[R] mgcv: how select significant predictor vars when using gam(...select=TRUE) using automatic optimization

[Simon Wood]

Jan,

What mgcv version are you using, please? (Older versions have a poor 
p-value approximation when select=TRUE, but of course it's possible that 
you've managed to break the newer approximation as well)

The 'select=TRUE' option adds a penalty to each smooth, to allow it to 
be penalized out of the model altogether via optimization of the 
smoothing parameter selection criterion. Usually it is better to use 
REML for smoothing parameter selection in this case using 
'method="REML"' as an option to gam. This is because REML is less prone 
to undersmoothing than GCV. So 'select=TRUE' is not selecting on the 
basis of the p-values, themselves, but obviously this sort of 
discrepancy should not be happening.

best,
Simon

On 17/04/13 15:50, Jan Holstein wrote:
> I have 11 possible predictor variables and use them to model quite a few
> target variables.
> In search for a consistent manner and possibly non-manual manner to identify
> the significant predictor vars out of the eleven I thought the option
> "select=T" might do.
>
> Example: (here only 4 pedictors)
> first is vanilla with "select=F"
>
>> fit1<-gam(target~s(mgs)+s(gsd)+s(mud)+s(ssCmax),family=quasi(link=log),data=wspe1,select=F)
>> summary(fit1)
>
> Family: quasi
> Link function: log
> Formula:
> target ~ s(mgs) + s(gsd) + s(mud) + s(ssCmax)
> Parametric coefficients:
>              Estimate Std. Error t value Pr(>|t|)
> (Intercept)   -34.57      20.47  -1.689   0.0913 .
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> Approximate significance of smooth terms:
>              edf Ref.df      F  p-value
> s(mgs)    2.335  2.623  0.260    0.829
> s(gsd)    6.868  7.506 13.955  < 2e-16 ***
> s(mud)    8.990  9.000 11.727  < 2e-16 ***
> s(ssCmax) 6.770  6.978  6.664 7.68e-08 ***
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> R-sq.(adj) =  0.402   Deviance explained = 40.4%
> GCV score = 8.8563e+05  Scale est. = 8.8053e+05  n = 4511
>
>
>
> then turn select=TRUE
>
>
>
>
> fit2<-gam(target~s(mgs)+s(gsd)+s(mud)+s(ssCmax),family=quasi(link=log),data=wspe1,select=TRUE)
>> summary(fit2)
>
> Family: quasi
> Link function: log
>
> Formula:
> target ~ s(mgs) + s(gsd) + s(mud) + s(ssCmax)
> Parametric coefficients:
>              Estimate Std. Error t value Pr(>|t|)
> (Intercept)   0.1585     1.7439   0.091    0.928
> Approximate significance of smooth terms:
>              edf Ref.df     F p-value
> s(mgs)    2.456      8 24.50  <2e-16 ***
> s(gsd)    7.272      9 14.33  <2e-16 ***
> s(mud)    7.678      9 20.38  <2e-16 ***
> s(ssCmax) 6.556      9 14.36  <2e-16 ***
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> R-sq.(adj) =  0.397   Deviance explained =   40%
> GCV score = 8.9209e+05  Scale est. = 8.8715e+05  n = 4511
>
> I seem to not fully understand how to work with "select".
> The predictor "mgs" is obviously not significant, as seen from "fit"
> (above), yet here it appears as significant. Why was it not dropped? How are
> not-significant predictors are identified?
>
>
>
>
>
> --
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-- 
Simon Wood, Mathematical Science, University of Bath BA2 7AY UK
+44 (0)1225 386603               http://people.bath.ac.uk/sw283