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

[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:
> 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
>> but i will look up nls() and see how to fit the model without
>> transformation.
>>
>>
>> On Tue, Aug 20, 2013 at 2:45 PM, Rolf Turner <rolf.turner at xtra.co.nz
>> <mailto:rolf.turner at xtra.co.nz>> wrote:
>>
>>
>>     (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:
>>
>>         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?
>>
>>
>
>
>         [[alternative HTML version deleted]]
>
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-- 

Bert Gunter
Genentech Nonclinical Biostatistics

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