Dear Roger, I think that there is a problem with your strategy. The problem is that, because you have included random slopes within your model, the quantity of variance explained by the random effects varies as a function of Age. Therefore it is not possible to pin down a single repeatability, as I understand it. Had you included only random intercepts then you'd be on safe ground.
See, for example, Partitioning Variation in Multilevel Models. By: Goldstein, Harvey; Browne, William; Rasbash, Jon. Understanding Statistics, 2002, Vol. 1 Issue 4, p223, 9p; (AN 8655390) Cheers Andrew On Wed, May 17, 2006 at 09:14:20AM +0200, Roger Sch?rch wrote: > Dear Spencer Graves > > First I would like to thank you very much for answering to my mail. Then I > would like to clarify some points, so that I would eventually find a > solution to my problem. > > --- > SG: I have not done a serious literature search of "repeatability", but I > would not assume that it is defined in exactly the same way by all sources > that use that term. > --- > > Well, as stated in the introduction, I am following Lessells & Boag (1987), > who define (in words): "REPEATABILITY is a measure used in quantitative > genetics to describe the proportion of variance in a character that occurs > among rather than within individuals." > > So, I would like to know, how consistent my fish behave, whether the > variance is rather between the individuals that I have observed or within > the individuals. > > I could use an anova, but I'd rather stick to mixed effects models, as it > seems to be common sense to use that with longitudinal data (though it seems > not to be widely used in zoological/behavioural research ...). > > --- > SG: What "slope" are you describing here? Consider the following > modification of one of the standard 'lme' examples: > > > [...] > > > (fm1.1 <- lme(distance ~ age, > + random=~age|Subject, data = Orthodont)) # random is ~ age > > [...] > > > (fm1.0 <- lme(distance ~ age, > + random=~1|Subject, data = Orthodont)) # random is ~ age > > The first model estimates a "slope" for "age" as a fixed effect AND a > variation in that for each Subject. The second assumes this slope is > constant between Subjects, and only the "(Intercept)" varies between > subjects. > --- > > I allow a different slope for every subject, so my model is similar to the > first model. Additionally I have a fixed effect for "sex": > > myLme <- lme(fixed = explorationScore ~ Sex*I(Sequence - 1), data = myData, > random = ~ I(Sequence - 1) | Fish, method = "ML") > > Sequence = 1st to 6th measurement (each measurement 30 d apart; do I have to > specify that it is not a continuous variable??) > Fish = Subject > > --- > SG: I would encourage you to first think carefully about the problem(s) > you want to solve. What would people want to do with the results of > your study? After you've answered that question, if some definition of > "repeatability" (carefully defined with an appropriate citation) seems > to provide some insight, I'd try to explain why it does, then give the > quantitative answer with my interpretation and with appropriate > citations to show that my logic here is not completely original. If > however, "repeatability" did NOT seem to support my main message, then I > would likely ignore it. > --- > > So, here are my questions for that particular model that I am investigating: > > 1. Do the fish change their behaviour during ontogeny? > 2. Do the sexes differ in their behaviour? > 3. Do my fish behave consistently (when one accounts for the change over > time (see 1. point))? > > Let us consider you example again, but add "Sex" as a fixed effect, so that > it is more similar to my analysis: > > > fm1.1 <- lme(distance ~ age*Sex,random=~age|Subject, data = Orthodont) > > And then have a look at the variance components: > > > VarCorr(fm1.1) > Subject = pdLogChol(age) > Variance StdDev Corr > (Intercept) 5.78842347 2.4059143 (Intr) > age 0.03255509 0.1804303 -0.668 > Residual 1.71611214 1.3100046 > > We see that an individual's true intercept is deviating from the mean > intercept considerably, but the differences in rate of change seem to be > rather small. Then there is some residual variance that is not accounted for > by fitting a change trajectory for every individual, a scatter around an > individual's true change trajectory. > > Now, if I am interested in the ratio (among_variance / (within_variance + > among_variance)), how is that computed? For our example here I would > suggest: > > > (as.numeric(VarCorr(fm1.1)[1])+as.numeric(VarCorr(fm1.1)[2])) / > (as.numeric(VarCorr(fm1.1)[1])+as.numeric(VarCorr(fm1.1)[2])+as.numeric(VarC > orr(fm1.1)[3])) > [1] 0.772311 > > To my understanding, this would be the repeatability of the character > "distance", and would therefore result in a statement like this: most of the > variance in distance is found between subjects, rather than within (r = > 0.772311). > > The only question I would have liked to pose to the r-help list, is, whether > I compute the among_variance from the R output correctly or whether I am > lacking something that is not directly available from the standard output R > produces. > > Repeatability is widely used in zoological literature, but it is usually > assumed that there are no time effects. That is why I would like to use lme > AND provide the readers with a familiar number ... Furthermore, it provides > a guess for the maximal heritability that I can expect for that particular > trait, which might prove very useful for further studies, and it would be > comparable with other behaviours, e.g. in a table. > > This has become a somewhat lengthy e-mail, so here are my apologies. But I > am still not sure whether I could make myself understood. Thanks anyway for > your kind help! > > Yours > Roger > > P.S.: There is a study that has done similar things (M?ller & Schrader, > 2005, Behaviour 142, 1289--1306), but it rather confused me, and the > corresponding author does not seem willing to correspond ... But perhaps it > helps in understanding my problem. > > ______________________________________________ > [email protected] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html -- Andrew Robinson Department of Mathematics and Statistics Tel: +61-3-8344-9763 University of Melbourne, VIC 3010 Australia Fax: +61-3-8344-4599 Email: [EMAIL PROTECTED] http://www.ms.unimelb.edu.au ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
