Multivariate Random Regression using Proc Mixed ?
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From: Dale McLerran on 14 Jan 2010 16:19 --- On Tue, 1/12/10, John Stinchcombe <john.stinchcombe(a)UTORONTO.CA> wrote: > From: John Stinchcombe <john.stinchcombe(a)UTORONTO.CA> > Subject: Multivariate Random Regression using Proc Mixed ? > To: SAS-L(a)LISTSERV.UGA.EDU > Date: Tuesday, January 12, 2010, 10:15 AM > Hi All- > > I have a question for the group that I am hoping you can give me some > insight on. My goal is to do a multivariate random regression in SAS > with Proc Mixed.. I'll describe the experimental design (briefly), and > am hopeful that someone on the list can tell me if my what I am aiming > to do is called multivariate random regression, and moreover, if/how > Proc Mixed can do it. > > I have many replicate individuals of many inbred lines that were grown > in several different experimental environments. I measured size of all > of these individuals 6 times over their life cycle. My goal is as > follows: I want to fit a random regression that describes size as a > function of time for each inbred line, which is straightforward. (So far > so good). However, rather than estimating the covariance between slope > and intercept within an individual experimental environment, I want to > estimate the covariance between the inbred line slope estimates /across > /the different experimental environments. E.g., is there a positive > covariance, at the inbred line level, between slopes in environments A & > B? i.e., are inbred lines with positive deviations for their slopes in > environment A the same as those with positive deviations for their > slopes in environment B ? > > It is relatively straightforward to fit random regressions for each > experimental environment separately, save the slope estimates for each > inbred line, and then estimate the variance and covariance of these > slopes across environments. However, this is a two-step process, and > seems to make inefficient use of the data. Moreover, my eventual goal > would be to estimate the variance covariance matrix of these slopes, at > the inbred line level, using a factor analytic structure.... as most of > the variation of interest will lie in only a few directions. > > I would appreciate any help. > > Thanks, > > John > > -- > ----------------------------------------------------------- > John Stinchcombe > Department of Ecology and Evolutionary Biology > University of Toronto, 25 Willcocks St. > Toronto, ON > Canada M5S 3B2 > > 416-946-5986 > > http://labs.eeb.utoronto.ca/stinchcombe/ > John, Let me first summarize my understanding of your problem. You have a number of experimental environments. You also have several inbred lines, each producing multiple individuals. Some of the individuals from each line are grown in each environment. Each individual is observed repeatedly over time. Interest is in measured size as a function of time. Environment and time are both predictors of size which would enter as fixed effects. There may be variability across inbred lines in the slope of the regression. Also, there may be variability in the inbred line slope across environments. I would wonder if there might not also be intercept differences across inbred lines (which could also vary by environment). So, you would have a model with the following characteristics: Fixed effects: environment, time Random effects: 1) Within environment intercept and time effects for each inbred line. We are interested in the covariance of the inbred line random effects across the different environments 2) Individual from inbred line intercept and time effects I believe the following model would express all of the terms of interest, including the covariance of inbred line slope estimates across different environments. proc mixed data=mydata; class env line indiv; model y = env time / s; random env env*time / subject=line type=un; random intercept time / subject=indiv type=un; run; You might want to compare this to a model which assumes that the intercept and slope random effects do not differ by environment. You can construct a likelihood ratio test to assess the hypothesis that the inbred line random effect intercept and slope effects are the same for all environments. The model with random intercept and slope effects which are the same for all environments would be fit with the code: proc mixed data=mydata; class env line indiv; model y = env time / s; random intercept time / subject=line type=un; random intercept time / subject=indiv type=un; run; The difference in -2LL for these two models is distributed as chi-square with df 2*(E-1) where E is the number of experimental environments in your study. HTH, Dale --------------------------------------- Dale McLerran Fred Hutchinson Cancer Research Center mailto: dmclerra(a)NO_SPAMfhcrc.org Ph: (206) 667-2926 Fax: (206) 667-5977 --------------------------------------- |