-------- Original Message -------- Subject: RE: multiple correlated variables Date: Tue, 26 Feb 2008 18:27:22 -0800 (PST) From: F. James Rohlf <[EMAIL PROTECTED]> Reply-To: [EMAIL PROTECTED] Organization: Stony Brook University To: [email protected] References: <[EMAIL PROTECTED]>
It may not be that easy. Jason said he has only one dependent variable and many independent variables. The problem for a general analysis is that Jason says that the independent variables are highly correlated - which means that standard regression methods may fail because one cannot reliably invert their covariance matrix. There are alternative methods such as ridge regression, partial least squares, and principal components regression.
If the question really is just "which independent variable is more important in explaining variation in the dependent one" then just regress the dependent variable on each of the independent variables one at a time and see which gives the highest R^2 value. However, usually the question is what set of independent variables gives the best prediction and that requires simultaneous testing and introduces the problems mentioned in my first paragraph.
------------------------ F. James Rohlf, Distinguished Professor Ecology & Evolution, Stony Brook University www: http://life.bio.sunysb.edu/ee/rohlf
-----Original Message----- From: morphmet [mailto:[EMAIL PROTECTED] Sent: Tuesday, February 26, 2008 3:30 PM To: morphmet Subject: Re: multiple correlated variables -------- Original Message -------- Subject: Re: multiple correlated variables Date: Mon, 25 Feb 2008 17:16:01 -0800 (PST) From: Joseph Kunkel <[EMAIL PROTECTED]> To: [email protected] CC: Joseph Kunkel <[EMAIL PROTECTED]> References: <[EMAIL PROTECTED]> Jason, The appropriate approach is Analysis of Dispersion which is the multivariate extension of Analysis of Variance. It allows multiple Yi observations that may be correlated via a Cov(Yi,Yj) covariance matrix. These are related to a traditional X design matrix via the generalized matrix equation Y = XB where Y is n by p for p dependent characters and sample size n. X is n by k for k design elements or independent variables. That results in a k by p matrix of parameters, B, to be estimated. One can ask the question for design feature q, a portion of the k design elements: Given characters say 1 to 10 of the p available, if characters 1-5 are corrected for characters 6-10 is there any additional information in 1-5 that is significant on the design feature q. This type of question answers your query of whether one variable or a set of variables is more important or more predictive than another set and answers it with an F-test. I have a set of R-scripts that carry out this analysis if you are willing to use the Gnu Public R calculation environment and are somewhat familiar with setting up the X design matrices. I have not seen another convenient implementation of this although I am sure it can be found somewhere else. Analysis of Dispersion is well described in C. Radhakrishna Rao (1965) Linear Statistical Inference and Its Applications, 1st Edition. Joe Kunkel [EMAIL PROTECTED] On Feb 25, 2008, at 11:30 AM, morphmet wrote: > -------- Original Message -------- > Subject: multiple correlated variables > Date: Sun, 24 Feb 2008 04:48:15 -0800 (PST) > From: Jason S <[EMAIL PROTECTED]> > To: [email protected] > > > > > Dear all, > > I have a quick question, and I'd love to hear any suggestions you > might > have. > > I got one dependent variable (body size) and several independent > variables, and I'm trying to figure out which independent variable is > more important in explaining variation in the dependent one > (experiments > are not feasible). The problem is that many of the independent > variables > are themselves highly correlated. I thought about calculating partial > correlation coefficients, but I'm not very confident with that choice. > Any suggestions? > > Thanks a lot! > > Jason > > --------------------------------------------------------------------- --- > Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try > it now. > <http://us.rd.yahoo.com/evt=51733/*http://mobile.yahoo.com/;_ylt=Ahu06i 62sR8HDtDypao8Wcj9tAcJ > > > > -- > Replies will be sent to the list. > For more information visit http://www.morphometrics.org -·. .· ·. .><((((º>·. .· ·. .><((((º>·. .· ·. .><((((º> .··.· >=- =º}}}}}>< Joseph G. Kunkel, Professor Biology Department University of Massachusetts Amherst Amherst MA 01003 http://www.bio.umass.edu/biology/kunkel/ -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
-- Replies will be sent to the list. For more information visit http://www.morphometrics.org
