R help - Dec 2008 - explaining a model with rcs() terms

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

2. the '!x' found in :

+log(conc) [ ?0.0118sand + 9.58
! ?
!10?6 (sand ? 11.6)
? 0.000128(sand ? 37.5)
+0.00045(sand ? 47.2)
? 0.000350(sand ? 51)
+ 1.86
! ?
!10?5 (sand ? 69.8) ]


.... 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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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
> <complex_equation.png>______________________________________________
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