pMCMC and HPD in MCMCglmm

2 messages · m.fenati at libero.it, Jarrod Hadfield

Original

m.fenati at libero.it

Wed, Aug 24, 2011 8:14 AM #

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

_______________________________________________
R-sig-mixed-models at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

_______________________________________________
R-sig-mixed-models at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

Jarrod Hadfield

Wed, Aug 24, 2011 9:11 AM #

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

_______________________________________________
R-sig-mixed-models at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

_______________________________________________
R-sig-mixed-models at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

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