 0.5 * (lv1-1)^2) lambda3 = exp(2 - 0.5 * ((lv1+4)/2)^2) y1 = rpois(n, lambda1) y2 = rpois(n, lambda2) y3 = rpois(n, lambda3) p1 = cqo(cbind(y1,y2,y3) ~ x2 + x3 + x4, poissonff, EqualTol=FALSE, ITol=FALSE) summary(p1) # # Three dispersion parameters are all unity ## Not run: lvplot(p1, y=TRUE, lcol=2:4, pch=2:4, pcol=2:4, rug=FALSE) ## End(Not run)