I have developed a GAM model in order to predict Y using 4 X variables.  2 of 
these X's are factors, and 1 is a spline.

Part of the data looks like:


Days    WRM     variety PWM     O_EC
31      75      1       90      234
31      79      1       78      283
31      82      1       92      281
31      84      1       96      213
31      99      2       69      247
31      100     2       77      324
31      104     2       74      259
31      118     2       81      282
31      61      3       58      478
31      98      3       83      429
31      98      3       70      379
31      156     3       87      467
31      78      4       56      283
31      97      4       67      282
31      106     4       69      368
31      184     4       78      386
39      66      1       204     233
39      83      1       265     360
39      87      1       270     308
39      236     1       243     323
39      174     2       244     300
39      181     2       257     366
39      241     2       305     408
39      282     2       299     599
39      125     3       153     402
39      156     3       213     384
39      183     3       227     408
39      217     3       235     360
39      159     4       205     362
39      180     4       182     314
39      189     4       224     488
39      246     4       265     468


fdays = factor(Days)
fvar = factor(variety)

my model is:

test1 <- gam(O_EC~s(WRM)+PWM+fdays+fvar)

Now, I can easily measure O_EC, PWM, fvar, and fdays, but not WRM.

I can get a good estimate for s(WRM) by straight algebra and get a rough 
eyeball estimate of WRM from the s(WRM) vs WRM plot:

s(WRM) ~ O_EC - B0 - B1*PWM - B2*fdays - B3*fvar

Is there any way of using a backSpline or other inverse spline since s(WRM) is 
not monotone?  Or is it possible to obtain a formula for the smooth that I can
mathematically solve for?


Thank you,

Geoff


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