Linear Model with curve fitting parameter?
Steven: You are exactly right sorry I was confused. ####################################################### so log(y-intercept)+log(K) is a constant called b0 (is this right?) lm(log(Q)~log(A)+log(R)+log(S)-1) is fitting the model log(Q)=a*log(A)+r*log(R)+s*log(S) (no beta 0) and lm(log(Q)~log(A)+log(R)+log(S)) is fitting the model log(Q)=b0+a*log(A)+r*log(R)+s*log(S) ###################################################### These are the models I am trying to fit and if I have reasoned correctly above then I should be able to fit the below models similarly. manning log(Q)=log(b0)+log(K)+log(A)+r*log(R)+s*log(S) dingman log(Q)=log(b0)+log(K)+a*log(A)+r*log(R)+s*(log(S))^2 bjerklie log(Q)=log(b0)+log(K)+a*log(A)+r*log(R)+s*log(S) ####################################################### Thank you for all of your help! Stephen
On Fri, Apr 1, 2011 at 2:44 PM, Steven McKinney <smckinney at bccrc.ca> wrote:
-----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? ? ? ? ? ?? ? ? | |___________________________________| 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? ? ? ? ? ?? ? ? | |___________________________________| 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
Stephen Sefick ____________________________________ | Auburn University? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? | | Biological Sciences ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ?? ? ? ?| | 331 Funchess Hall? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?| | Auburn, Alabama? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ??? | | 36849? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? | |___________________________________| | sas0025 at auburn.edu? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ?| | http://www.auburn.edu/~sas0025? ? ? ? ? ?? ? ? | |___________________________________| 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