R help - Sep 2013 - Comparing two GAMs using anova (mgcv)

Hey all,

I've fitted two GAMs to some data using mgcv. The only difference between
the two models is that one includes an additional smooth term (the smooth terms
are s(x), s(y) and s(log(y)), the difference being that one model contains s(y)
as additional term whereas the other one only contains s(x) and s(log(y)) - x
and y being my explanatory variables).

I'm now trying to decide between those two models. There's no difference
in deviance explained or R^2 and the diagnostic plots returned by gam.check()
look fairly similar although the one of the fuller model looks slightly more
satisfactory as far as the histogram of the residuals is concerned.

I'm wondering whether it is appropriate to conduct an approximate F test
using the anova function. I'm not 100% clear I've understood the
documentation on that completely. Is it appropriate to conduct such a test if
the only difference between models is the inclusion/exclusion of a smooth term?

Conducting the test, I get the result that there's no reason to reject the
null hypothesis that the simpler model (without s(y)) is correct.

Thanks!

It's ok to use an approximate F test here, provided you are careful with 
the interpretation. e.g. do look at the differences in EDF and not just 
the p-value (negative or very small EDF differences will render the 
p-value essentially meaningless). however...

Where-ever possible it is usually better to test using `summary' or 
`anova' with a single model argument. The approximations used by these 
are better founded than the approximate F-test. i.e. take a look at the 
p-values associated with the 's(y)' term in the larger model.

best,
Simon

On 20/09/13 13:37, Lucas Holland wrote:
> Hey all,
>
> I've fitted two GAMs to some data using mgcv. The only difference
between the two models is that one includes an additional smooth term (the
smooth terms are s(x), s(y) and s(log(y)), the difference being that one model
contains s(y) as additional term whereas the other one only contains s(x) and
s(log(y)) - x and y being my explanatory variables).
>
> I'm now trying to decide between those two models. There's no
difference in deviance explained or R^2 and the diagnostic plots returned by
gam.check() look fairly similar although the one of the fuller model looks
slightly more satisfactory as far as the histogram of the residuals is
concerned.
>
> I'm wondering whether it is appropriate to conduct an approximate F
test using the anova function. I'm not 100% clear I've understood the
documentation on that completely. Is it appropriate to conduct such a test if
the only difference between models is the inclusion/exclusion of a smooth term?
>
> Conducting the test, I get the result that there's no reason to reject
the null hypothesis that the simpler model (without s(y)) is correct.
>
> Thanks!
>
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>

-- 
Simon Wood, Mathematical Science, University of Bath BA2 7AY UK
+44 (0)1225 386603               http://people.bath.ac.uk/sw283