pMCMC and HPD in MCMCglmm

Hi,
when I set the fixed effect priors for the first example with repeated
measures I  follow the indication of both the coursenote and past  
post (https:
//stat.ethz.ch/pipermail/r-sig-mixed-models/2010q3/004415.html):

V=diag(n)*((varUNITS+varCLASS)+pi^2/3)

where
n= number of fixed effects
varUNITS= residual variance (var of e)
varCLASS = variance of random effect (var of Zu)

You suggest  to assume 1 for the residual variance (varUNITS) + ~2 for the
random variable variance (varCLASS).

How do you decide to set ~2 for varCLASS? is there an indication about a
possible range of this value?

Thank a lot

Massimo

 -----------------------
 Massimo Fenati
 DVM
 Padova - Italy

----Messaggio originale----
Da: j.hadfield at ed.ac.uk
Data: 25/08/2011 18.17
A: "m.fenati at libero.it"<m.fenati at libero.it>
Cc: <r-sig-mixed-models at r-project.org>
Ogg: Re: R: Re: [R-sig-ME] pMCMC and HPD in MCMCglmm

Hi,

You have specified a strong prior correlation (~0.5) between the
intercept and sex effect:

prior$B

$mu
[1] 0 0

$V
         [,1]     [,2]
[1,] 6.289868 3.289868
[2,] 3.289868 6.289868

Since the data have 50 0's and one 1 the data give a lot of weight to
the intercept being negative. As you believe, the data are not very
informative about sex-differences in this example but with your prior
specification we expect a priori that the intercept and sexM effect
are positively correlated. Hence, the "signifcant" negative sex effect.

Perhaps you had mistyped the prior specification, and had intended

V=diag(2)*(1+pi^2/3) rather than V=diag(2)+pi^2/3 ?

as in Section 2.6 of the CourseNotes. Treating the effects as
independent in the prior gives results closer to what you would hope
for.

Jarrod



Quoting "m.fenati at libero.it" <m.fenati at libero.it> on Thu, 25 Aug 2011
17:54:21 +0200 (CEST):

Hi Jarrod,
In the past example, where HPD and pMCMC were slightly different, I tested

an

extreme dataset: 1 positive event on 51 sample of 34 animals. In this
circumstance, even assuming not repeated data, the posterior distribution

of

the sex beta coefficient MCMC estimates seems to suggest a possible effect

of

?sex? on the response ?dis?. But if I perform the analysis on the
same dataset
under frequentist approach this fails (using glm for perfect separation) or
returns with high p-value (using aalysis of frequency table via fisher

exact

test). See the following example:

sex<-c(rep("F",21),rep("M",30))
dis<-c(1,rep(0,50))
dat<-data.frame(sex,dis)
prior<-list(R=list(V=1,fix=1),G=list(G1=list(V=1,nu=0.002)),B=list(mu=c(rep
(0,2)),V=diag(2)*3+pi^2/3))
m.1<-MCMCglmm(dis~sex,slice=T,prior=priorS,data=dat,nitt=800000,thin=100,
burnin=250000,family="categorical",verbose=FALSE)
summary(m.1)

fisher.test(dat$dis,dat$sex)

summary(glm(dis~sex,data=dat,family=binomial))


How can I interpret the differences between Bayesian (MCMCglmm) and
Frequentist approaches in these circumstances?

Sorry for the basic question, but I am new in Bayesian world!

Thanks

Massimo




-----------------------
Massimo Fenati
DVM
Padova - Italy

----Messaggio originale----
Da: j.hadfield at ed.ac.uk
Data: 24/08/2011 18.11
A: "m.fenati at libero.it"<m.fenati at libero.it>
Cc: <r-sig-mixed-models at r-project.org>
Ogg: Re: [R-sig-ME] pMCMC and HPD in MCMCglmm

Hi,

pMCMC is the two times the smaller of the two quantities: MCMC
estimates of i) the probability that a<0 or ii) the probability that
a>0, where a is the parameter value. Its not a p-value as such, and
better ways of obtaining Bayesian p-values exist.

HPDinterval finds the closest points (c and d) for which Fa(d)-Fa(c) =
0.95 (If prob=0.95 in HPDinterval) and Fa is the empirical cumulative
distribution of a.

Cheers,

Jarrod





On 24 Aug 2011, at 16:14, m.fenati at libero.it wrote:

Hi Jarrod,
thanks for your answer, but I have again a lot of confusion. If
possible,
could you explain to me the definition of pMCMC?
Maybe, knowing  the right definition of pMCMC I will be able to
understand
completely your answer.

Thank a lot!

Massimo

-----------------------
Massimo Fenati
DVM
Padova - Italy

----Messaggio originale----
Da: j.hadfield at ed.ac.uk
Data: 24/08/2011 13.24
A: "m.fenati at libero.it"<m.fenati at libero.it>
Cc: <ndjido at gmail.com>, <r-sig-mixed-models at r-project.org>
Ogg: Re: [R-sig-ME] pMCMC and HPD in MCMCglmm

Hi Massimo,

They only need to be slightly skewed (even up to Monte Carlo error
probably) - conclusions drawn from HPDinterval and pMCMC are in
reality almost identical in your example, it is the consequences  of
the (arbitrary) distinction between <0.05 and >0.05  that makes them
"feel" different.  Lets say we used the cutoff <0.06 and >0.06.  Does
HPDinterval(m1$Sol[,3], prob=0.94) overlap zero? If not then
HPDinterval and pMCMC "agree" with respect to which side of the
cutoff
the probability lies ? It may make us happier, but it shouldn't.

Jarrod




On 24 Aug 2011, at 11:45, m.fenati at libero.it wrote:

The posterior distribution seem to be only slightly skewed.
However the question remains: what is the sense of the discrepancy
between HPD
and pMCMC?

Thanks

Massimo



----Messaggio originale----
Da: ndjido at gmail.com
Data: 24/08/2011 11.43
A: "m.fenati at libero.it"<m.fenati at libero.it>
Cc: <r-sig-mixed-models at r-project.org>
Ogg: Re: [R-sig-ME] pMCMC and HPD in MCMCglmm

Check your posterior distributions, the one corresponding to GENDER
seems to
be skewed.
Ardo.
On Wed, Aug 24, 2011 at 11:33 AM, m.fenati at libero.it <m.fenati at libero.

it

wrote:
As suggested by Ben Bolker, I re-post the following question in this
list.
Thanks

Dear R users,
I?d like to pose aquestion about pMCMC and HDP.
I have performed a mixed logistic regression by MCMCglmm (a very
good

package)

obtaining the following results:

Iterations = 250001:799901
Thinning interval = 100
Sample size = 5500

DIC: 10.17416

G-structure: ~ID_an

post.mean l-95% CI u-95% CIeff.samp
ID_an 0.7023 0.0001367 3.678 2126

R-structure: ~units

post.mean l-95% CIu-95% CI eff.samp
units 1 1 1 0

Location effects: febbreq~ as.factor(sex)

post.mean l-95% CIu-95% CI eff.samp pMCMC
(Intercept) -3.6332 -5.6136 -1.7719 3045 <2e-04 ***
as.factor(sex)M -2.9959 -6.0690 0.1969 2628 0.0455 *
---
Signif. codes: 0 ?***?0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1


As you can see, pMCMC for gender is just less than 5%, but the
credible
interval (HPD) is wide and includes the 0 value.
How can I interpret these different results?

Thank you in advance

Massimo

-----------------------
Massimo Fenati
DVM
Padova - Italy

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--
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.

--
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.