On May 27, 2012, at 10:10 , array chip wrote: > Hi Peter, I might be unclear in my description of the data. Each patient was > measured for a response variable "y" at 3 time points, there is no drug or > other treatment involved. The objective was to examine the repeatability of > the measurements of response variable "y". Since this is repeated measure, I > thought it should be analyzed by a simple mixed model? When you suggested a > MxK (K=3) design, what is M then?
Number of patients, what else? The basic point is that time (visit #) is treated as a "treatment" in a block design (which pretty obviously can't be randomized). This may or may not be relevant, but it won't hurt to include a null effect, except for the loss of a couple of DF. > Thanks very much, > > John > > > > From: peter dalgaard <pda...@gmail.com> > To: array chip <arrayprof...@yahoo.com> > Cc: "r-help@r-project.org" <r-help@r-project.org> > Sent: Sunday, May 27, 2012 12:09 AM > Subject: Re: [R] a simple mixed model > > > On May 27, 2012, at 07:12 , array chip wrote: > > > Hi, I was reviewing a manuscript where a linear mixed model was used. The > > data is simple: a response variable "y" was measured for each subject over > > 3 time points (visit 1, 2 and 3) that were about a week apart between 2 > > visits. The study is a non-drug study and one of the objectives was to > > evaluate the repeatability of response variable "y". > > > > > > The author wanted to estimate within-subject variance for that purpose. > > This is what he wrote "within-subject variance was generated from SAS 'Prog > > Mixed' procedure with study visit as fixed effect and subject as random > > effect". I know that the study visit was a factor variable, not a numeric > > variable. Because each subject has 3 repeated measurements from 3 visits, > > how can a model including subject as random effect still use visit as fixed > > factor? If I would do it in R, I would just use a simple model to get > > within-subject variance: > > > > obj<-lmer(y~1+(1|subject),data=data) > > > > What does a model "obj<-lmer(y~visit+(1|subject),data=data)" mean? > > > > appreciate any thoughts! > > Sounds like a pretty standard two-way ANOVA with random row effects. > > If the design is complete (M x K with K = 3 in this case), you look at the > row and column means. An additive model is assumed and the residual > (interaction) is used to estimate the error variance. > > The variation of the row means is compared to the residual variance. If tau > is the variance between row levels, the variance of the row means is > sigma^2/K + tau, and tau can be estimated by subtraction. > > The column averages can be tested for systematic differences between visits > with the usual F test. A non-zero effect here indicates that visits 1, 2, 3 > have some _systematic_ difference across all individuals. > > For an incomplete design, the model is the same, but the calculations are > less simple. > > -- > Peter Dalgaard, Professor, > Center for Statistics, Copenhagen Business School > Solbjerg Plads 3, 2000 Frederiksberg, Denmark > Phone: (+45)38153501 > Email: pd....@cbs.dk Priv: pda...@gmail.com > > > > > > > > > > -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ 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.
