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List: r-sig-mixed-models
Subject: Re: [R-sig-ME] Interpreting fixed effects of mcmcglmm interaction and randomisation
From: Rob Griffin <robgriffin247 () hotmail ! com>
Date: 2016-05-27 10:44:26
Message-ID: DUB124-W49CD3D7E93AE7CF2936082FA420 () phx ! gbl
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When you suggest "Mort*SexF" do you mean
mod1 = MCMCglmm(Life ~ Mort*Sex,
... such that the "-1" is removed from my original model specification?
Furthermore, if I added a second categorical fixed effect (e.g. whether the \
individual had 0, 1, or >1 older siblings [ie. whether it was the first, second, or a \
later offspring]) would the calculations for predictions be first born & female: (b1 \
+ b2) * xfirst born & male: (b1 + b3) + (b2 + b6) * xsecond born & female: (b1 + b5) \
+ (b2 + b8) * xsecond born & male: (b1 + b3 + b5 + b10) + (b2 + b6 + b8 + b12) * \
xlater & female: (b1 + b4) + (b2 + b7) * xlater & male: (b1 + b3 + b4 + b9) + (b2 + \
b6 + b7 + b11) * x where
b1 = (Intercept), b2 = Mort, b3 = SexM, b4 = GroupLater, b5 = GroupSecond, \
b6 = Mort:SexM, b7 = Mort:GroupLater, b8 = Mort:GroupSecond, b9 = \
SexM:GroupLater, b10 = SexM:GroupSecond, b11 = Mort:SexM:GroupLater, b12 = \
Mort:SexM:GroupSecond and should I include all or just the significant effects?
Cheers, Rob
----------------------------------------------------------
Robert M. GriffinPostdoctoral Researcher, University of \
Turkuwww.griffinevo.wordpress.com
> Subject: Re: [R-sig-ME] Interpreting fixed effects of mcmcglmm interaction and \
> randomisation
> To: robgriffin247@hotmail.com; r-sig-mixed-models@r-project.org
> From: j.hadfield@ed.ac.uk
> Date: Mon, 16 May 2016 17:26:11 +0100
>
> Hi,
>
> You should use ~Mort*SexF. At the moment you force the male and female
> intercepts through the origin. You will get four terms; an intercept and
> Mort effect (which are the female intercpet and slope) and a SexM and
> Mort:SexM effect (which are the deviations of the male inetcept and
> slope from the female intercept and slope. The two lines will cross at
> some value of Mort. If we denote the four effects as b1 (intercept), b2
> (Mort), b3 (SexM) and b4 (Mort:SexM) and a value of Mort as x then
>
> female prediction = b1+b2*x
> male prediction = b1+b3+(b2+b4)*x
>
> and so the value of x when female prediction = male prediction is -b3/b4
>
> You could test whether the posterior distribution of -b3/b4 lies outside
> the range of observed x in which case sexual-dimorophism always
> increases as x (if -b3/b4 is smaller than the minimum of x) increases or
> always increases as x (if -b3/b4 is larger than the maximum of x)
> decreases. If -b3/b4 lies at intermediate values of x the change in
> sexual dimorphism will flip across the range of x.
>
> Cheers,
>
> Jarrod
>
>
>
>
> On 13/05/2016 13:51, Rob Griffin wrote:
> > Dear list,
> >
> > I am trying learn how to model the relationship between an environmental factor \
> > and sexual dimorphism using MCMCglmm, and have based analysis on the data in \
> > Garratt et al 2015* - a study looking at the relationship between sexual \
> > dimorphism in lifespan, and juvenile mortality. They use two populations measured \
> > over a number of years, giving cohorts (for which juvenile mortality can be \
> > estimated), and information on the identity, lifespan, and sex of each \
> > individual. The script below** creates the dummy data I am using to develop the \
> > model which is similar to the data set they would have used (though entirely \
> > artificial - I have forced a positive relationship between juvenile mortality and \
> > male lifespan, while female lifespan is random). They fit a general linear mixed \
> > model to "assess the relationship between survival to the onset of actuarial \
> > senescence (dependent variable) and cohort-specific juvenile mortality \
> > (independent variable), while including sex as a fixed effect, year and \
> > population as random effects, with year nested within population." I have \
> > attempted to recreate this analysis (but using MCMCglmm) as the following (where \
> > 'Life' is lifespan, 'Mort' is juvenile mortality within the individuals cohort, \
> > 'Sex' is the sex of the individual, 'Pop' and 'Year' are the population and year \
> > of the individual):
> >
> > mod1 = MCMCglmm(Life ~ Mort:Sex - 1,
> > random = ~ Pop:Year,
> > rcov = ~units,
> > nitt = 13000, burnin = 3000, thin = 10,
> > prior = prior1,
> > pr = T,
> > family = "gaussian",
> > start = list(QUASI = FALSE),
> > data = DF1)
> >
> > > summary(mod1)
> > Iterations = 3001:12991
> > Thinning interval = 10
> > Sample size = 1000
> >
> > DIC: 1437.558
> >
> > G-structure: ~Pop:Year
> >
> > post.mean l-95% CI u-95% CI eff.samp
> > Pop:Year 34.23 19.4 55.2 1000
> >
> > R-structure: ~units
> >
> > post.mean l-95% CI u-95% CI eff.samp
> > units 4.746 3.946 5.487 909.7
> >
> > Location effects: Life ~ Mort:Sex - 1
> >
> > post.mean l-95% CI u-95% CI eff.samp pMCMC
> > Mort:SexF 25.17 20.61 30.46 1000 <0.001 ***
> > Mort:SexM 43.81 38.82 48.71 1000 <0.001 ***
> > ---
> > Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> >
> >
> > Which brings me to my main subject(s) of interest: essentially, how to interpret \
> > the fixed effect estimates, given that I am aiming to answer the question, is \
> > juvenile mortality related to sexual dimorphism in lifespan?
> > Going from 'Life ~ Mort -1' to 'Life ~ Mort:Sex -1' improves the fit of the model \
> > (DIC 1902 -> 1438), so could I conclude that there is a significant sex-specific \
> > effect/interaction with juvenile mortality on lifespan? What do the actual values \
> > of the posterior mean (post.mean) tell me - is it just that the Mort:SexM \
> > interaction effect is significantly larger than the Mort:SexF effect (CI's of the \
> > two estimates do not overlap)? Using Mort*Sex gives SexM and SexF estimates which \
> > seem to better reflect the true mean values of the population, where the \
> > post.means of Mort is ~0, SexF and SexM are ~12, and the Mort:SexM fixed effect \
> > is ~18, which makes me more inclined to think that Mort*Sex is a more appropriate \
> > model (but brings up the question what does the post.mean of ~18 for Mort:SexM \
> > actually mean?).
> > I have also done randomisation where I randomise the mortality rates among \
> > cohorts for 50 chains, in the 'Mort:Sex' model this results in the Mort:SexF and \
> > Mort:SexM estimates remaining similar to the raw data model - does randomisation \
> > offer insight in to the relationship between sexual dimorphism and juvenile \
> > mortality? Using a model where 'Mort*Sex' is the fixed effect then the \
> > randomisation shifts the estimates of Mort:SexM to ~0, and that difference is \
> > absorbed in to the SexM fixed effect (because there is sexual dimorphism, but the \
> > relationship to juvenile mortality disappears). Could I effectively use this as a \
> > kind of significance test (e.g. I do 1000 randomisations, the mean Mort:SexM \
> > estimate is> the actual estimate in 11/1000 cases, thus pseudo-p is ~0.011).
> > Finally, (and on a slightly different topic) I have used 'pr = T' which means I \
> > can get posterior distributions for each level of the Pop:Year combination - i.e. \
> > a posterior distribution for each cohort. Could this information be used to get \
> > an estimate of the sex-specific lifespans for each population? For example, \
> > summing the posterior distribution of 'Mort:SexM' with 'Pop:Year.A.1983' would \
> > give a distribution of the estimated lifespan for males in population A for the \
> > year 1983? I don't think this is the case - as the numbers seem too different \
> > from the data - so how could I derive cohort-sex-specific lifespans?
> > Long story short - I'm looking for some insight on how to correctly define and \
> > interpret the fixed effects... Overall I'm inclined to think that 'Mort*Sex' \
> > gives the correct specification of the model, and the randomisation shows whether \
> > the environmental factor has an effect on sexual dimorphism. Thanks - full script \
> > below, Rob
> >
> > * Garratt et al 2015, Current Biology "High juvenile mortality is associated with \
> > sex-specific adult survival and lifespan in wild roe deer."
> > **
> > #### R-SCRIPT ####
> > rm(list=ls())
> > set.seed(255)
> > library("reshape")
> > library("MCMCglmm")
> >
> > DF1 = data.frame(c(1:320), rep(c("A", "B"), each = 10), rep(1983:1998, each = \
> > 20), sample(c("M", "F"), replace = T, size = 320), rnorm(320, 12, 2), \
> > rep((1/(1+abs(rnorm(16, 2, 1 )))), each = 20)) colnames(DF1) = c("ID", "Pop", \
> > "Year", "Sex", "Life", "Mort")
> > # Make SD related to juvenile mortality
> > DF1$Life = ifelse(DF1$Sex == "M", DF1$Life + DF1$Mort*18, DF1$Life)
> > # Mean zero, unit variance
> > DF1$Life0 = (DF1$Life-mean(DF1$Life))/sqrt(var(DF1$Life))
> >
> > prior1 = list( G = list(G1 = list(V = 1, nu = 1, alpha.mu = 0, alpha.V = 1000)),
> > R = list(V = 1, nu = 0.002))
> >
> > mod1 = MCMCglmm(Life ~ Mort:Sex - 1,
> > random = ~ Pop:Year,
> > rcov = ~units,
> > nitt = 13000, burnin = 3000, thin = 10,
> > prior = prior1,
> > pr = T,
> > family = "gaussian",
> > start = list(QUASI = FALSE),
> > data = DF1)
> >
> > summary(mod1)
> >
> >
> >
> > ----------------------------------------------------------
> >
> > Robert M. Griffin
> > Postdoctoral Researcher, University of Turku
> > www.griffinevo.wordpress.com
> > _______________________________________________
> > R-sig-mixed-models@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
>
>
>
> --
> The University of Edinburgh is a charitable body, registered in
> Scotland, with registration number SC005336.
>
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