Maximum likelihood estimation of the degrees of freedom for an inverse chi–squared distribution using Fisher scoring.
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
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).
chisq, the degrees of freedom are
treated as a parameter to be estimated using (by default) the
loglink. However, the mean can also
be modelled with this family function.
for specific details about this.
This family VGAM function handles multiple responses.
An object of class
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,
zero = NULL.
To model η as intercept–only set
zero = "dof".
zero for more details about this.
Chisquare, the degrees of freedom are
non–negative but allowed to be non–integer.
1 2 3 4 5 6 7 8 9 10 11
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.