Hi Gordon, I've been out for a while and finally read your detailed reply. Thanks so much - it really helps clarify things for me!! Cheers, Jenny At 05:55 PM 11/27/2008, Gordon K Smyth wrote: >Hi Jenny, > >Should blocks be fixed (in the design matrix) or treated as random >(hence enter the covariance matrix as correlations)? This question >has a long history in mathematical statistics, so long that you can >be sure than the answer is somewhat subtle. > >Neither approach is right or wrong. The random approach makes more >assumptions and allows you, in some circumstances, to extract more >information. The limma approach with dupcor etc makes even more >assumptions than classical random effects models. If the blocks are >treated as fixed, then treatments can only be compared within >blocks. If blocks are treated as random, then it is possible to >compare treatments between blocks as well as within. > >So the first key issue is whether treatment comparisons are made >between blocks or within blocks. > >Suppose you do an experiment on random samples of subjects from two >groups, in which each subject is subjected to several tests. The >subjects are blocks. The total sums of squares can be divided into >between and within subject sums of squares. In other words, the >information in the data can be divided into a between-subject error >strata and a within-subject strata. > >Suppose you want to compare the two groups. All the information is >in the between-subject error strata. You cannot do any statistical >test unless you treat the subjects as random. > >Suppose now you want to compare the treatments. If the experiment >is balanced (all subjects do all tests), then all the information >about the treatments is in the within-block strata. So you may as >well treat the subjects as fixed effects (as for example is done in >a paired t-test). > >If the experiment is unbalanced (each subject does only a subset of >the tests, subjects do tests a different number of times), then you >can extract more information about the treatment comparisons from >the between-subject error strata. To do this, you have to treat the >blocks as random. > >The second key issue to consider is whether it makes sense >scientifically to treat the blocks as random. If there are only two >or three blocks, then there is little to be gained by treating them >as random. If the blocks have large unpredictable effects, then it >is much safer to treat them as fixed. If you want to make specific >conclusions about each of the blocks, then it doesn't make sense to >treat them as a random. In general, random is natural if there are >lots of blocks with relatively small effects and not of interest in >themselves. Sometimes you can go either way. > >Hope this helps >Gordon > >On Tue, 25 Nov 2008, Jenny Drnevich wrote: > >>Hi Jim, >> >>I've seen you suggest this way for account for blocks by fitting >>extra columns in the design matrix before. I'm just wondering how >>this differs from the suggestion in the limma vignette (Section 8.2 >>Technical Replication) to use duplicateCorrelation() to determine >>the average correlation between blocks. I know they are not >>mathematically equivalent; the coefficients for the treatment >>groups are slightly different, they use different DF, and the >>p-values tend to be larger using the duplicateCorrelation() method >>(at least for the one experiment I'm using). So, is one more >>"correct" than the other? Or are blocks of technical replicates >>different somehow than blocks of patients or cell lines, etc.? >> >>Thanks, >>Jenny > >Jenny Drnevich, Ph.D. > >Functional Genomics Bioinformatics Specialist >W.M. Keck Center for Comparative and Functional Genomics >Roy J. Carver Biotechnology Center >University of Illinois, Urbana-Champaign > >330 ERML >1201 W. Gregory Dr. >Urbana, IL 61801 >USA > >ph: 217-244-7355 >fax: 217-265-5066 >e-mail: drnevich at illinois.edu