Random effects in GAMs

Description

The smooth components of GAMs can be viewed as random effects for estimation purposes. This means that more conventional random effects terms can be incorporated into GAMs in two ways. The first method converts all the smooths into fixed and random components suitable for estimation by standard mixed modelling software. Once the GAM is in this form then conventional random effects are easily added, and the whole model is estimated as a general mixed model. gamm and gamm4 from the gamm4 package operate in this way.

The second method represents the conventional random effects in a GAM in the same way that the smooths are represented — as penalized regression terms. This method can be used with gam by making use of s(...,"re") terms in a model: see smooth.construct.re.smooth.spec. Alternatively, but less straightforwardly, the paraPen argument to gam can be used: see gam.models. If smoothing parameter estimation is by ML or REML (e.g. gam(...,method="REML")) then this approach is a completely conventional likelihood based treatment of random effects.

gam can be slow for fitting models with large numbers of random effects, because it does not exploit the sparcity that is often a feature of parametric random effects. It can not be used for models with more coefficients than data. However gam is often faster and more relaiable than gamm or gamm4, when the number of random effects is modest.

To facilitate the use of random effects with gam, gam.vcomp is a utility routine for converting smoothing parameters to variance components. It also provides confidence intervals, if smoothness estimation is by ML or REML.

Note that treating random effects as smooths does not remove the usual problems associated with testing variance components for equality to zero: see summary.gam and anova.gam.

Author(s)

Simon Wood <simon.wood@r-project.org>

References

Wood, S.N. (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. Journal of the Royal Statistical Society (B) 73(1):3-36

Wood, S.N. (2008) Fast stable direct fitting and smoothness selection for generalized additive models. Journal of the Royal Statistical Society (B) 70(3):495-518

Wood, S.N. (2006) Low rank scale invariant tensor product smooths for generalized additive mixed models. Biometrics 62(4):1025-1036

See Also

gam.vcomp, gam.models, smooth.terms, smooth.construct.re.smooth.spec, gamm

Examples

## see also examples for gam.models, gam.vcomp and gamm

## simple comparison of lme and gam

require(nlme)
b0 <- lme(travel~1,data=Rail,~1|Rail,method="REML") 

b <- gam(travel~s(Rail,bs="re"),data=Rail,method="REML")

intervals(b0)
gam.vcomp(b)