R: Distribution families in mgcv

family.mgcv {mgcv} | R Documentation

## 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`. These are described here.

### 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. See `tw` to estimate `p`.

- `negbin` The negative binomial. See `nb` to estimate the `theta` parameter of the negative binomial.

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 only 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).

- `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.

### Author(s)

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

### 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. http://arxiv.org/abs/1511.03864

[Package mgcv version 1.8-17 Index]