I don’t think these are actually opposite camps, just two related but different 
issues. Sure, functions can be nonlinear, but we shouldn’t create arbitrary 
nonlinearities due to the selection of x values.

What I was thinking of was measurements at baseline and 3,6,9,12,18,24 mo into 
treatment (as in ISwR::alkfos). Fitting a linear trend with the factor codes 
will de facto assume a kink at 12 months. The jump from time 0 to 3mo may well 
be deviate from a linear trend (AFAIR, it does), but that is another issue. 

- Peter

> On 25 Oct 2025, at 17.15, Therneau, Terry M., Ph.D. <[email protected]> wrote:
> 
> Peter wrote:
> A related issue that has bugged me "forever" is that we treat ordered factors 
> as if their levels are equidistant even when that is patently untrue. The use 
> of polynomial contrasts for ordered factors reflects this - it would really 
> be more sensible to use e.g. successive differences or (ick!) Helmert 
> contrasts for the ordered case and reserve poly() for factors with actual 
> numerical levels. To me, this effectively makes ordered factors conceptually 
> useless.  
>  I actually fall into the opposite camp.  We teach students that they *must* 
> code factors as  having non-equal increments but that continuous variables  
> are okay s is  (the old interval vs. ordinal dichotomy).   In my medical 
> work, a lot of the categorical variables actually are close to evenly spaced, 
> a disease grade for instance, since that is what the original authors of the 
> scale were trying to do.   It is the continuous variables that violate equal 
> spacing most violently.    A cardiac ejection fraction drop from 70 to 60 is 
> "meh", a drop from 30 to 20 is "I hope your affairs are in order".    We 
> don't check this nearly often enough.
>  Also, I use as.integer(factor) quite when creating a an analysis data set 
> from input data.   It's just another tool for creating new variables.
>  Terry T.

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