> -----Original Message----- > From: stephen sefick [mailto:ssef...@gmail.com] > Sent: April-04-11 2:49 PM > To: Steven McKinney > Subject: Re: [R] Linear Model with curve fitting parameter? > > Steven: > > I am really sorry for my confusion. I hope this now makes sense. > > b0 == y intercept == y-intercept == (intercept) fit by lm > > a <- 1:10 > b <- 1:10 > > summary(lm(a~b)) > #to show what I was calling b0 > > So... > > ################################################ > manning > > Q = K*A*(R^b2)*(S^b3) > > log(Q) = log(K)+log(A)+(b2*log(R))+(b3*log(S))
Okay, using this notation, this appears to be the original model you queried about. So for this model, as I showed before, Let Z = log(Q) - log(A) E(Z) = b0 + b2*log(R) + b3*log(S) = log(K) + b2*log(R) + b3*log(S) Fitting the model lm(Z ~ log(R) + log(S)) will yield parameter estimates b_hat_0, b_hat_2, b_hat_3 where b_hat_0 (the fitted model intercept) is an estimate of b0 (which is log(K)), b_hat_2 is an estimate of b2, b_hat_3 is an estimate of b3. So in answer to your previous question, b0 is an estimate of log(K), not ( log(Qintercept)+log(K) ) so an estimate for K is exp(b_hat_0) > > ################################################ > dingman > Q = K*(A^b1)*(R^b2)*(S^b3*log(S)) > > log(Q) = log(K)+(b1*log(A))+(b2*log(R))+(b3*(log(S))^2) The dingman model notation is ambiguous. Is the last term S^(b3*log(S)) or (S^b3)*log(S) ? Previous email showed > dingman > log(Q)=log(b0)+log(K)+a*log(A)+r*log(R)+s*(log(S))^2 which implies (if I ignore the log(b0) term) Q = K*(A^a)*(R^r)*(exp(log(S)*log(S))^s) = K*(A^a)*(R^r)*(S^(log(S)*s)) This is linearizable as log(Q) = log(K) + a*log(A) + r*log(R) + s*(log(S))^2 = b0 + b1*log(A) + b2*log(R) + b3*(log(S)^2) Fitting lm(log(Q) ~ log(A) + log(R) + I(log(S)^2) ... ) will yield estimates b_hat_0, b_hat_1, b_hat_2 and b_hat_3 where b_hat_0 is an estimate of b0 = log(K) so an estimate of K is exp(b_hat_0), b_hat_1 is an estimate of b1 = a, b_hat_2 is an estimate of b2 = r, b_hat_3 is an estimate of b3 = s > > ################################################ > > Bjerklie > > Q = K*(A^b1)*(R^b2)*(S^b3) > > log(Q) = log(K)+(b1*log(A))+(b2*log(R))*(b3*log(S)) Fitting lm(log(Q) ~ log(A) + log(R) + log(S) ... ) will yield estimates b_hat_0, b_hat_1, b_hat_2 and b_hat_3 where b_hat_0 is an estimate of b0 = log(K) so an estimate of K is exp(b_hat_0), b_hat_1 is an estimate of b1 = a, b_hat_2 is an estimate of b2 = r, b_hat_3 is an estimate of b3 = s Best Steve McKinney > > ################################################ > > > > > > On Mon, Apr 4, 2011 at 2:58 PM, Steven McKinney <smckin...@bccrc.ca> wrote: > > > >> -----Original Message----- > >> From: stephen sefick [mailto:ssef...@gmail.com] > >> Sent: April-03-11 5:35 PM > >> To: Steven McKinney > >> Cc: R help > >> Subject: Re: [R] 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?) > > > > Doesn't look right to me based on the information you've provided. > > I don't see anything labeled "y" in your previous emails, so I'm > > not clear on what y is and how it relates to the original model > > you described > > > > > >> 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. > > > > 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) > > > > Let 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 > > > > and these are the only parameters you described in the original model. > > > > > >> > >> 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) > > > > K has disappeared from these equations so these model fits do > > not correspond to the model originally described. Now a b0 > > appears, and is used in models below. I think changing notation > > is also adding confusion. What are "y" and "intercept" you > > discuss above, in relation to your original notation? > > > >> > >> ###################################################### > >> > >> 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. > > > > You will be able to fit models appropriately once you have a > > clearly defined system of notation that allows you to map between > > the proposed data model, the parameters in that model, and the > > corresponding regression equations. > > > > Once you have consistent notation, you will be able to see > > if you can express your model as a linear regression, or > > if not, what kind of non-linear regression you will need to > > do to get estimates for the parameters in your model. > > > > Best > > > > Steve McKinney > > > >> > >> 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 <smckin...@bccrc.ca> wrote: > >> > > >> >> -----Original Message----- > >> >> From: stephen sefick [mailto:ssef...@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 <smckin...@bccrc.ca> > >> >> wrote: > >> >> > > >> >> >> -----Original Message----- > >> >> >> From: r-help-boun...@r-project.org > >> >> >> [mailto:r-help-boun...@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 | > >> >> >> |___________________________________| > >> >> >> | sas0...@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@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 | > >> >> |___________________________________| > >> >> | sas0...@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 | > >> |___________________________________| > >> | sas0...@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 | > |___________________________________| > | sas0...@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@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.