explaining a model with rcs() terms

On Nov 30, 2008, at 10:23 PM, Dylan Beaudette wrote:

Hi, I am using the rcs() function in the Design library to model
non-linearity that is not well characterized by an otherwise
mechanistic function. I am able to make the model 'available' to
others through the excellent nomogram() function and the set of tables
that it can create. However, I would like to present the model in an
'expanded' format-- probably what rcspline.restate() or latex.Design()
produce on a model fit object.

Here is how the model was fit:

fit.ols <- ols( log(k) ~ (rcs(activity) * (log(conc) + sar)) +
(rcs(sand) * (log(conc) + sar)), data=sm.clean, x=TRUE, y=TRUE)

Here is how I am accessing the 'expanded' format of the model structure:

options(digits=3)
latex(fit.ols, file='fit_rcs.tex')

The output contains several notation elements that I am not familiar 
with:

1. x_{+}  --> it seems that this represent a term that should be set
to 0, when x is 0?

It is set to zero when the term inside the cubic is less than zero. See 
pages 20-21 of Harrell's book where the basis functions are described 
and illustrated.

i.e.  the entire expression   ?453(activity ? 0.842)_{+}^{3}  = 0 when
'activity' = 0 ??

.... whenever (activity ? 0.842) < 0

2. the '!x' found in :

+log(conc) [ ?0.0118sand + 9.58
! ?
!10?6 (sand ? 11.6)

My guess is that this is 9.58 x 10^-6

? 0.000128(sand ? 37.5)
+0.00045(sand ? 47.2)
? 0.000350(sand ? 51)
+ 1.86
! ?
!10?5 (sand ? 69.8) ]

I don't see anything like that in Harrell's text and I am wondering if a 
different character is getting rendering incorrectly. The only time you 
see it is when the exponent is below -4.

.... what exactly does that mean?


An image version of the equation in question is attached.

Any input would be greatly appreciated!

Cheers,

Dylan

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