[R] Multiple interaction terms in GAMM-model

[Jeroen]

Dear all,

I am trying to correlate a variable tau1 to a set of other variables (x1,
x2, x3, x4), taking into account an interaction with time ('doy') and place
('region'), and taking into account dependency of data in time per object
ID. My dataset looks like:

  doy  objectID    region     tau1                x1              x2                   
x3         x4
      1         1             A              0.000000        0.08          
0.3657            64.1      0.001100
      1         2             C              0.000000        0.10          
0.3150            74.3      0.000847
      1         3             B              0.000000        0.07          
0.3264            60.9      0.000854
      1         4             B              0.000000        0.08          
0.3058            63.2      0.000713
      1         5             D              2.716998        0.11          
0.2835            93.7      0.000660
....
 365         1             A              0.010000        0.06          
0.5489            27.3      0.003878
 365         2             C              0.234000        0.12          
0.1798            23.1      0.000278
 365         3             B              1.353500        0.09          
0.3417            37.8      0.000271
 365         4             B              0.000000        0.40          
0.1347            13.4      0.000173
 365         5             D              3.478008        0.21          
0.2384            37.7      0.000703

The total dataset consists of 151,840 rows (365 days x 416 object ID's)

Since the data is dependent in time per objectID, I use a GAMM model with an
autocorrelation function. Since each variable x1, x2, etc. is dependent on
time and place, I should incorporate this as well. 

Therefore I am wondering if the following gamm-model is correct for my
situation:

model <- gamm( tau1 ~ te( x1, by= doy ) + te( x1, by= factor( region ) ) +
... + te( x4, by= doy ) + te( x4, by= factor( region ) ) + factor( region ),
correlation= corAR1(form= ~ doy|objectID ), na.action= na.omit ).

Does anyone know if this is ok? 

Or should I use a model which also includes terms like " te( x1 ) + ... +
te( x4 )".
And is the correlation function correct?

Thanks so much!!

Jeroen



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