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.TweedieAn exponential family distribution for which the variance of the response is given by the mean response to the powerp.pis in (1,2) and must be supplied. Seetwto estimatep.negbinThe negative binomial. Seenbto estimate thethetaparameter 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).
ocatfor ordered categorical data.twfor Tweedie distributed data, when the power parameter relating the variance to the mean is to be estimated.nbfor negative binomial data when thethetaparameter is to be estimated.betarfor proportions data on (0,1) when the binomial is not appropriate.scatscaled t for heavy tailed data that would otherwise be modelled as Gaussian.ziPfor zero inflated Poisson data, when the zero inflation rate depends simply on the Poisson mean.gam and only with REML smoothing parameter estimation.
cox.phthe Cox Proportional Hazards model for survival data.gaulssa Gaussian location-scale model where the mean and the standard deviation are both modelled using smooth linear predictors.ziplssa `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.mvnmultivariate normal additive models.