Dear Pierre,
Thank you again for the answer and the new prior!
I have been working on the model last week and your question if I have
enough data got me thinking. I therefore reconsidered my available data and
also looked into if I can simplify my model.
The model I submitted before had 378 observations. The observations came
from 28 different individuals. However, I think one problem could have been
that most of these individuals only had 1 observation because they only
appeared at a provisioning event once. I therefore decided to remove all
the individuals that have less than 5 total observations from the data set
so that theoretically every animal had at least 5 opportunities to make a
decision to attend (and for how long) a provisioning event or not. That
left me with 13 individuals and a total of 405 observations (as I do not
have temperature as a fixed effect I could keep the rows with temperature
== NA, resulting in more observations than before). The nr. observations
per individual are:
id 12 13 14 16 17 19 20 21 34 38 39 40 42
#obs 27 54 67 52 44 34 26 35 41 7 7 5 6
Trying to simplify my model had me removing two fixed effects (temperature
and gender) from my model formula. That left me with the model:
priorP2 <- list(R = list(V = diag(2), nu = 2, fix = 2),
G = list(
G1 = list(V = diag(2), nu = 1000, alpha.mu = c(0,0),
alpha.V = diag(2))
,G2 = list(V = diag(2), nu = 1000, alpha.mu = c(0,0),
alpha.V = diag(2))))
NITT <- 320000
BURN <- 20000
THIN <- 200
MULT <- 10
model3.1 <- MCMCglmm(bait ~ trait - 1
+ trait:individuals + trait:tourists + trait:operators
+ at.level(trait,1):presence
, random = ~idh(trait):id + idh(trait):event
, rcov =~ idh(trait):units
, data=df, family="zipoisson", prior=priorP2
, nitt=NITT*MULT, burnin=BURN*MULT, thin = THIN*MULT,
verbose=FALSE)
The model resulted in the following summary:
Iterations = 200001:3198001
Thinning interval = 2000
Sample size = 1500
DIC: 4295.048
G-structure: ~idh(trait):id
post.mean l-95% CI u-95% CI eff.samp
baitIntake.id 0.1969 0.0204 0.5101 1500
zi_baitIntake.id 9.6323 4.3901 17.0756 151
~idh(trait):dive
post.mean l-95% CI u-95% CI eff.samp
baitIntake.event 0.2955 1.501e-01 0.4423 1720.47
zi_baitIntake.event 0.6166 1.873e-06 2.2227 91.55
R-structure: ~idh(trait):units
post.mean l-95% CI u-95% CI eff.samp
baitIntake.units 0.5085 0.4217 0.6023 1641
zi_baitIntake.units 1.0000 1.0000 1.0000 0
Location effects: bait ~ trait - 1 + trait:individuals + trait:tourists +
trait:operators + at.level(trait, 1):presence
post.mean l-95% CI u-95% CI eff.samp pMCMC
baitIntake 5.800698 5.169356 6.423403 1500.0 <7e-04 ***
zi_baitIntake -0.607708 -3.430961 2.148515 719.3 0.6467
baitIntake:individuals -0.053430 -0.120854 0.018248 1500.0 0.1347
zi_baitIntake:individuals 0.070798 -0.207224 0.358939 340.2 0.6307
baitIntake:tourists 0.054909 0.024764 0.089098 1500.0 <7e-04 ***
zi_baitIntake:tourists -0.111844 -0.248268 0.023882 222.7 0.0840 .
baitIntake:operators 0.119909 0.016259 0.208378 1500.0 0.0253 *
zi_baitIntake:operators -0.181109 -0.552908 0.211214 316.1 0.3520
presence 0.009881 0.008174 0.011563 1500.0 <7e-04 ***
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
The new model formula and adjusting the df for only animals that have
attended the events at least 5 times helped I think. The variance in the
zi.baitintake.id is a lot smaller now (from 140 in the previous model to 9
in this model). I think there is still a rather large uncertainty in some
of the fixed effects and the intercept for each trait but am not sure if
that would be within the range that is acceptable?
The autocorrelation diagnostics looked as follows:
autocorr.diag(model3.1$Sol)
baitIntake zi_baitIntake baitIntake:individuals
zi_baitIntake:individuals baitIntake:tourists zi_baitIntake:tourists
Lag 0 1.000000000 1.00000000 1.000000000
1.000000000 1.000000000 1.0000000
Lag 2000 0.026012481 0.26311228 0.011550676
0.566133816 -0.006107718 0.5590814
Lag 10000 -0.036331924 0.01332843 0.003078598
0.132021786 -0.023601403 0.1855635
Lag 20000 0.026546529 -0.01065644 0.005180587
0.003356647 -0.006827257 0.0705329
Lag 1e+05 0.009254395 0.02910151 0.003647482
-0.045349648 -0.033278001 -0.0276361
baitIntake:operators zi_baitIntake:operators presence
Lag 0 1.000000000 1.00000000 1.0000000000
Lag 2000 0.017853409 0.53269135 0.0309542019
Lag 10000 -0.001788713 0.15219674 0.0039462749
Lag 20000 -0.067415168 0.04973919 -0.0084329378
Lag 1e+05 -0.010173980 0.03747686 -0.0009911261
autocorr.diag(model3.1$VCV)
baitIntake.id zi_baitIntake.id baitIntake.event
zi_baitIntake.event baitIntake.units zi_baitIntake.units
Lag 0 1.000000000 1.000000000 1.000000000
1.00000000 1.00000000 NaN
Lag 2000 0.010988496 0.279553940 -0.006822039
0.78582472 -0.04529223 NaN
Lag 10000 0.005850551 0.255547273 -0.020832316
0.48146906 0.01942578 NaN
Lag 20000 0.006862719 0.175722325 -0.080220078
0.29263378 -0.01864084 NaN
Lag 1e+05 0.036323891 0.003939182 -0.005860269
-0.01147487 -0.01569073 NaN
I attached the trace and density plots to this message. I think overall the
mixing improved. The mixing of the random effects improved compared to the
previous model but is still looking a bit off when I compare it to the
mixing of the fixed effects.
Thank you for your suggestion how to correctly report the prior choice in a
paper - that is very helpful.
Kind regards,
Vital
[[alternative HTML version deleted]]