[R] how to interpret coefficients for a natural spline smooth function in a GLM

[spencerg]

      I have not seen a reply to this question, so I will offer a 
comment;  someone who knows more than I may correct or add to my comments. 


      There are many different kinds of splines.  Perhaps the most 
common are B-splines, which sum to 1 inside their range of definition 
and are 0 outside.  Natural splines are similar, but support 
extrapolation outside the (finite) range of definition.  A natural cubic 
spline extrapolates as straight lines 
(http://en.wikipedia.org/wiki/Spline_interpolation). 


      The coefficients are weights for a B-spline basis for the natural 
spline, defined in terms of the knots. 


      The "fda" package includes a "TaylorSpline" function to translate 
spline coefficients into the coefficients of Taylor expansions about the 
midpoints of the intervals between knots.  However, I do not know if it 
will work with a natural spline. 


      This is far from a complete answer to your question, but I hope it 
helps. 


      Spencer Graves

ltracy wrote:
> Hello-
>
> I am trying to model infections counts over 120 months using a GLM in R. 
> The model is simple really including a factor variable for year (10 yrs in
> total) and another variable consisting of a natural spline function for time
> in months.  
>
> My code for the GLM is as follows:
> model1<-glm(ALL_COUNT~factor(FY)+ns(1:120, 10), offset=log(TOTAL_PTS),
> family=poisson, data=TS1)
>
> The summary output pertaining to the smooth function consists of 10
> coefficients for each df in the model.  Here are the coefficients:
>
> ns(1:120, 10)1  -0.72438    0.32773  -2.210 0.027084 *  
> ns(1:120, 10)2  -1.19097    0.37492  -3.177 0.001490 ** 
> ns(1:120, 10)3  -1.40250    0.42366  -3.310 0.000931 ***
> ns(1:120, 10)4  -0.82722    0.47459  -1.743 0.081334 .  
> ns(1:120, 10)5  -0.46139    0.49657  -0.929 0.352812    
> ns(1:120, 10)6  -0.44892    0.51909  -0.865 0.387137    
> ns(1:120, 10)7  -0.53060    0.54783  -0.969 0.332778    
> ns(1:120, 10)8  -0.25699    0.55582  -0.462 0.643814    
> ns(1:120, 10)9  -0.74091    0.63899  -1.160 0.246249    
> ns(1:120, 10)10  0.41142    0.56317   0.731 0.465054   
>
> What is still unclear to me is what these 10 coefficients from the natural
> spline represent.  
>
> Thanks in advace-
>
>
>
>
>