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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