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

ltracy lareet at hotmail.com
Mon Jun 15 16:19:59 CEST 2009


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-




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