mgcv (version 1.8-40)

# family.mgcv: Distribution families in mgcv

## Description

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.

## Author

Simon N. Wood (s.wood@r-project.org) & Natalya Pya

## 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.

• `gammals` a gamma location-scale model, where the mean and standared deviation are modelled with separate linear predictors.

• `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.

• `gumbls` a Gumbel location-scale model (2 linear predictors).

• `shash` Sinh-arcsinh location scale and shape model family (4 linear predicors).

• `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 tools:::Rd_expr_doi("10.1080/01621459.2016.1180986")