[R-sig-ME] Poor mixing and autocorrelation of ZIP data in MCMCglmm

[Vital Heim]

Dear Ben and Pierre,

Thank you very much for the quick response - that is amazing and very
helpful!

I have not centered the continuous predictors as I had the feeling that
this would not be necessary in my model. Would you recommend to center them?

Thank you for the prior suggestion. From reading the course notes to
MCMCglmm I thought that I have to fix all the random effects variances to 1
in the ZI part. I am very new to Bayesian statistics and MCMCglmm and
therefore used the MCMCglmm course notes to write and understand my model.
There was one part in the course notes that said that there is no residual
variance for the zero-inflated process and that we cannot estimate the
residual covariance between the zero-inflation and the Poisson process but
that we can deal with this by fixing the residual variance for the ZI
portion at 1. Therefore I thought I have to do the same for my model.

I used the new prior and the model ran fine and showed some improvement.
The mixing of the random effects improved but the ZI portion of the random
effects did not mix well. Do you think the mixing could be/needs to be
further improved? Would you increase nu? I added you the model summary and
the autocorrelation diagnostics below:

> summary(model10)

 Iterations = 150001:1849501
 Thinning interval  = 1500
 Sample size  = 1134

 DIC: 4039.85

 G-structure:  ~idh(trait):id

                 post.mean l-95% CI u-95% CI eff.samp
baitIntake.id       0.2097  0.01955   0.5446  1134.00
zi_baitIntake.id  140.2144 10.39550 412.5714    16.88

               ~idh(trait):dive

                   post.mean  l-95% CI u-95% CI eff.samp
baitIntake.event      0.2386 1.113e-01   0.3711    544.1
zi_baitIntake.event   1.6603 1.054e-07   5.7216     64.6

 R-structure:  ~idh(trait):units

                    post.mean l-95% CI u-95% CI eff.samp
baitIntake.units       0.5084    0.423   0.5999     1134
zi_baitIntake.units    1.0000    1.000   1.0000        0

 Location effects: bait ~ trait - 1 + trait:sharks + trait:divers +
trait:boats + at.level(trait, 1):presence + at.level(trait, 1):temperature
+ trait:gender

                          post.mean   l-95% CI   u-95% CI eff.samp   pMCMC

baitIntake                -0.989171  -8.506002   7.022529   1036.3 0.80071

zi_baitIntake              5.726646  -0.731875  14.671429    118.8 0.09171
.
baitIntake:conspecifics   -0.049999  -0.115503   0.015834   1134.0 0.13757

zi_baitIntake:conspecifics  0.185816  -0.129883   0.601750    437.8 0.31922

baitIntake:tourists        0.044321   0.010587   0.075382   1134.0 0.00529
**
zi_baitIntake:tourists    -0.154735  -0.341183   0.021306    258.0 0.05996
.
baitIntake:operators       0.157988   0.069429   0.255920   1134.0 0.00176
**
zi_baitIntake:operators   -0.232157  -0.776007   0.249766    472.4 0.35979

presence                   0.010091   0.008344   0.011620   1134.0 < 9e-04
***
temperature                0.260196  -0.062494   0.536471   1027.0 0.08466
.
baitIntake:gendermale      0.355938  -0.329717   1.143065   1134.0 0.28571

zi_baitIntake:gendermale  -1.787142 -16.777974  10.576166    200.1 0.80952

---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> autocorr.diag(model10$Sol)
           baitIntake zi_baitIntake baitIntake:conspec zi_baitIntake:consp.
baitIntake:tourists zi_baitIntake:tourists
Lag 0      1.00000000    1.00000000       1.000000000          1.000000000
         1.00000000           1.0000000000
Lag 1500   0.04457168    0.32629918       0.011215824          0.400247111
        -0.02362611           0.4065199561
Lag 7500  -0.01118381    0.21355704      -0.056422233          0.050903050
        -0.06575857           0.1543329508
Lag 15000 -0.01182550    0.14366161      -0.004787545          0.048794655
         0.01045932           0.1180500281
Lag 75000 -0.06205008    0.05428778      -0.012689660          0.004470857
        -0.01587028          -0.0001966966
          baitIntake:operators zi_baitIntake:operators     presence
 temperature baitIntake:gendermale zi_baitIntake:gendermale
Lag 0              1.000000000              1.00000000  1.000000000
 1.000000000           1.000000000               1.00000000
Lag 1500           0.018702637              0.34990109 -0.005337675
 0.049056906          -0.008540371               0.11797192
Lag 7500           0.029576245              0.04236116  0.051737798
-0.004486268          -0.043298182               0.10059317
Lag 15000         -0.006467939              0.07262102  0.020471250
-0.011604859           0.010096511               0.04657296
Lag 75000          0.050869606             -0.01289837  0.034904725
-0.064627241          -0.019433089               0.04871585

> autocorr.diag(model10$VCV)
          baitIntake.id zi_baitIntake.id baitIntake.event
zi_baitIntake.event baitIntake.units zi_baitIntake.units
Lag 0        1.00000000        1.0000000       1.00000000
 1.000000000        1.00000000                 NaN
Lag 1500    -0.01347780        0.6908849       0.03201474
 0.789290686        0.02634913                 NaN
Lag 7500    -0.04617914        0.5013689      -0.03223097
 0.519696189       -0.02148069                 NaN
Lag 15000    0.01414618        0.5099142      -0.04454962
 0.341925156       -0.04412612                 NaN
Lag 75000   -0.03180043        0.2266740      -0.01645174
-0.003025432       -0.01177512                 NaN

And then I would have another question regarding the prior which I am not
sure if that is ok to post here. If not feel free to let me know. I have
been looking up papers to learn how to properly report my prior choice and
details in a publication. I found some papers that just wrote "we chose a
inverse gamma prior" but I am concerned that some reviewers would want more
specific information. Do you have a recommendation on how to correctly
report a prior in a publication?

Best wishes,
Vital
--
*Vital Heim *

*PhD student*
University of Basel, Switzerland

Bimini Biological Field Station Foundation
Bimini, Bahamas

+41 (0)79 732 05 57
vital.heim using gmail.com

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