FWIW p. 206 of the White Book gives the following for
names(binomial()): family, names, link, inverse, deriv, initialize,
variance, deviance, weight.
So $aic wasn't there In The Beginning. I haven't done any more
archaeology to try to figure out when/by whom it was first introduced
...
Section 6.3.3, on extending families, doesn't give any other relevant info.
A patch for src/library/stats/man/family.Rd below: please check what
I've said about $aic and $mu.eta to make sure they're correct! I can
submit this to the r bug list if preferred.
Index: family.Rd
===
--- family.Rd(revision 74904)
+++ family.Rd(working copy)
@@ -31,7 +31,7 @@
\arguments{
\item{link}{a specification for the model link function. This can be
a name/expression, a literal character string, a length-one character
-vector or an object of class
+vector, or an object of class
\code{"\link[=make.link]{link-glm}"} (such as generated by
\code{\link{make.link}}) provided it is not specified
\emph{via} one of the standard names given next.
@@ -45,7 +45,7 @@
the \code{Gamma} family the links \code{inverse}, \code{identity}
and \code{log};
the \code{poisson} family the links \code{log}, \code{identity},
-and \code{sqrt} and the \code{inverse.gaussian} family the links
+and \code{sqrt}; and the \code{inverse.gaussian} family the links
\code{1/mu^2}, \code{inverse}, \code{identity}
and \code{log}.
@@ -105,8 +105,8 @@
\note{
The \code{link} and \code{variance} arguments have rather awkward
semantics for back-compatibility. The recommended way is to supply
- them is as quoted character strings, but they can also be supplied
- unquoted (as names or expressions). In addition, they can also be
+ them as quoted character strings, but they can also be supplied
+ unquoted (as names or expressions). Additionally, they can be
supplied as a length-one character vector giving the name of one of
the options, or as a list (for \code{link}, of class
\code{"link-glm"}). The restrictions apply only to links given as
@@ -130,10 +130,18 @@
\item{dev.resids}{function giving the deviance residuals as a function
of \code{(y, mu, wt)}.}
\item{aic}{function giving the AIC value if appropriate (but \code{NA}
-for the quasi- families). See \code{\link{logLik}} for the assumptions
- made about the dispersion parameter.}
- \item{mu.eta}{function: derivative \code{function(eta)}
-\eqn{d\mu/d\eta}.}
+for the quasi- families). More precisely, this function
+returns \eqn{-2 L + 2 s}, where \eqn{L} is the log-likelihood and \eqn{s}
+is the number of estimated scale parameters; the penalty term for the
+location parameters is added elsewhere.
+See \code{\link{logLik}} for the assumptions
+made about the dispersion parameter.}
+ \item{mu.eta}{function: derivative of the inverse-link function
+with respect to the linear predictor. If the inverse-link
+function is \eqn{\mu=g^{-1}(\eta)}{mu=ginv(eta)}
+where \eqn{eta}{\eta} is the value
+of the linear predictor, then this function returns
+\eqn{d(g^{-1})/d\eta=d\mu/d\eta}{d(ginv(eta))/d(eta)=d(mu)/d(eta)}.}
\item{initialize}{expression. This needs to set up whatever data
objects are needed for the family as well as \code{n} (needed for
AIC in the binomial family) and \code{mustart} (see \code{\link{glm}}).}
@@ -224,8 +232,8 @@
## which case use an offset of 0 in the corresponding formula
## to get the null deviance right.
-## Binomial with identity link: often not a good idea.
-\dontrun{binomial(link = make.link("identity"))}
+## Binomial with identity link: often computationally and
conceptually difficult
+\dontrun{binomial(link = "identity")}
## tests of quasi
x <- rnorm(100)
@@ -236,7 +244,7 @@
glm(y ~ x, family = quasi(variance = "mu^2", link = "log"))
\dontrun{glm(y ~ x, family = quasi(variance = "mu^3", link = "log")) # fails}
y <- rbinom(100, 1, plogis(x))
-# needs to set a starting value for the next fit
+# need to set a starting value for the next fit
glm(y ~ x, family = quasi(variance = "mu(1-mu)", link = "logit"),
start = c(0,1))
}
\keyword{models}
On Mon, Jun 4, 2018 at 10:46 AM, Martin Maechler
wrote:
>> Ben Bolker
>> on Sun, 3 Jun 2018 17:33:18 -0400 writes:
>
> > Is it generally known/has it been previously discussed here that the
> > $aic() component in GLM-family objects (e.g. results of binomial(),
> > poisson(), etc.) does not as implemented actually return the AIC, but
> > rather -2*log-likelihood + 2*(model_has_scale_parameter) ?
>
> This rings a faint bell from the last millennium with me,
> and the following "fortune" may contain the answer implicitly :
>
>
> > if(!require("fortunes")) install.packages("fortunes")
> > fortune("bug compatib")
>
> F
