Note that your equations can be written: y = alpha*A + (1-alpha)*B, which is equivalent to
y = (A-B) * alpha + B , i.e. of form y = C*alpha + B a simple linear equation in alpha You have two different values of alpha at which y was measured, so just stack up all your results into a single regression setup with these two different alphas. Except for your constraints. But if I understand you correctly, the problem is not that C and B must be between 0 and 1, it is that the response, y, must be (it is a frequency). If so, this suggests that you need to set this up as a glm, probably with a binomial link. Trivial to do, but I suspect you don't know about glm's, which is why I said that you may be out of your depth and seek local help. If I'm wrong, my apologies for misunderstanding. If I'm not, I'm sorry, but I don't wish to teach you about basic statistics on this list. Read up on "generalized linear models," for which there are undoubtedly a host of good web tutorials available. Cheers, Bert On Mon, Mar 19, 2012 at 12:48 PM, Diviya Smith <diviya.sm...@gmail.com> wrote: > Hello Bert, > > This is definitely not for a homework problem. I am trying to estimate > frequencies of mutations in different groups. The mutation frequencies can > be modeled as a linear relation in cases of mixtures. So I have a lot of > populations that follow the relationship - > > y = alpha*A + beta*B and I want to estimate A and B; given y, alpha and > beta. A and B are both vectors of the same size as y. > > Can you suggest where I can find some information about your suggestion > #4...that is exactly what I was hoping to do. > > Thanks, > Diviya > > > > On Mon, Mar 19, 2012 at 3:02 PM, Bert Gunter <gunter.ber...@gene.com> wrote: >> >> 1. Homework assignment? We don't do homework here. >> >> 2. If not, a mixture model of some sort? I suggest you state the >> context of the problem more fully. R has several packages to do >> mixture modeling, if that's what you're trying to do. >> >> 3. In any case, this cannot be done with lm() (at least without tricks). >> >> 4. In your notation below, the "separate" regressions can be stacked >> into a single constrained regression model. >> >> 5. You might do better to find local statistical help, as you may have >> bitten off more than you can chew. >> >> -- Bert >> >> On Mon, Mar 19, 2012 at 11:29 AM, Diviya Smith <diviya.sm...@gmail.com> >> wrote: >> > Hello there, >> > >> > I am new to using regression in R. I wanted to solve a simple regression >> > problem where I have 2 equations and 2 unknowns. >> > >> > So lets say - >> > y1 = alpha1*A + beta1*B >> > y2 = alpha2*A + beta2*B >> > >> > y1 <- runif(100000, 0,1) >> > y2 <- runif(100000,0,1) >> > >> > alpha1 <- 0.6 >> > alpha2 <- 0.75 >> > >> > beta1 <- 1-alpha1 >> > beta2 <- 1-apha2 >> > >> > I now want this equation to estimate the values of A and B. Both A and B >> > are constrained to be between (0,1). I would like to use lm with these >> > constraints and I am having a little trouble in defining the equations >> > correctly. Any help would be most appreciated. >> > >> > Thank you, >> > Diviya >> > >> > [[alternative HTML version deleted]] >> > >> > ______________________________________________ >> > 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. >> >> >> >> -- >> >> Bert Gunter >> Genentech Nonclinical Biostatistics >> >> Internal Contact Info: >> Phone: 467-7374 >> Website: >> >> http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm > > -- Bert Gunter Genentech Nonclinical Biostatistics Internal Contact Info: Phone: 467-7374 Website: http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm ______________________________________________ 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.