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

[Ben Bolker]

On 13-08-21 05:17 PM, Rolf Turner wrote:
> 
> 
> Thott about this a bit more and have now decided that I don't understand
> after all.
> 
> Doesn't
> 
>     glm(1/y~x,family=gaussian(link="inverse"))
> 
> fit the model
> 
>     1/y ~ N(1/(a+bx), sigma^2)
> 
> whereas what the OP wanted was
> 
>     y ~ N(x/(a+x),sigma^2)  ???

  I goofed slightly.

y ~ 1/x with inverse link gives

1/y = a + b*(1/x)
y = 1/(a+b*(1/x))
  = x/(a*x+b)

  Hmmm. Is there an offset trick we can use?

  y = x/(a+x)
1/y = (a+x)/x
1/y = (a/x) + 1
1/y = a*(1/x) + 1

  So I *think* we want

glm(y~1/x+0+offset(1),family=gaussian(link="inverse"))

  I'm forwarding this back to r-help.



> 
> I can't see how these models can be equivalent.  What am I missing?
> 
> cheers,
> 
> Rolf
> 
> 
> 
> On 22/08/13 03:49, Ben Bolker wrote:
>> Rolf Turner <rolf.turner <at> xtra.co.nz> writes:
>>
>>> On 21/08/13 11:23, Ye Lin wrote:
>>>> T
>>>> hanks for your insights Rolf! The model I want to fit is y=x/a+x with
>>>> no intercept, so I transformed it to 1/y=1+a/x as they are the same.
>>> For crying out loud, they are ***NOT*** the same.  The equations y =
>>> x/(a+x) and
>>> 1/y = 1 + a/x are indeed algebraically identical, but if an "error" or
>>> "noise" term is added
>>> to each then then the nature of the error term is vastly different. It
>>> is the error or
>>> noise term that is of central concern in a statistical context.
>>>
>>>       cheers,
>>>
>>>       Rolf
>>
>>    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.
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>