| enrich.family {enrichwith} | R Documentation |
Enrich objects of class family
Description
Enrich objects of class family with family-specific
mathematical functions
Usage
## S3 method for class 'family'
enrich(object, with = "all", ...)
Arguments
object |
an object of class |
with |
a character vector with enrichment options for |
... |
extra arguments to be passed to the |
Details
family objects specify characteristics of the
models used by functions such as glm. The
families implemented in the stats package include
binomial, gaussian,
Gamma, inverse.gaussian,
and poisson, which are all special cases of
the exponential family of distributions that have probability mass
or density function of the form
f(y; \theta, \phi) =
\exp\left\{\frac{y\theta - b(\theta) - c_1(y)}{\phi/m} -
\frac{1}{2}a\left(-\frac{m}{\phi}\right) + c_2(y)\right\} \quad y
\in Y \subset \Re\,, \theta \in \Theta \subset \Re\, , \phi >
0
where m > 0 is an observation
weight, and a(.), b(.),
c_1(.) and c_2(.) are sufficiently
smooth, real-valued functions.
The current implementation of family objects
includes the variance function (variance), the deviance
residuals (dev.resids), and the Akaike information criterion
(aic). See, also family.
The enrich method can further enrich exponential
family distributions with \theta in
terms of \mu (theta), the functions
b(\theta) (bfun), c_1(y)
(c1fun), c_2(y) (c2fun),
a(\zeta) (fun), the first two derivatives of
V(\mu) (d1variance and d2variance,
respectively), and the first four derivatives of
a(\zeta) (d1afun, d2afun,
d3afun, d4afun, respectively).
Corresponding enrichment options are also avaialble for
quasibinomial,
quasipoisson and wedderburn
families.
The quasi families are enriched with
d1variance and d2variance.
See enrich.link-glm for the enrichment of
link-glm objects.
Value
The object object of class family with
extra components. get_enrichment_options.family()
returns the components and their descriptions.
See Also
Examples
## An example from ?glm to illustrate that things still work with
## enriched families
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
print(d.AD <- data.frame(treatment, outcome, counts))
glm.D93 <- glm(counts ~ outcome + treatment, family = enrich(poisson()))
anova(glm.D93)
summary(glm.D93)