[R] te( ) interactions and AIC model selection with GAM

[Simon Wood]

Ricardo,

Your second construction (b) is the correct one (in a you are asking for 
one marginal to be a 2 dimensional cubic regression spline, which 
doesn't exist in mgcv).

For visualization, would the example at the end of ?te be the thing to 
do? In 3d I find looking at a series of 2d slices quite useful.

For AIC model comparison, the usual advice applies that although the 
comparisons are a bit more reliable for nested models (since then some 
of the AIC approximations errors are the same in both cases, and cancel 
in the comparison), it is still ok to use AIC for non-nested models 
(i.e. it is *not* like most hypothesis testing where everything falls 
apart if you don't have nesting).

best,
Simon

On 30/07/12 16:50, Ricardogg wrote:
> Hello R users,
>
> I'm working with a time-series of several years and to analyze it, I’m using
> GAM smoothers from the package mgcv. I’m constructing models where
> zooplankton biomass (bm) is the dependent variable and the continuous
> explanatory variables are:
> -time in Julian days (t), to creat a long-term linear trend
> -Julian days of the year (t_year) to create an annual cycle
> - Mean temperature of Winter (temp_W), Temperature of September (temp_sept)
> or Chla.
> Questions:
> 1) To introduce a tensor product modifying the annual cycle in my model, I
> tried 2 different approaches:
> - a) gam ( bm ~ t + te (t_year, temp_W, temp_sept, k = c( 5,30), d= ( 1,2),
> bs = c( “cc”,”cr”)), data = data)
> -b) gam ( bm ~ t + te (t_year, temp_W, temp_sept, k = 5, bs = c(
> “cc”,”cr”,”cr”)), data = data)
> Here is my problem: when I’m using just 2 variables (e.g., t_year and
> temp_W) for the tensor product, I can understand pretty well how the
> interpolation works and visualize it with vis.gam() as a 3d plot or a
> contour one. But with 3 variables is difficult to me to understand how it
> works. Besides, I don’t which one is the proper way to construct it, a) or
> b). Finally, when I plot a) or b) as vis.gam (model_name , view= c(“t_year”,
> “temp_W”)), How should I interpret the plot? The effect of temp_W on the
> annual cycle after considering already the effect of temp_sept or just the
> individual effect of Temp_W on the annual cycle?
> 2) I’m trying to do a model selection using AIC criteria. I have several
> questions about it:
> - Should I use always the same type of smoothing basis (bs), the same type
> of smoother ( e.g te) and the same dimension of the basis (k)? Example:
> Option 1:
> a) mod1 <- gam (bm ~ t, data = data)
> b) mod2 <- gam (bm ~ te (t, k = 5, bs = “cr”), data = data)
> c) mod3 <- gam (bm ~ te (t_year, k = 5, bs = “cc”), data = data)
> d) mod4 <- gam (bm ~ te (t_year, temp_W, k = 5, bs = c(“cc”,”cr”)), data =
> data)
> e) mod5 <- gam (bm ~ te (t_year, temp_W, temp_sept, k = 5, bs =
> c(“cc”,”cr”,”cr”)), data = data).
> Here the limitation for k = 5, is due to mod5, I don’t use s () because in
> mod4 and mod5 te () is used and finally, I always use “cr” and “cc”.
> Option 2:
> a) mod1 <- gam (bm ~ t, data = data)
> b) mod2 <- gam (bm ~ s (t, k = 13, bs = “cr”), data = data)
> c) mod3 <- gam (bm ~ s (t_year, k = 13, bs = “cc”), data = data)
> d) mod4 <- gam (bm ~ te (t_year, temp_W, k = 11, bs = c(“cc”,”cr”)), data =
> data)
> e) mod5 <- gam (bm ~ te (t_year, temp_W, temp_sept, k = 5, bs =
> c(“cc”,”cr”,”cr”)), data = data).
> I can get lower AIC for each of the models with Option 2, but are they
> comparable when I use AIC criteria? Is it therefore the proper way to do it
> as in Option 1? AIC (mod1, mod2, mod3, mod4, mod5).
>
> Thank you in advance,
> Best regards,
> Ricardo González-Gil
>
>
>
>
> --
> View this message in context: http://r.789695.n4.nabble.com/te-interactions-and-AIC-model-selection-with-GAM-tp4638368.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>


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