I've got a small problem.
I have some observational data (environmental samples: abiotic explanatory
variable and biological response) to which I've fitted both a multiple linear
regression model and also a gam (mgcv) using smooths for each term. The gam
clearly fits far better than the lm model based on AIC (difference in AIC ~ 8),
in addition the adjusted R squared for the gam is clearly better.
I then want to make some plots of predicted values from both models with
confidence intervals. So I can get my predictions usng
predict(my.model(....se.fit=TRUE))
My problem is that this results in the prediction se's (and consequent CI's for
the mean prediction) being much wider for the gam than for the linear model.
This seems rather counter-intuitive given that the gam appears to fit better,
and hence I will find it hard to explain my choice of a gam model in a journal
article, despite clear non-linearity.
It's not so easy for me to post my own example. The following code gives a
flavour, clearly in this instance the gam will fit MUCH better because it is
the generating model. Even in this case, most gam se's line above the 1:1 line.
In my example, with some observational data, the difference between linear and
gam fit is not so pronounced but the gam still clearly fits better than linear,
but all gam se's are WAY above their linear equivalents when used to predict
for representative new data in order to present results as interaction plots.
cheers
Mike
require(mgcv)
require(MASS)
dat <- gamSim(1,n=200,dist="normal",scale=2)
summary(b <- gam(y~s(x0)+s(x1)+s(x2)+s(x3),data=dat))
summary(a <- lm(y~x0 + x1 + x2 + x3,data=dat))
se.result <- data.frame(linear.se=predict(a, se.fit=TRUE)$se.fit,
gam.se=predict(b, se.fit=TRUE)$se.fit)
with(se.result, eqscplot(linear.se, gam.se))
abline(a=0, b=1)
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