inv.chisq {VGAMextra} | R Documentation |
Maximum likelihood estimation of the degrees of freedom for an inverse chi–squared distribution using Fisher scoring.
inv.chisq(link = "loge", zero = NULL)
link, zero |
For further details, see
|
The inverse chi–squared distribution with df = ν ≥ 0 degrees of freedom implemented here has density
f(x; ν) = 2^(-ν / 2) x^(-ν/2 - 1) e^(-1 / (2x)) / Γ(ν / 2),
where x > 0, and
Γ is the gamma
function.
The mean of Y is 1 / (ν - 2) (returned as the fitted
values), provided ν > 2.
That is, while the expected information matrices used here are
valid in all regions of the parameter space, the regularity conditions
for maximum likelihood estimation are satisfied only if ν > 2.
To enforce this condition, choose
link = logoff(offset = -2)
.
As with, chisq
, the degrees of freedom are
treated as a parameter to be estimated using (by default) the
link loge
. However, the mean can also
be modelled with this family function.
See inv.chisqMeanlink
for specific details about this.
This family VGAM function handles multiple responses.
An object of class "vglmff"
.
See vglmff-class
for further details.
By default, the single linear/additive predictor in this family
function, say η = log (dof),
can be modeled in terms of covariates,
i.e., zero = NULL
.
To model η as intercept–only set zero = "dof"
.
See zero
for more details about this.
As with chisq
or
Chisquare
, the degrees of freedom are
non–negative but allowed to be non–integer.
V. Miranda.
loge
,
CommonVGAMffArguments
,
inv.chisqMeanlink
,
zero
.
set.seed(17010504) dof <- 2.5 yy <- rinv.chisq(100, df = dof) ics.d <- data.frame(y = yy) # The data. fit.inv <- vglm(cbind(y, y) ~ 1, family = inv.chisq, data = ics.d, trace = TRUE, crit = "coef") Coef(fit.inv) summary(fit.inv)