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

[Jan Holstein]

Simon,

thanks for the reply,  I guess I'm pretty much up to date using
 mgcv 1.7-22.
Upgrading to R 3.0.0 also didn't do any change.

Unfortunately using method="REML" does not make any difference:

####### first with "select=FALSE"
> fit<-gam(target
> ~s(mgs)+s(gsd)+s(mud)+s(ssCmax),family=quasi(link=log),data=wspe1,method="REML",select=F)
> summary(fit)

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)   -4.724      7.462  -0.633    0.527
Approximate significance of smooth terms:
            edf Ref.df      F p-value    
s(mgs)    3.118  3.492  0.099   0.974    
s(gsd)    6.377  7.044 15.596  <2e-16 ***
s(mud)    8.837  8.971 18.832  <2e-16 ***
s(ssCmax) 3.886  4.051  2.342   0.052 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
R-sq.(adj) =  0.403   Deviance explained = 40.6%
REML score =  33186  Scale est. = 8.7812e+05  n = 4511





#### Then using "select=T"

> fit2<-gam(target
> ~s(mgs)+s(gsd)+s(mud)+s(ssCmax),family=quasi(link=log),data=wspe1,method="REML",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)   -6.406      5.239  -1.223    0.222
Approximate significance of smooth terms:
            edf Ref.df     F p-value    
s(mgs)    2.844      8 25.43  <2e-16 ***
s(gsd)    6.071      9 14.50  <2e-16 ***
s(mud)    6.875      8 21.79  <2e-16 ***
s(ssCmax) 3.787      8 18.42  <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
R-sq.(adj) =    0.4   Deviance explained = 40.1%
REML score =  33203  Scale est. = 8.8359e+05  n = 4511







I played around with other families/link functions with no success regarding
the "select" behaviour.

Well, look at the structure of my data:
<http://r.789695.n4.nabble.com/file/n4664586/screen-capture-1.png> 

All possible predictor variables in principle look like this, and taken
alone, each and every is significant according to p-value (but not all can
at the same time). 
In theory, the target variable should be a hypersurface in 11dim space with
lots of noise, but interaction of more than 2 vars gets costly (not to think
of 11) and often enough (also without interaction) the solution does not
converge at minimal step size. If it does, results are usually not as good
as without interaction.

Any comment/advice on model setup is warmly welcome here.

Since I don't want to try out all possible 2047 combinations of up to eleven
predictor variables for each target variable, I currently see no other way
than educated manual guessing. 

If you know another way of (semi-)automated model tunig/reduction, I would
very much appreciate it
 
best regards,
Jan






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