[R] compare gam fits

[Simon Wood]

You can do this using the predict.gam(...,type="lpmatrix"). Here's some code 
providing an example....


## example of smooths conditioned on factors from ?gam.models
library(mgcv)
dat <- gamSim(4)
## fit model...
b <- gam(y ~ fac+s(x2,by=fac)+s(x0),data=dat)
plot(b,pages=1)
## now predict on x2 grid at 2 levels of `fac'...
x2 <- seq(0,1,length=100);x3 <- c(x2,x2)
newd <- data.frame(x2=x3,x0=rep(.5,100),fac=c(rep("1",100),rep("2",100)))
Xp <- predict(b,newd,type="lpmatrix")
X <- Xp[1:100,]-Xp[101:200,]
X[,1:3] <- 0;X[,22:39] <- 0
## Now X%*%coef(b) gives difference between smooths for fac=="1" and
## fac=="2"...
md <- X%*%coef(b)
## following evaluates diag(X%*%vcov(b)%*%t(X)) the s.e. of
## difference just computed....
se <- rowSums((X%*%vcov(b))*X)
## So getting upper and lower confidence limits is easy
## (could use qt(.975,b$df.residual) in place of 2 below)
ul <- md + 2 * se;ll <- md - 2 * se
## plot smooths and difference
par(mfrow=c(2,2));plot(b,select=1);plot(b,select=2)
plot(x2,md,ylim=range(c(ul,ll)),type="l")
lines(x2,ul,col=2);lines(x2,ll,col=2)



On Thursday 05 August 2010 17:49, Mike Lawrence wrote:
> Hi folks,
>
> I originally tried R-SIG-Mixed-Models for this one
> (https://stat.ethz.ch/pipermail/r-sig-mixed-models/2010q3/004170.html),
> but I think that the final steps to a solution aren't mixed-model
> specific, so I thought I'd ask my final questions here.
>
> I used gamm4 to fit a generalized additive mixed model to data from a
> AxBxC design, where A is a random effect (human participants in an
> experiment), B is a 2-level factor predictor variable, and C is a
> continuous variable that is likely non-linear. I tell gamm4 to fit a
> smooth across C to each level of B independently, and I can use
> predict.gam(...,se.fit=T) to obtain predictions from the fitted model
> as well as the standard error for the prediction. I'd like to
> visualize the BxC interaction to see if smoothing C within each level
> of B was really necessary, and if so, where it is (along the C
> dimension) that B affects the smooth. It's easy enough to obtain the
> predicted B1-B2 difference function, but I'm stuck on how to convey
> the uncertainty of this function (e.g. computing the confidence
> interval of the difference at each value of C).
>
> One thought is that predict.gam(...,se.fit=T) returns SE values, so if
> I could find out the N on which these SE values are computed, I could
> compute the difference CI as
> sqrt( ( (SD_B1)^2 + (SD_B2)^2 ) / N ) * qt( .975, df=N-1 )
>
> However, I can't seem to figure out what value of N was used to
> compute the SEs that predict.gam(...,se.fit=T) produces. Can anyone
> point me to where I might find N?
>
> Further, is N-1 the proper df for the call to qt()?
>
> Finally, with a smooth function and 95% confidence intervals computed
> at each of a large number of points, don't I run into a problem of an
> inflated Type I error rate? Or does the fact that each point is not
> independent from those next to it make this an inappropriate concern?
>
> Cheers,
>
> Mike

-- 
> Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK
> +44 1225 386603  www.maths.bath.ac.uk/~sw283