[R] interpretation of F-statistics in GAMs

[Simon Wood]

On Friday 15 June 2007 08:06, robert.ptacnik at niva.no wrote:
> dear listers,
> I use gam (from mgcv) for evaluation of shape and strength of relationships
> between a response variable and several predictors.
> How can I interpret the 'F' values viven in the GAM summary? Is it
> appropriate to treat them in a similar manner as the T-statistics in a
> linear model, i.e. larger values mean that this variable has a stronger
> impact than a variable with smaller F?
- I'd be a bit cautious about this (even for T-statistics and linear models 
it's not quite clear to me what `impact' means if judged this way). These gam 
F statistics are only meant to provide a rough and ready means of judging 
approximate significance of terms, and I'm unsure about interpreting a  
comparison of such F ratios: for example the F statistics can be based on 
differerent numbers of degrees of freedom, depending on the term concerned...

> When I run my analysis for two different response varables (but identical
> predictors), is there a way to compare the F values among tests (like to
> standardize them by teh sum of F within each test?) I append two summaries
> below.
- Again, I don't really known how this would work. I'd be more inclined to 
compare the plotted terms and associated CIs (and maybe the p-values), 
especially if you are using GAMs in a quite exploratory way (e.g. if the 
assumption of an additive structure is really a convenience, rather than 
being something that is suggested by the underlying science). 

best,
Simon

>
>
> ### example 1 ###
>
> Family: gaussian
> Link function: identity
>
> Formula:
> dep[sel, i] ~ s(date, k = 3) + s(depth, k = kn) + s(temp, k = kn) +
>     s(light, k = kn) + s(PO4, k = kn) + s(DIN, k = kn) + s(prop.agpla,
>     k = kn)
>
> Parametric coefficients:
>             Estimate Std. Error t value Pr(>|t|)
> (Intercept)   5.1048     0.0384   132.9   <2e-16 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Approximate significance of smooth terms:
>                 edf Est.rank      F  p-value
> s(date)       1.669        2 12.161 1.07e-05 ***
> s(depth)      1.671        2 36.125 4.85e-14 ***
> s(temp)       1.927        2  6.686  0.00156 **
> s(light)      1.886        2 12.604 7.20e-06 ***
> s(PO4)        1.676        2  3.237  0.04143 *
> s(DIN)        1.000        1 38.428 3.41e-09 ***
> s(prop.agpla) 1.405        2 15.987 3.79e-07 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> R-sq.(adj) =  0.687   Deviance explained = 70.5%
> GCV score = 0.31995   Scale est. = 0.30076   n = 204
>
> ### example 2 ###
> Family: gaussian
> Link function: identity
>
> Formula:
> dep[sel, i] ~ s(date, k = 3) + s(depth, k = kn) + s(temp, k = kn) +
>     s(light, k = kn) + s(PO4, k = kn) + s(DIN, k = kn) + s(prop.agpla,
>     k = kn)
>
> Parametric coefficients:
>             Estimate Std. Error t value Pr(>|t|)
> (Intercept)  7.13588    0.05549   128.6   <2e-16 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Approximate significance of smooth terms:
>                 edf Est.rank      F  p-value
> s(date)       1.944        2 15.997 3.67e-07 ***
> s(depth)      1.876        2 25.427 1.52e-10 ***
> s(temp)       1.000        1  2.866   0.0921 .
> s(light)      1.751        2  4.212   0.0162 *
> s(PO4)        1.950        2 10.632 4.14e-05 ***
> s(DIN)        1.805        2 10.745 3.73e-05 ***
> s(prop.agpla) 1.715        2  2.674   0.0715 .
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
>  R-sq.(adj) =  0.479   Deviance explained = 50.9%
> GCV score = 0.6863   Scale est. = 0.64348   n = 209
>
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-- 
> Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK
> +44 1225 386603  www.maths.bath.ac.uk/~sw283