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persistant autocorrelation in binomial MCMCglmm

4 messages · Aiello, Christina, Jarrod Hadfield

#
Dear list,

I'm very new to MCMCglmm but have done my best to read-up on Jarrod
Hadfield's package documents, tutorials and various examples posted online
and discussed on this forum. I'm having trouble fitting what I thought was
a fairly simple binomial mixed effects model using MCMCglmm. I'll start by
describing the data, then the model, then my problem and questions:

My dataset is comprised of unique dyads - pairs of animals located at one
of four sites (C1, C2, R1, R2). The response variable, 'contact' indicates
that the dyad did (1) or did not (0) interact over the course of the study.
The unique id of the members of the dyad are 'tort1' and 'tort2'. Because
individuals appear in multiple dyads, I've included a random effect for
tortID using the multiple membership function available in the package to
account for the non-independence of observations and the fact that some
individuals may have a tendency to contact more than others. For fixed
effects, in this simplified model I only have one categorical variable,
'site' (which I would have entered as a random effect but I only have 4
levels) and one continuous variable, 'overlap' - which is an estimate of
space-use similarity for each dyad. I centered and scaled this variable by
the non-zero mean value and standard deviation (though I've also tried the
model without centering). This may be relevant to my problem: 'overlap's
distribution is highly skewed and mostly zero values - similarly, the
response variable 'contact' is rare and characterized by mostly zeros.
C1  C2  R1  R2
  0 241 229 176 181
  1  35  24  14   9

The model:

pr<-list( R= list(V=1,  n=0, fix=1), G= list(G1=list(V=1, n=0.002)) )

m1 <- MCMCglmm(

fixed = contact ~ (1 + site + overlap ) ,

random = ~mm(tort1 +tort2),

data = datafi,

family = "categorical", verbose = FALSE,

pr=TRUE, pl=TRUE, prior=pr,

nitt=4100000 , thin=2000 , burnin= 100000

)
Iterations = 100001:4098001
 Thinning interval  = 2000
 Sample size  = 2000

 DIC: 207.4525

 G-structure:  ~mm(tort1 + tort2)

            post.mean  l-95% CI u-95% CI eff.samp
tort1+tort2     2.128 0.0002693    5.488    414.6

 R-structure:  ~units

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

 Location effects: contact ~ (1 + site + overlap)

            post.mean l-95% CI u-95% CI eff.samp  pMCMC
(Intercept)   -2.2102  -3.6055  -0.7437   1505.6  0.004 **
siteC2        -0.4143  -2.7572   1.4982   1808.4  0.708
siteR1        -1.2543  -4.0794   0.8424   1069.0  0.268
siteR2        -1.4753  -3.9300   0.9782   1348.9  0.205
overlap        3.9025   2.8273   5.1260    488.5 <5e-04 ***


As far as I can tell, the chains themselves look good and if I run multiple
chains and run the Gelman-Rubin diagnostic, the PSRF values are all 1 or
1.01. The parameter estimates are consistent and make sense. The problem
lies in the autocorrelation - large amounts in the 'overlap' variable and
many of the random intercepts. Here's a sample of the autocorr results:
##these are the worst offenders
  (Intercept)    tort1.4534    tort1.3719      tort1.33    tort1.3620
 tort1.30    tort1.3045
 0.0926484964  0.0938622549  0.1009204749  0.1049459123  0.1065261665
 0.1090179501  0.1237642453
       siteR2    tort1.3150    tort1.5579        siteR1    tort1.5473
 tort1.2051    tort1.3092
 0.1339370132  0.1359132027  0.1383816060  0.1506535457  0.1639062068
 0.1682852625  0.1683907054
   tort1.5044     tort1.804    tort1.5141    tort1.5103    tort1.4148
 tort1.4678    tort1.4428
 0.1752670493  0.1767909176  0.1865412328  0.1919929722  0.2257633018
 0.2318115800  0.2521806794
   tort1.3633    tort1.3335    tort1.5101    tort1.3043      tort1.26
 tort1.2014       tort1.6
 0.2577034325  0.2593673083  0.2602145001  0.2717718040  0.3487288823
 0.3748047689  0.4478979043
      overlap
 0.5400325556
tort1+tort2 units
Lag 0      1.00000000   NaN
Lag 2000   0.58292962   NaN
Lag 10000  0.12771910   NaN
Lag 20000  0.05262786   NaN
Lag 1e+05  0.01757316   NaN

I've attempted to fit the model with both uninformative (shown above) and
parameter expanded priors (
pr2<-list( R= list(V=1, n=0, fix=1), G=list(G1=list(V=1, nu=1, alpha.mu=0,
alpha.V=1000)) )), with parameter expanded priors performing slightly
worse. I've attempted incrementally larger iteration, thinning, and burn in
values, increasing the thinning to as high as 2000 with a large burn-in
(100000) in hopes of improving convergence and reducing autocorrelation.
I've tried slice sampling and saw little improvement. Nothing I tried while
retaining this model structure improved the acfs. I checked the latent
variable estimates and all were under 20, with mean of -5.

The only way I was able to reduce the autocorrelation was to fit a model
without the random effect, which isn't ideal as I'm ignoring repeated
measures of individuals among dyads. I've read on this forum that random
effects in binomial models are notoriously hard to estimate with this
package and I've also read that one should not just increase thinning to
deal with the problem (MEE 2012 Link & Eaton
<http://onlinelibrary.wiley.com/store/10.1111/j.2041-210X.2011.00131.x/asset/j.2041-210X.2011.00131.x.pdf?v=1&t=j29nl332&s=e0f97f28309122f2bbfa66bccb0cd445696e2f15>).
Interestingly, I have count responses association with all interacting
dyads and I can fit zero truncated models to those responses just fine with
the same fixed and random effects.

My questions are then:
1) Do you think there is something inherently wrong with the data or just
problems with the mixing algorithms in the context of this data?
2) Are there any other changes to the MCMCglmm specification I might try to
improve mixing? Or any problems with my current specification?
3) Any suggestions on where to go from here?


I would greatly appreciate any insights and happy to provide further info
as needed!

Christina
#
Hi Christina,

1/ The model syntax looks fine, it is just that MCMCglmm is not very 
efficient for this type of problem. You say there are no numerical 
issues because the latent variable is under 20. However, are they 
commonly under -20?

2/ Centering and scaling the covariates will not effect the mixing 
because MCMCglmm is block updating all location effects.  Moving from a 
logistic model (family="categorical") to a probit model 
(family="threshold") will probably improve mixing, and the inferences 
will be pretty much the same.

3/ You could also up the number of iterations - but perhaps this takes 
too much time? Link and Eaton's recommendation not to thin is fine if 
you are not worried about filling your hard drive. You reduce the Monte 
Carlo error by saving additional correlated samples, but if the total 
number of samples you can store is limited you are better storing 
uncorrelated samples (obtained by thinning) because this reduces the 
Monte Carlo error more.

Cheers,

Jarrod
On 04/05/2017 01:24, Aiello, Christina wrote:

  
    
#
Hi Jarrod,

Appreciate the quick response and thoughts

1) I thought I had checked the absolute value of the latent variables, but
now that I look again, I must not have examined both ends of the
distribution. There are 167 observations whose latent variable
distributions dip below -20 (minimum was -32). In each of these cases, the
left tail of the distribution includes very few estimates at such low
values. Do you think this has to do with the rarity of a response of 1 in
the dataset? Or might this be indicative of another problem?

2) I'll give the probit link a try today and see how the results compare

3) I can definitely let the chains run longer, and continue increasing
thinning? I was hesitant to keep upping the values because I haven't seen
many published analyses using iterations and intervals beyond what I've
been trying. I was worried having to run the chain so long might be
indicative of other underlying problems that I wasn't considering.

Many thanks!
Christina

Christina M. Aiello
Biologist- U.S. Geological Survey
Las Vegas Field Station
160 N. Stephanie St.
Henderson, NV 89074
(702) 481-3957
caiello at usgs.gov
On Wed, May 3, 2017 at 9:31 PM, Jarrod Hadfield <j.hadfield at ed.ac.uk> wrote:

            

  
  
1 day later
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Hi Jarrod,

I have an update on the model performance with a probit link - the
autocorrelation is much better behaved with the "threshold" family. All ACF
values are <0.1 for iteration and thinning #s that were resulting in
autocorrelation using the logit link.

Looking at the latent variables, though, a lot of the distributions
included values below -7 (lowest was -10). All of the means where within
the -7 to 7 range though, because only a few estimates per observation
tended to reach very low negative values. Are *any* estimates outside the
range considered problematic?

I noticed on the forum a post where someone else had this issue (
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2012q3/019067.html) and I
also tried the chi square prior you suggested for that problem (V=1,
nu=1000, alpha.mu=0, alpha.V=1) but the result was the same.

In terms of the data and system, I would expect an extremely low, near zero
probability of interaction for some of these dyads because they are not
using similar areas and so are not physically able to interact. Is this
signal perhaps too strong? If my goal is to weed out these improbable
interactions, though, will the model not serve this purpose?

Many thanks,

Christina

Christina M. Aiello
Biologist- U.S. Geological Survey
Las Vegas Field Station
160 N. Stephanie St.
Henderson, NV 89074
(702) 481-3957
caiello at usgs.gov
On Thu, May 4, 2017 at 10:17 AM, Aiello, Christina <caiello at usgs.gov> wrote: