Re: [R] Linear Model with curve fitting parameter?

From: Steven McKinney <smckinney_at_bccrc.ca>
Date: Fri, 01 Apr 2011 12:44:23 -0700

> -----Original Message-----
> From: stephen sefick [mailto:ssefick_at_gmail.com]
> Sent: April-01-11 5:44 AM
> To: Steven McKinney
> Cc: R help
> Subject: Re: [R] Linear Model with curve fitting parameter?
>
> Setting Z=Q-A would be the incorrect dimensions. I could Z=Q/A.

I suspect this is confusion about what Q is. I was presuming that the Q in this following formula was log(Q) with Q from the original data.

> >> I have taken the log of the data that I have and this is the model
> >> formula without the K part
> >>
> >> lm(Q~offset(A)+R+S, data=x)

If the model is   

   Q=K*A*(R^r)*(S^s)

then

   log(Q) = log(K) + log(A) + r*log(R) + s*log(S)

Rearranging yields

   log(Q) - log(A) = log(K) + r*log(R) + s*log(S)

so what I labeled 'Z' below is

   Z = log(Q) - log(A) = log(Q/A)

so

   Z = log(K) + r*log(R) + s*log(S)

and a linear model fit of    

   Z ~ log(R) + log(S)

will yield parameter estimates for the linear equation

   E(Z) = B0 + B1*log(R) + B2*log(S)

(E(Z) = expected value of Z)

so B0 estimate is an estimate of log(K)

   B1 estimate is an estimate of r
   B2 estimate is an estimate of s

More details and careful notation will eventually lead to a reasonable description and analysis strategy.

Best

Steve McKinney

> Is fitting a nls model the same as fitting an ols? These data are
> hydraulic data from ~47 sites. To access predictive ability I am
> removing one site fitting a new model and then accessing the fit with
> a myriad of model assessment criteria. I should get the same answer
> with ols vs nls? Thank you for all of your help.
>
> Stephen
>
> On Thu, Mar 31, 2011 at 8:34 PM, Steven McKinney <smckinney_at_bccrc.ca> wrote:
> >
> >> -----Original Message-----
> >> From: r-help-bounces_at_r-project.org [mailto:r-help-bounces_at_r-project.org] On Behalf Of stephen
> sefick
> >> Sent: March-31-11 3:38 PM
> >> To: R help
> >> Subject: [R] Linear Model with curve fitting parameter?
> >>
> >> I have a model Q=K*A*(R^r)*(S^s)
> >>
> >> A, R, and S are data I have and K is a curve fitting parameter.  I
> >> have linearized as
> >>
> >> log(Q)=log(K)+log(A)+r*log(R)+s*log(S)
> >>
> >> I have taken the log of the data that I have and this is the model
> >> formula without the K part
> >>
> >> lm(Q~offset(A)+R+S, data=x)
> >>
> >> What is the formula that I should use?
> >
> > Let Z = Q - A for your logged data.
> >
> > Fitting lm(Z ~ R + S, data = x) should yield
> > intercept parameter estimate = estimate for log(K)
> > R coefficient parameter estimate = estimate for r
> > S coefficient parameter estimate = estimate for s
> >
> >
> >
> > Steven McKinney
> >
> > Statistician
> > Molecular Oncology and Breast Cancer Program
> > British Columbia Cancer Research Centre
> >
> >
> >
> >>
> >> Thanks for all of your help.  I can provide a subset of data if necessary.
> >>
> >>
> >>
> >> --
> >> Stephen Sefick
> >> ____________________________________
> >> | Auburn University                                         |
> >> | Biological Sciences                                      |
> >> | 331 Funchess Hall                                       |
> >> | Auburn, Alabama                                         |
> >> | 36849                                                           |
> >> |___________________________________|
> >> | sas0025_at_auburn.edu                                  |
> >> | http://www.auburn.edu/~sas0025%c2                |
> >> |___________________________________|
> >>
> >> Let's not spend our time and resources thinking about things that are
> >> so little or so large that all they really do for us is puff us up and
> >> make us feel like gods.  We are mammals, and have not exhausted the
> >> annoying little problems of being mammals.
> >>
> >>                                 -K. Mullis
> >>
> >> "A big computer, a complex algorithm and a long time does not equal science."
> >>
> >>                               -Robert Gentleman
> >> ______________________________________________
> >> 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.
> >
>
>
>
> --
> Stephen Sefick
> ____________________________________
> | Auburn University                                         |
> | Biological Sciences                                      |
> | 331 Funchess Hall                                       |
> | Auburn, Alabama                                         |
> | 36849                                                           |
> |___________________________________|
> | sas0025_at_auburn.edu                                  |
> | http://www.auburn.edu/~sas0025%c2                |
> |___________________________________|
>
> Let's not spend our time and resources thinking about things that are
> so little or so large that all they really do for us is puff us up and
> make us feel like gods.  We are mammals, and have not exhausted the
> annoying little problems of being mammals.
>
>                                 -K. Mullis
>
> "A big computer, a complex algorithm and a long time does not equal science."
>
>                               -Robert Gentleman



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