[R] splines and ns equation

[Ranae]

Hi,

I am looking at the change in N concentration in plant roots over 4 time
points and I have fit a spline to the data using ns and lme:

fit10 <- lme( N~ns(day, 3), data = rcn10G)

I may want to adjust the model a little bit, but for now, let's assume it's
good.  I get output for the fixed effects:

Fixed: N ~ ns(day, 3) 
(Intercept) ns(day, 3)1 ns(day, 3)2 ns(day, 3)3 
 1.15676524  0.14509171  0.04459627  0.09334428 
 
and coefficients for each experimental unit in my experiment:

   (Intercept) ns(day, 3)1 ns(day, 3)2 ns(day, 3)3
24    1.050360 -0.42666159 -0.56290877 -0.10714407
13    1.104464 -0.30825350 -0.53311653 -0.05558150
31    1.147878 -0.14548512 -0.78673906 -0.07231781
46    1.177781 -0.22278380 -0.80278177 -0.02321460
15    1.144215 -0.04484519 -0.06084798  0.07633663
32    1.213007  0.00741061  0.03896933  0.15325849
23    1.274615  0.16477514  0.00872224  0.23128320
41    1.215626  0.57050767  0.11415467  0.10608867
43    1.134203  0.48070741  0.72112899  0.18108193
12    1.091422  0.39563632  1.01521528  0.22597459
21    1.100631  0.44589314  0.98526322  0.23535739
35    1.226980  0.82419937  0.39809568  0.16900841

NOW, I want to write a spline function where I can incorporate these
coefficients to get the predicted N concentration value for each day. 
However, I am having trouble finding the right spline equation, since there
are many forms on the internets.  

I know it won't be a simple one, but can some one direct me to the equation
that would be best to use for ns?

Thanks a lot,

Ranae



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