From: Simon Wood <sw283_at_maths.bath.ac.uk>

Date: Thu 20 Jul 2006 - 07:13:20 EST

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Thu Jul 20 05:19:20 2006

Date: Thu 20 Jul 2006 - 07:13:20 EST

Sorry for the delay replying: I was on holiday, but have foolishly come back.

> I am a bit confused about gamm in mgcv. Consulting Wood (2006) or

*> Ruppert et al. (2003) hasn't taken away my confusion.
**>
**> In this code from the gamm help file:
**>
**> b2<-gamm(y~s(x0)+s(x1)+s(x2)+s(x3),family=poisson,random=list(fac=~1))
**>
**> Am I correct in assuming that we have a random intercept here....but
**> that the amount of smoothing is also changing per level of the factor??
**> Or is it only the intercept that is changing?
**>
*

- the degree of smoothing is the same for each level of `fac' but there is
a different intercept for each level of `fac': these intercepts are
assumed Normally distributed. i.e. all `s()' terms apply to all data,
they are not nested within groups.

> And where can I find some explanation on the magic output below?

mgcv::gamm is basically a wrapper that turns a GAMM into the sort of model that nlme::lme or MASS::glmmPQL expects to see.... `gamm' returns an object with two parts - the `lme' part is the object that was returned by glmmPQL or lme; the `gam' part is an object with most of the attributes of a `gam' object (all those that can be reconstructed from an lme/glmmPQL fitted model object).

So the `lme' object contains a bunch of opaque stuff that results from turning the original GAMM into something that lme/glmmPQL can work with... further detail below.

*>
*

> summary(b2$lme)

*> Random effects:
*

- The output starting here relates to the random components of the 4 smooths in the model. Each smooth starts with 10 degrees of freedom, but one of these is lost to the GAM centering constraint that ensures additive identifiability, and one is treated as a fixed effect (see Wood, 2006, for details), so each smooth have 8 random coefficients. Each of these coefficients is treated as having the same variance (after some preparatory reparameterization), but this variance (which plays the role of a smoothing parameter) is unknown and is estimated as part of model estimation.

[Note that g.1 to g.4 below are dummy grouping factors, each having only one level - they force the smooths to apply to all the data, rather than being nested within, e.g. the levels of `fac'].

> Formula: ~Xr.1 - 1 | g.1

*> Structure: pdIdnot
**> Xr.11 Xr.12 Xr.13 Xr.14 Xr.15 Xr.16 Xr.17 Xr.18
**> StdDev: 1.680679 1.680679 1.680679 1.680679 1.680679 1.680679 1.680679 1.680679
**> Formula: ~Xr.2 - 1 | g.2 %in% g.1
**> Structure: pdIdnot
**> Xr.21 Xr.22 Xr.23 Xr.24 Xr.25 Xr.26 Xr.27 Xr.28
**> StdDev: 1.57598 1.57598 1.57598 1.57598 1.57598 1.57598 1.57598 1.57598
**> Formula: ~Xr.3 - 1 | g.3 %in% g.2 %in% g.1
**> Structure: pdIdnot
**> Xr.31 Xr.32 Xr.33 Xr.34 Xr.35 Xr.36 Xr.37 Xr.38
**> StdDev: 20.06377 20.06377 20.06377 20.06377 20.06377 20.06377 20.06377 20.06377
**> Formula: ~Xr.4 - 1 | g.4 %in% g.3 %in% g.2 %in% g.1
**> Structure: pdIdnot
**> Xr.41 Xr.42 Xr.43 Xr.44 Xr.45
**> StdDev: 0.0001063304 0.0001063304 0.0001063304 0.0001063304 0.0001063304
**> Xr.46 Xr.47 Xr.48
**> StdDev: 0.0001063304 0.0001063304 0.0001063304
*

- that's the random component information relating to the smooths done with. What follows is the information realting to the random intercept. Note that the rather complicated Formula is really equivalent to ~1|fac since the g.j are degenerate.

> Formula: ~1 | fac %in% g.4 %in% g.3 %in% g.2 %in% g.1

*> (Intercept) Residual
**> StdDev: 0.6621173 1.007227
**> Variance function:
**> Structure: fixed weights
**> Formula: ~invwt
*

- What follows is information about the fixed effects. In this case there is one fixed effect for each smooth, and an overall intercept: `X(Intercept)'.

> Fixed effects: y.0 ~ X - 1

*> Value Std.Error DF t-value p-value
**> X(Intercept) 2.0870364 0.3337787 392 6.252755 0.0000
**> Xs(x0)Fx1 -0.0000325 0.1028794 392 -0.000316 0.9997
**> Xs(x1)Fx1 0.3831694 0.0957323 392 4.002509 0.0001
**> Xs(x2)Fx1 1.4584330 0.3909237 392 3.730736 0.0002
**> Xs(x3)Fx1 -0.0123951 0.0143162 392 -0.865809 0.3871
**> Correlation:
**>
*

Hope that's some use.

Simon

>- Simon Wood, Mathematical Sciences, University of Bath, Bath BA2 7AY

*>- +44 (0)1225 386603 www.maths.bath.ac.uk/~sw283/
*

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