# family.mgcv

##### Distribution families in mgcv

As well as the standard families documented in `family`

(see also `glm`

) which can be used with functions `gam`

, `bam`

and `gamm`

, `mgcv`

also supplies some extra families, most of which are currently only usable with `gam`

, although some can also be used with `bam`

. These are described here.

- Keywords
- models, regression

##### Details

The following families are in the exponential family given the value of a single parameter. They are usable with all modelling functions.

`Tweedie`

An exponential family distribution for which the variance of the response is given by the mean response to the power`p`

.`p`

is in (1,2) and must be supplied. Alternatively, see`tw`

to estimate`p`

(`gam`

only).`negbin`

The negative binomial. Alternatively see`nb`

to estimate the`theta`

parameter of the negative binomial (`gam`

only).

The following families are for regression type models dependent on a single linear predictor, and with a log likelihood
which is a sum of independent terms, each coprresponding to a single response observation. Usable with `gam`

, with smoothing parameter estimation by `"REML"`

or `"ML"`

(the latter does not integrate the unpenalized and parameteric effects out of the marginal likelihood optimized for the smoothing parameters). Also usable with `bam`

.

`ocat`

for ordered categorical data.`tw`

for Tweedie distributed data, when the power parameter relating the variance to the mean is to be estimated.`nb`

for negative binomial data when the`theta`

parameter is to be estimated.`betar`

for proportions data on (0,1) when the binomial is not appropriate.`scat`

scaled t for heavy tailed data that would otherwise be modelled as Gaussian.`ziP`

for zero inflated Poisson data, when the zero inflation rate depends simply on the Poisson mean.

The following families implement more general model classes. Usable only with `gam`

and only with REML smoothing parameter estimation.

`cox.ph`

the Cox Proportional Hazards model for survival data.`gaulss`

a Gaussian location-scale model where the mean and the standard deviation are both modelled using smooth linear predictors.`gevlss`

a generalized extreme value (GEV) model where the location, scale and shape parameters are each modelled using a linear predictor.`ziplss`

a `two-stage' zero inflated Poisson model, in which 'potential-presence' is modelled with one linear predictor, and Poisson mean abundance given potential presence is modelled with a second linear predictor.`mvn`

: multivariate normal additive models.`multinom`

: multinomial logistic regression, for unordered categorical responses.

##### References

Wood, S.N., N. Pya and B. Saefken (2016), Smoothing parameter and model selection for general smooth models. Journal of the American Statistical Association 111, 1548-1575 http://dx.doi.org/10.1080/01621459.2016.1180986

*Documentation reproduced from package mgcv, version 1.8-31, License: GPL (>= 2)*