[R-sig-ME] strong effect of prior on residual variance

[Jarrod Hadfield]

Hi,

It doesn't make sense to have B as a random effect - it should be a 
fixed effect. The sensitivity of the prior is because there are almost 
as many levels of B as there are observations, so there is a one-to-one 
mapping between B and the residuals.

If you want to model sexual dimorphism (for example as a function of B) 
why not have a sex by B interaction?

Cheers,

Jarrod


On 05/05/2016 14:08, Rob Griffin wrote:
> Hi Jarrod,
>
> Thanks for the speedy response,
>
> There is just one measure of T per cohort. T is sexual dimorphism in a 
> trait, so its a cohort level value - individuals can't be sexually 
> dimorphic: it was calculated using mcmcglmm to estimate 
> cohort-specific posterior distributions for both male and female trait 
> values, then randomising the order of the distributions and dividing 
> them (Male[sample_i]/Female[sample_i]) where i is 1:1000. I then took 
> the mean of the posterior for each cohort as my response variable. 
> It's much the same as one could do to derive a posterior distribution 
> of heritability when given posterior distributions of additive and 
> phenotypic variation (also as stated on page 5 of the course notes). 
> Perhaps it would be more appropriate to use the entire posterior 
> distributions of SD for all 90 cohort rather than the just means (so 
> there would be 1000 samples of SD per cohort)?
>
> B is a numerical variable, if expressed as a factor it has 65 levels 
> (not all years have a measure of B). Should this be converted to a factor?
>
> Cheers,
> Rob
>
> > Subject: Re: [R-sig-ME] strong effect of prior on residual variance
> > To: robgriffin247 at hotmail.com; r-sig-mixed-models at r-project.org
> > From: j.hadfield at ed.ac.uk
> > Date: Thu, 5 May 2016 13:47:37 +0100
> >
> > Hi Rob,
> >
> > 1) how many observations are there per cohort on average?
> > 2) how many levels does B have in it?
> > 3) nu=1 is typical in a parameter expanded prior, as this is flat for
> > the standard deviation.
> >
> > Cheers,
> >
> > Jarrod
> >
> >
> >
> > On 05/05/2016 13:34, Rob Griffin wrote:
> > >
> > >
> > > Dear list members,
> > > I'm using MCMCglmm to model variance among ~90 cohorts as a result 
> of an environmental factor ("B" - numerical). "T" is the response 
> variable, which is formed as a ratio, with mean ~1 & is normally 
> distributed. The cohorts come from two different populations, where 
> each cohort is defined by the place and year of birth (e.g. one cohort 
> is all individuals born in one area, A1, in 2014), such that there is 
> one value of T per cohort. B is measured on a larger level, so there 
> is one score of B per year, regardless of population. I include Area 
> as a fixed effect (factor with two levels) because in some years only 
> one area is measured so it may induce sampling bias of the 
> environmental effect (e.g. one year where only one area is measured 
> has an extreme B score). From a biological perspective I expect B to 
> have a small impact on the among-cohort variance in T so I've used 
> parameter expanded priors for the random effect and inverse-wishart 
> for the residual (as suggested to a previou!
> > > s thread I started - on priors for small variance components - 
> last year: 
> https://stat.ethz.ch/pipermail/r-sig-mixed-models/2015q1/023370.html).
> > > When I used similar set up to my previous model (see code below) I 
> find that, contrary to my expectation, B has a relatively large 
> variance estimate compared to the residual (both mean and median of 
> the posterior for B is 10x higher than residual). It seems unlikely 
> that 90% of the variance in T is explained by B.
> > > This prompted me to fiddle with the prior specification to make 
> sure nothing was wrong... Settings used were nu = 0.002 or 2, & V = 1 
> or 10 (for the priors in R with all four combinations of V and nu 
> tested), also producing 4 independent chains with 100k iterations, 25k 
> burnin, and thinning interval of 50 for each; autocorrelation is low 
> (<0.1 between successive samples), convergence appears good for both B 
> and Residual. The estimate of variance (both the median and mean of 
> the posterior) is similar across the four chains, within each 
> combination of nu and V, for both B and Residual.
> > > In the previous thread it is pointed out that "Usually the data 
> overwhelm the prior for the residual variance so you can probably be 
> pretty relaxed about that." I find that estimates of B and residual 
> (units) are generally insensitive to changes in any of the parameters 
> in G, but highly sensitive to changes in both the belief and variance 
> inputs for R (increases in nu and V both increase the estimate of 
> residual, while also absorbing variance from the random effect B). 
> Given the statement that data usually overwhelm the prior, should I be 
> concerned that the prior is strongly affecting the estimate of 
> residual (and random effects) variance in this case? How should this 
> be interpreted and dealt with? The consistency across independent 
> chains suggests to me that the model is able to estimate B and 
> residual variances well, but is drawing too much information from the 
> prior rather than the data, and therefore I'm using the wrong prior.
> > > Thanks,Rob
> > > ####################prior1 = list(G = list( G1 = list(V = 1, 
> nu=0.001, alpha.mu=0, alpha.V=1000) ), R = list(V = 1, nu=0.001)) M1A 
> = MCMCglmm( T ~ 1 + Area ,random = ~ B ,data = DF3 ,nitt = nitt 
> ,burnin = burnin ,thin = thin ,family = "gaussian" ,prior = prior1 )
> > >
> > >
> > >
> > > [[alternative HTML version deleted]]
> > >
> > > _______________________________________________
> > > R-sig-mixed-models at 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.
> >

-------------- next part --------------
An embedded and charset-unspecified text was scrubbed...
Name: not available
URL: <https://stat.ethz.ch/pipermail/r-sig-mixed-models/attachments/20160505/f4badedb/attachment.pl>