[R] Inversing a non-monotonic spline

[Geoff Mercer]

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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