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how to code y~x/(x+a) in lm() function

7 messages · David L Carlson, Rolf Turner, Ye Lin +2 more

Original
Rolf Turner
# 
(1) It is not acceptable to use "wanna" in written English.  You should say
      "I want to fit a model ....".

(2) The model you have fitted is *not* equivalent to the model you first 
state.

If you write "y ~ x/(a+x)" you are tacitly implying that

     y = x/(a+x) + E

where the "errors" E are i.i.d. with mean 0.

If this is the case then it will *not* be the case that

     1/y = 1 + a/x + E

with the E values being i.i.d. with mean 0.

If the model "y ~ x/(a+x)" is really what you want to fit, then you should
be using non-linear methods, e.g. by applying the function nls().

     cheers,

     Rolf Turner
On 21/08/13 09:39, Ye Lin wrote:
David L Carlson
# 
?curve

set.seed(42)
x <- 1:15
y <- x/(1+x)+rnorm(15, 0, .02)
plot(y~x)
lm.out <- lm((1/y-1)~I(1/x)+0)
curve(x/(coef(lm.out)+x), 1, 15, add=TRUE)

-------------------------------------
David L Carlson
Associate Professor of Anthropology
Texas A&M University
College Station, TX 77840-4352

-----Original Message-----
From: r-help-bounces at r-project.org
[mailto:r-help-bounces at r-project.org] On Behalf Of Ye Lin
Sent: Tuesday, August 20, 2013 4:40 PM
To: R help
Subject: [R] how to code y~x/(x+a) in lm() function

Hey All,

I wanna to fit a model y~x/(a+x) to my data, here is the code I
use now:

lm((1/y-1)~I(1/x)+0, data=b)

and it will return the coefficient which is value of a

however, if I use the code above, I am not able to draw  a curve
the
presents this equation. How can I do this?

Thanks for your help!


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code.
Bert Gunter
# 
Rolf:

Thanks for this.

It nicely illustrates what to me is a fundamental problem: For many
scientists, it is not math ("stats") that is the stumbling block, but
rather the failure to understand how variability ("noise") affects the
experimental/observational process. One does tend to get more
philosophical in old age, I suppose...

My personal experience is that this problem is widespread, but mine is
a highly biased sample, of course. Nevertheless, it is hard to fault
those who stumble: Nothing in the usual basic science education
process discusses the issue (coherently, anyway);  and certainly
standard applied statistics courses that I know of gloss over it.  Nor
do I think the concepts are easy to grasp (a measurement is a sample
of size one from a population of measurements that one could get) --
at least I did not find them so.

No reply necessary, whether you agree or disagree. You just afforded
me a nice opportunity to vent.

Best,
Bert
On Tue, Aug 20, 2013 at 3:59 PM, Rolf Turner <rolf.turner at xtra.co.nz> wrote:

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Ben Bolker
    

    

      
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Rolf Turner <rolf.turner <at> xtra.co.nz> writes:

            

      
      
      
    

        
For what it's worth this model can also be fitted (without messing
up the error structure) via

 glm(1/y~x,family=gaussian(link="inverse"))

Although you may not get the parameters in exactly the form you
want.