Question: Two interaction coefficients not estimable in limma's lmFit() in a 2^3 factorial design - does this change my contrast matrix now?
1
10.3 years ago by
Massimo Pinto390
Massimo Pinto390 wrote:
Greetings all, I have noticed that several users have presented the issue of parameters not estimated in some cases of linear model fittings with the limma function lmFit(). In trying to implement my 2^3 factorial design, I have followed Bioinformatics and Computational Biology Solutions using R and Bioconductor's examples as at Chapter 14 (Multifactor experiments). I have encountered my own problem with two such parameters: > fit <- lmFit(esetSub, disegno) Coefficients not estimable: Ageing6mo:LabLNGS Dose1Gy:Ageing6mo:LabLNGS Warning message: Partial NA coefficients for 2176 probe(s) whereby > disegno (Intercept) Dose1Gy Ageing6mo LabLNGS Dose1Gy:Ageing6mo Dose1Gy:LabLNGS Ageing6mo:LabLNGS Dose1Gy:Ageing6mo:LabLNGS 1 1 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 5 1 1 0 0 0 0 0 0 6 1 1 0 0 0 0 0 0 7 1 1 0 0 0 0 0 0 8 1 1 0 0 0 0 0 0 9 1 0 1 0 0 0 0 0 10 1 0 1 0 0 0 0 0 11 1 0 1 0 0 0 0 0 12 1 0 1 0 0 0 0 0 13 1 1 1 0 1 0 0 0 14 1 1 1 0 1 0 0 0 15 1 1 1 0 1 0 0 0 16 1 1 1 0 1 0 0 0 17 1 0 1 1 0 0 1 0 18 1 0 1 1 0 0 1 0 19 1 0 1 1 0 0 1 0 20 1 0 1 1 0 0 1 0 21 1 1 1 1 1 1 1 1 22 1 1 1 1 1 1 1 1 23 1 1 1 1 1 1 1 1 24 1 1 1 1 1 1 1 1 attr(,"assign") [1] 0 1 2 3 4 5 6 7 attr(,"contrasts") attr(,"contrasts")$Dose [1] "contr.treatment" attr(,"contrasts")$Ageing [1] "contr.treatment" attr(,"contrasts")$Lab [1] "contr.treatment" I have checked my design and it does make good sense to me. But, I believe I was asking too much from my parameter estimation. I am wondering how is this going to change the way I design my contrast matrix? I am trying to define my contrast matrix following the formulation of null hypotheses as at the 'yellow' book, p244. Thanking you very much, Massimo Massimo Pinto Post Doctoral Research Fellow Enrico Fermi Centre and Italian Public Health Research Institute (ISS), Rome http://claimid.com/massimopinto limma • 1.9k views ADD COMMENTlink modified 10.3 years ago by James W. MacDonald51k • written 10.3 years ago by Massimo Pinto390 Answer: Two interaction coefficients not estimable in limma's lmFit() in a 2^3 factorial 2 10.3 years ago by United States James W. MacDonald51k wrote: Hi Massimo, Massimo Pinto wrote: > Greetings all, > > I have noticed that several users have presented the issue of > parameters not estimated in some cases of linear model fittings with > the limma function lmFit(). > > In trying to implement my 2^3 factorial design, I have followed > Bioinformatics and Computational Biology Solutions using R and > Bioconductor's examples as at Chapter 14 (Multifactor experiments). > I have encountered my own problem with two such parameters: > >> fit <- lmFit(esetSub, disegno) > Coefficients not estimable: Ageing6mo:LabLNGS Dose1Gy:Ageing6mo:LabLNGS > Warning message: > Partial NA coefficients for 2176 probe(s) Well, you don't show how you built this design matrix, but I would bet you didn't use model.matrix because the matrix isn't of full rank, so you can't solve for all the coefficients you are trying to estimate here. The lmFit function is nice enough to let you know that, but you could have checked using either is.fullrank() to see if the matrix is of full rank, or nonEstimable() to see which coefficients aren't going to be estimated. Best, Jim > > whereby > >> disegno > (Intercept) Dose1Gy Ageing6mo LabLNGS Dose1Gy:Ageing6mo > Dose1Gy:LabLNGS Ageing6mo:LabLNGS Dose1Gy:Ageing6mo:LabLNGS > 1 1 0 0 0 0 > 0 0 0 > 2 1 0 0 0 0 > 0 0 0 > 3 1 0 0 0 0 > 0 0 0 > 4 1 0 0 0 0 > 0 0 0 > 5 1 1 0 0 0 > 0 0 0 > 6 1 1 0 0 0 > 0 0 0 > 7 1 1 0 0 0 > 0 0 0 > 8 1 1 0 0 0 > 0 0 0 > 9 1 0 1 0 0 > 0 0 0 > 10 1 0 1 0 0 > 0 0 0 > 11 1 0 1 0 0 > 0 0 0 > 12 1 0 1 0 0 > 0 0 0 > 13 1 1 1 0 1 > 0 0 0 > 14 1 1 1 0 1 > 0 0 0 > 15 1 1 1 0 1 > 0 0 0 > 16 1 1 1 0 1 > 0 0 0 > 17 1 0 1 1 0 > 0 1 0 > 18 1 0 1 1 0 > 0 1 0 > 19 1 0 1 1 0 > 0 1 0 > 20 1 0 1 1 0 > 0 1 0 > 21 1 1 1 1 1 > 1 1 1 > 22 1 1 1 1 1 > 1 1 1 > 23 1 1 1 1 1 > 1 1 1 > 24 1 1 1 1 1 > 1 1 1 > attr(,"assign") > [1] 0 1 2 3 4 5 6 7 > attr(,"contrasts") > attr(,"contrasts")$Dose > [1] "contr.treatment" > > attr(,"contrasts")$Ageing > [1] "contr.treatment" > > attr(,"contrasts")$Lab > [1] "contr.treatment" > > I have checked my design and it does make good sense to me. But, I > believe I was asking too much from my parameter estimation. > I am wondering how is this going to change the way I design my > contrast matrix? I am trying to define my contrast matrix following > the formulation of null hypotheses as at the 'yellow' book, p244. > > Thanking you very much, > > Massimo > > Massimo Pinto > Post Doctoral Research Fellow > Enrico Fermi Centre and Italian Public Health Research Institute (ISS), Rome > http://claimid.com/massimopinto > > _______________________________________________ > Bioconductor mailing list > Bioconductor at stat.math.ethz.ch > https://stat.ethz.ch/mailman/listinfo/bioconductor > Search the archives: http://news.gmane.org/gmane.science.biology.informatics.conductor -- James W. MacDonald, M.S. Biostatistician Douglas Lab University of Michigan Department of Human Genetics 5912 Buhl 1241 E. Catherine St. Ann Arbor MI 48109-5618 734-615-7826
thank you Jim, you are indeed correct: I did not specify how I created my matrix. Here it comes ==== Dose <- factor(targets$Dose, levels=c("Cn", "1Gy")) # It's very important that you define the levels now, with their order, as otherwise he will do it for you and this may not be the way you want it. Lab <- factor(targets$Lab, levels=c("ISS", "LNGS")) Ageing <- factor(targets$Ageing, levels=c("t0", "6mo")) disegno <- model.matrix(~Dose*Ageing*Lab) # makes a design matrix with several interaction parameters and a total of eight param. ==== given that my data set includes six independent samples (with four biological replicates each), I suppose I cannot estimate more than 6 parameters. But model.matrix() went on anyway... I suppose I could erase the last two columns of my 'disegno' Yours Massimo On Wed, Aug 5, 2009 at 6:30 PM, James W. MacDonald<jmacdon at="" med.umich.edu=""> wrote: > Hi Massimo, > > Massimo Pinto wrote: >> >> Greetings all, >> >> I have noticed that several users have presented the issue of >> parameters not estimated in some cases of linear model fittings with >> the limma function lmFit(). >> >> In trying to implement my 2^3 factorial design, I have followed >> Bioinformatics and Computational Biology Solutions using R and >> Bioconductor's examples as at Chapter 14 (Multifactor experiments). >> ?I have encountered my own problem with two such parameters: >> >>> fit <- lmFit(esetSub, disegno) >> >> Coefficients not estimable: Ageing6mo:LabLNGS Dose1Gy:Ageing6mo:LabLNGS >> Warning message: >> Partial NA coefficients for 2176 probe(s) > > Well, you don't show how you built this design matrix, but I would bet you > didn't use model.matrix because the matrix isn't of full rank, so you can't > solve for all the coefficients you are trying to estimate here. > > The lmFit function is nice enough to let you know that, but you could have > checked using either is.fullrank() to see if the matrix is of full rank, or > nonEstimable() to see which coefficients aren't going to be estimated. > > Best, > > Jim > > >> >> whereby >> >>> disegno >> >> ? (Intercept) Dose1Gy Ageing6mo LabLNGS Dose1Gy:Ageing6mo >> Dose1Gy:LabLNGS Ageing6mo:LabLNGS Dose1Gy:Ageing6mo:LabLNGS >> 1 ? ? ? ? ? ?1 ? ? ? 0 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 2 ? ? ? ? ? ?1 ? ? ? 0 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 3 ? ? ? ? ? ?1 ? ? ? 0 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 4 ? ? ? ? ? ?1 ? ? ? 0 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 5 ? ? ? ? ? ?1 ? ? ? 1 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 6 ? ? ? ? ? ?1 ? ? ? 1 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 7 ? ? ? ? ? ?1 ? ? ? 1 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 8 ? ? ? ? ? ?1 ? ? ? 1 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 9 ? ? ? ? ? ?1 ? ? ? 0 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 10 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 11 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 12 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 13 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 1 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 14 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 1 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 15 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 1 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 16 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 1 >> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 17 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 18 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 19 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 20 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 0 >> ?0 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 0 >> 21 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 1 >> ?1 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 1 >> 22 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 1 >> ?1 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 1 >> 23 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 1 >> ?1 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 1 >> 24 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 1 >> ?1 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 1 >> attr(,"assign") >> [1] 0 1 2 3 4 5 6 7 >> attr(,"contrasts") >> attr(,"contrasts")$Dose >> [1] "contr.treatment" >> >> attr(,"contrasts")$Ageing >> [1] "contr.treatment" >> >> attr(,"contrasts")$Lab >> [1] "contr.treatment" >> >> I have checked my design and it does make good sense to me. But, I >> believe I was asking too much from my parameter estimation. >> I am wondering how is this going to change the way I design my >> contrast matrix? I am trying to define my contrast matrix following >> the formulation of null hypotheses as at the 'yellow' book, p244. >> >> Thanking you very much, >> >> Massimo >> >> Massimo Pinto >> Post Doctoral Research Fellow >> Enrico Fermi Centre and Italian Public Health Research Institute (ISS), >> Rome >> http://claimid.com/massimopinto >> >> _______________________________________________ >> Bioconductor mailing list >> Bioconductor at stat.math.ethz.ch >> https://stat.ethz.ch/mailman/listinfo/bioconductor >> Search the archives: >> http://news.gmane.org/gmane.science.biology.informatics.conductor > > -- > James W. MacDonald, M.S. > Biostatistician > Douglas Lab > University of Michigan > Department of Human Genetics > 5912 Buhl > 1241 E. Catherine St. > Ann Arbor MI 48109-5618 > 734-615-7826 >
James and all, I thought of reporting here a few final remarks on this issue, in case anyone will be every taking advantage from this thread. Here I was trying to estimate 8 parameters when I only had 6 data points (with four replicates each). At maximum, I could estimate just 6 parameters. In my 2^3 factorial design, model.matrix() was neatly preparing for me a design matrix with eight parameters, though the last two could not be estimated by lmFit(). It turned out that I needed those last two parameters and that I had to drop other two 'in bewteen', which could not be estimated in my experiment as they made no real sense. They were not needed in my model. Therefore, I proceeded from my design matrix by cutting two of the columns that were created by model.matrix(). > Dose <- factor(targets$Dose, levels=c("Cn", "1Gy")) # It's very important that you define the levels now, with their order, as otherwise he will do it for you and this may not be the way you want it. > Lab <- factor(targets$Lab, levels=c("ISS", "LNGS")) > Ageing <- factor(targets$Ageing, levels=c("t0", "6mo")) > disegno <- model.matrix(~Dose*Ageing*Lab) # makes a design matrix with several interaction parameters. > designo <- disegno[,1:3] > designo1 <- disegno[,5] # I don't need column 4 > designo <- cbind(designo, designo1) > colnames(designo[4])="Dose1Gy:Ageing6mo" > designo <- cbind(designo, disegno[,7:8]) # I don't need column 6 either > is.fullrank(designo) [1] TRUE After this, my lmFit() went well and it did not take too long before I could define all the contrasts of my interest. Massimo Massimo Pinto Post Doctoral Research Fellow Enrico Fermi Centre and Italian Public Health Research Institute (ISS), Rome http://claimid.com/massimopinto On Fri, Aug 7, 2009 at 4:34 PM, Massimo Pinto<pintarello at="" gmail.com=""> wrote: > thank you Jim, > > you are indeed correct: I did not specify how I created my matrix. > > Here it comes > ==== > Dose <- factor(targets$Dose, levels=c("Cn", "1Gy")) # It's very > important that you define the levels now, with their order, as > otherwise he will do it for you and this may not be the way you want > it. > Lab <- factor(targets$Lab, levels=c("ISS", "LNGS")) > Ageing <- factor(targets$Ageing, levels=c("t0", "6mo")) > disegno <- model.matrix(~Dose*Ageing*Lab) # makes a design matrix with > several interaction parameters and a total of eight param. > ==== > > given that my data set includes six independent samples (with four > biological replicates each), I suppose I cannot estimate more than 6 > parameters. But model.matrix() went on anyway... > > I suppose I could erase the last two columns of my 'disegno' > > Yours > Massimo > > On Wed, Aug 5, 2009 at 6:30 PM, James W. MacDonald<jmacdon at="" med.umich.edu=""> wrote: >> Hi Massimo, >> >> Massimo Pinto wrote: >>> >>> Greetings all, >>> >>> I have noticed that several users have presented the issue of >>> parameters not estimated in some cases of linear model fittings with >>> the limma function lmFit(). >>> >>> In trying to implement my 2^3 factorial design, I have followed >>> Bioinformatics and Computational Biology Solutions using R and >>> Bioconductor's examples as at Chapter 14 (Multifactor experiments). >>> ?I have encountered my own problem with two such parameters: >>> >>>> fit <- lmFit(esetSub, disegno) >>> >>> Coefficients not estimable: Ageing6mo:LabLNGS Dose1Gy:Ageing6mo:LabLNGS >>> Warning message: >>> Partial NA coefficients for 2176 probe(s) >> >> Well, you don't show how you built this design matrix, but I would bet you >> didn't use model.matrix because the matrix isn't of full rank, so you can't >> solve for all the coefficients you are trying to estimate here. >> >> The lmFit function is nice enough to let you know that, but you could have >> checked using either is.fullrank() to see if the matrix is of full rank, or >> nonEstimable() to see which coefficients aren't going to be estimated. >> >> Best, >> >> Jim >> >> >>> >>> whereby >>> >>>> disegno >>> >>> ? (Intercept) Dose1Gy Ageing6mo LabLNGS Dose1Gy:Ageing6mo >>> Dose1Gy:LabLNGS Ageing6mo:LabLNGS Dose1Gy:Ageing6mo:LabLNGS >>> 1 ? ? ? ? ? ?1 ? ? ? 0 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 2 ? ? ? ? ? ?1 ? ? ? 0 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 3 ? ? ? ? ? ?1 ? ? ? 0 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 4 ? ? ? ? ? ?1 ? ? ? 0 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 5 ? ? ? ? ? ?1 ? ? ? 1 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 6 ? ? ? ? ? ?1 ? ? ? 1 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 7 ? ? ? ? ? ?1 ? ? ? 1 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 8 ? ? ? ? ? ?1 ? ? ? 1 ? ? ? ? 0 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 9 ? ? ? ? ? ?1 ? ? ? 0 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 10 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 11 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 12 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 13 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 1 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 14 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 1 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 15 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 1 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 16 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 0 ? ? ? ? ? ? ? ? 1 >>> ?0 ? ? ? ? ? ? ? ? 0 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 17 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 18 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 19 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 20 ? ? ? ? ? 1 ? ? ? 0 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 0 >>> ?0 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 0 >>> 21 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 1 >>> ?1 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 1 >>> 22 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 1 >>> ?1 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 1 >>> 23 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 1 >>> ?1 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 1 >>> 24 ? ? ? ? ? 1 ? ? ? 1 ? ? ? ? 1 ? ? ? 1 ? ? ? ? ? ? ? ? 1 >>> ?1 ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? 1 >>> attr(,"assign") >>> [1] 0 1 2 3 4 5 6 7 >>> attr(,"contrasts") >>> attr(,"contrasts")$Dose >>> [1] "contr.treatment" >>> >>> attr(,"contrasts")$Ageing >>> [1] "contr.treatment" >>> >>> attr(,"contrasts")\$Lab >>> [1] "contr.treatment" >>> >>> I have checked my design and it does make good sense to me. But, I >>> believe I was asking too much from my parameter estimation. >>> I am wondering how is this going to change the way I design my >>> contrast matrix? I am trying to define my contrast matrix following >>> the formulation of null hypotheses as at the 'yellow' book, p244. >>> >>> Thanking you very much, >>> >>> Massimo >>> >>> Massimo Pinto >>> Post Doctoral Research Fellow >>> Enrico Fermi Centre and Italian Public Health Research Institute (ISS), >>> Rome >>> http://claimid.com/massimopinto >>> >>> _______________________________________________ >>> Bioconductor mailing list >>> Bioconductor at stat.math.ethz.ch >>> https://stat.ethz.ch/mailman/listinfo/bioconductor >>> Search the archives: >>> http://news.gmane.org/gmane.science.biology.informatics.conductor >> >> -- >> James W. MacDonald, M.S. >> Biostatistician >> Douglas Lab >> University of Michigan >> Department of Human Genetics >> 5912 Buhl >> 1241 E. Catherine St. >> Ann Arbor MI 48109-5618 >> 734-615-7826 >> >