Description Usage Arguments Details Value See Also Examples

Enrich objects of class `family`

with family-specific
mathematical functions

1 2 |

`object` |
an object of class |

`with` |
a character vector with enrichment options for |

`...` |
extra arguments to be passed to the |

`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((y * theta - b(theta) - c_1(y))/(phi/m) -
a(-m/phi)/2 + c_2(y))*

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).

See `enrich.link-glm`

for the enrichment of
`link-glm`

objects.

The `quasi`

families are enriched with
`d1variance`

and `d2variance`

.

The object `object`

of class `family`

with
extra components. `get_enrichment_options.family()`

returns the components and their descriptions.

1 2 3 4 5 6 7 8 9 | ```
## 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)
``` |

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