From: Andrew Robinson <A.Robinson_at_ms.unimelb.edu.au>

Date: Wed 17 May 2006 - 17:59:23 EST

Date: Wed 17 May 2006 - 17:59:23 EST

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.
**>
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*

-- Andrew Robinson Department of Mathematics and Statistics Tel: +61-3-8344-9763 University of Melbourne, VIC 3010 Australia Fax: +61-3-8344-4599 Email: a.robinson_at_ms.unimelb.edu.au http://www.ms.unimelb.edu.au ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.htmlReceived on Wed May 17 18:03:44 2006

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