mgcv (version 1.8-16)

gaulss: Gaussian location-scale model family

Description

The gaulss family implements Gaussian location scale additive models in which the mean and the logb of the standard deviation (see details) can depend on additive smooth predictors. Useable only with gam, the linear predictors are specified via a list of formulae.

Usage

gaulss(link=list("identity","logb"),b=0.01)

Arguments

link

two item list specifying the link for the mean and the standard deviation. See details.

b

The minumum standard deviation, for the "logb" link.

Value

An object inheriting from class general.family.

Details

Used with gam to fit Gaussian location - scale models. gam is called with a list containing 2 formulae, the first specifies the response on the left hand side and the structure of the linear predictor for the mean on the right hand side. The second is one sided, specifying the linear predictor for the standard deviation on the right hand side.

Link functions "identity", "inverse", "log" and "sqrt" are available for the mean. For the standard deviation only the "logb" link is implemented: $eta = log(sigma-b)$ and $sigma = b + exp(eta)$. This link is designed to avoid singularities in the likelihood caused by the standard deviation tending to zero.

The fitted values for this family will be a two column matrix. The first column is the mean, and the second column is the inverse of the standard deviation. Predictions using predict.gam will also produce 2 column matrices for type "link" and "response". The second column when type="response" is again on the reciprocal standard deviation scale (i.e. the square root precision scale).

The null deviance reported for this family is the sum of squares of the difference between the response and the mean response divided by the standard deviation of the response according to the model. The deviance is the sum of squares of residuals divided by model standard deviations.

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

Examples

library(mgcv);library(MASS)
b <- gam(list(accel~s(times,k=20,bs="ad"),~s(times)),
            data=mcycle,family=gaulss())
summary(b) 
plot(b,pages=1,scale=0)