Bayesian Analysis visit length less than or equal to 60 s
\(Results\ bayesian\ estimating\ of\ variance\ components\ (proportion\ of\ variance)\ with\ Stan\ program,\\ on\ 58255\ records\ of\ visit\ length\ time\ at\ the\ feeder\ when\ the\ next\ visit\ was\ greater\ than\ or\ equal\ to\ 60\ sc,\\ from\ 7\ trials,\ including\ locations\ (2\ per\ trial),\ median\ weight\ and\ hour\ entry\ at\ the\ feeder\ as\ fixed\ effects\ and\\ Eartag (135\ individuals)\ and\ followers\ (135)\ as\ random\ effects\ in\ the\ mixed\ models.\)
\(iter = 12000,\ chain= 3,\ burn-in = 2000,\ Thin=1.\)
\(For\ the\ fixed\ parameters\ in\ {\beta},\ flat\ priors\ were\ assumed,\ thus\ {\beta}\ {\sim} U(-\infty,+\infty),\\the\ priors\ distributions\ for\ covariance\ components\ {\sigma}_d^2,\ {\sigma}_f^2\ {\sim }\ U(0,100),\\ {\rho} {\sim}\ U(-1,1)\ and\ the\ prior\ distribution\ for\ the\ error\ variance\ was\ {\sigma}_e^2\ {\sim}\ U(0,\infty).\)
1. Mixed model: Location + Hours+ Median wt + Eartag
1.1.Convergence Diagnostic
Check autorrelation, effective sample size, traceplot
ggs_autocorrelation(ggs(outp1)%>%filter(Parameter%in%lt1))
ggs_autocorrelation(ggs(outp1)%>%filter(Parameter%in%lt2))
ggs_autocorrelation(ggs(outp1)%>%filter(Parameter%in%hent1))
ggs_autocorrelation(ggs(outp1)%>%filter(Parameter%in%hent2))
ggs_autocorrelation(ggs(outp1)%>%filter(Parameter%in%c("Median Weight",
"var_eartag","var_error","prp_var_eartag","prp_var_error")))
autocorr.diag(outp1)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4 Loc1_t_5
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 -0.134146884 -0.097383814 -0.089792907 -0.173706155 -0.164558502
## Lag 5 -0.002190731 -0.015000031 0.005530620 -0.004405251 0.006417729
## Lag 10 0.003868033 -0.003389565 -0.008967076 -0.000971424 0.005619884
## Lag 50 -0.015663761 0.003309419 0.005051397 -0.007774269 -0.004006807
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## Lag 0 1.000000000 1.0000000000 1.000000000 1.000000000 1.000000000
## Lag 1 -0.119370004 -0.1556186528 -0.130739915 -0.095338566 -0.117598533
## Lag 5 -0.005973660 -0.0038729507 0.009244498 0.001890684 -0.003510016
## Lag 10 0.005526263 0.0012538517 0.005350545 0.013066611 0.006989859
## Lag 50 0.012275753 -0.0002991794 -0.001837467 0.000542390 -0.014548944
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## Lag 0 1.0000000000 1.0000000000 1.000000000 1.000000000 1.0000000000
## Lag 1 -0.1591048652 -0.1693196987 -0.133590672 -0.150263920 0.0040291213
## Lag 5 -0.0019927955 0.0013517495 -0.002726634 -0.002948770 0.0056590783
## Lag 10 -0.0004544003 -0.0011022250 -0.003124837 -0.007187481 0.0025289025
## Lag 50 -0.0029335247 0.0005428793 0.003144976 0.004786065 0.0007022465
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.010759578 -0.003717884 0.007223549 0.004100060 0.007639855
## Lag 5 0.002298092 0.005143466 0.002979674 0.001697296 0.005114703
## Lag 10 0.002070686 0.003484112 0.004606396 0.008110892 0.005987664
## Lag 50 -0.011563203 -0.001543034 0.002376226 -0.004523680 -0.009950991
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## Lag 0 1.000000000 1.000000000 1.000000000 1.0000000000 1.000000000
## Lag 1 0.012495287 0.014639409 0.012291709 0.0115954579 0.013832710
## Lag 5 0.009115624 0.011289812 0.003687802 0.0092144742 0.006858310
## Lag 10 0.008890368 0.001287423 0.012139540 0.0001404958 0.005434857
## Lag 50 -0.008578271 -0.011023150 -0.007465262 -0.0035738233 -0.008823457
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.0000000000
## Lag 1 0.009797224 0.022052661 0.012474822 0.012752594 0.0216567206
## Lag 5 0.009202383 0.005796698 0.001140462 0.012136778 0.0141481917
## Lag 10 0.005122257 0.004374994 0.004652659 0.009253623 0.0093046067
## Lag 50 0.001503248 -0.002916302 -0.006632191 -0.013138306 -0.0008688945
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## Lag 0 1.000000000 1.000000000 1.000000000 1.0000000000 1.000000000
## Lag 1 0.008031990 0.012585556 0.009841948 0.0107845298 0.014785998
## Lag 5 0.008762995 0.002819084 -0.001333854 -0.0008820649 0.007271374
## Lag 10 0.012217448 -0.004427040 0.001658477 0.0033224613 -0.005588661
## Lag 50 0.003917083 -0.005032803 -0.005843925 -0.0079395852 -0.007831579
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## Lag 0 1.000000000 1.000000000 1.000000e+00 1.000000000 1.000000000
## Lag 1 -0.003492985 0.001681942 -1.990368e-02 0.016927219 -0.021227302
## Lag 5 0.010471669 0.009863692 -5.726912e-05 -0.004437937 0.002628811
## Lag 10 0.010825585 0.002039442 -9.895525e-03 0.005865564 -0.004539301
## Lag 50 -0.008824404 -0.023495687 3.585306e-03 -0.005632773 -0.007554565
## prp_var_eartag prp_var_error lp__
## Lag 0 1.000000000 1.000000000 1.000000000
## Lag 1 0.013192249 0.013192249 0.474237208
## Lag 5 -0.004139222 -0.004139222 0.025135439
## Lag 10 0.006319057 0.006319057 0.004716083
## Lag 50 -0.005334947 -0.005334947 0.001177363effectiveSize(outp1)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4 Loc1_t_5
## 38305.16 36436.08 35790.94 41225.53 41292.74
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## 37673.63 41343.74 38827.04 36177.41 38072.25
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## 41372.75 41942.83 38537.67 39877.30 28501.61
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 28658.87 30450.06 29187.01 28550.54 31175.42
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## 29789.19 29142.27 29353.86 29771.95 28873.59
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## 28892.11 28812.75 29351.85 29423.58 28242.96
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## 28941.11 29276.63 27997.85 29951.87 28798.53
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## 29195.39 30378.88 30940.66 28541.21 31206.01
## prp_var_eartag prp_var_error lp__
## 28696.81 28696.81 10883.71geweke.diag(outp1)## [[1]]
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4 Loc1_t_5
## 0.79959 -1.22820 0.94260 2.10450 -0.01592
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## 2.28679 0.40881 -2.54152 -1.62611 -0.42916
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## -0.64262 0.59307 -1.85951 0.80098 -0.11073
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 0.98661 -0.29875 -0.32365 0.28153 -0.30337
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## 0.81474 0.50148 0.49169 0.44605 1.05361
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## 0.55182 0.59159 0.70306 0.77426 -0.18125
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## 0.54507 0.94727 -0.33040 0.74573 0.18383
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## 0.20930 0.51576 -0.17413 0.16916 0.96184
## prp_var_eartag prp_var_error lp__
## 0.13629 -0.13629 1.37210
##
##
## [[2]]
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4 Loc1_t_5
## -0.37108 -0.19766 1.53939 1.47080 -0.77788
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## 1.02027 1.47826 -0.95856 1.74334 1.75019
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## 1.29297 -0.15620 -0.72304 0.25524 -0.79285
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## -0.25651 -1.25329 -0.35856 0.53588 0.68331
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## -0.74744 -0.48046 0.10130 0.11979 -0.84429
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## -0.08639 -0.65008 0.07024 -0.50198 -0.20185
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## -0.52682 -0.71272 -0.94077 0.04827 -0.95268
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## 0.81387 0.10862 -1.93413 -0.39033 -1.10286
## prp_var_eartag prp_var_error lp__
## -0.36336 0.36336 -0.53045
##
##
## [[3]]
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4 Loc1_t_5
## -0.95994 1.79310 -1.23184 0.72828 -0.72827
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## -1.05174 -0.49073 0.68512 0.98190 0.57675
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## 0.03956 0.29391 1.09049 0.35754 0.10222
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 1.41201 1.07603 -0.41372 -1.58659 -0.30730
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## -0.08959 -0.21032 1.24272 -0.41593 -0.02045
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## -1.14671 0.70362 -0.93211 0.64941 0.58458
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## 1.59331 -0.23732 0.56754 0.01700 0.58952
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## -0.58817 0.35408 -1.29471 -0.35953 -0.18319
## prp_var_eartag prp_var_error lp__
## -0.32322 0.32322 1.09951gelman.diag(outp1, transform = T)## Potential scale reduction factors:
##
## Point est. Upper C.I.
## Loc1_t_1 1 1.00
## Loc1_t_2 1 1.00
## Loc1_t_3 1 1.00
## Loc1_t_4 1 1.00
## Loc1_t_5 1 1.00
## Loc1_t_6 1 1.00
## Loc1_t_7 1 1.00
## Loc2_t_1 1 1.00
## Loc2_t_2 1 1.00
## Loc2_t_3 1 1.00
## Loc2_t_4 1 1.00
## Loc2_t_5 1 1.00
## Loc2_t_6 1 1.00
## Loc2_t_7 1 1.00
## h_ent_1 1 1.00
## h_ent_2 1 1.00
## h_ent_3 1 1.00
## h_ent_4 1 1.00
## h_ent_5 1 1.00
## h_ent_6 1 1.00
## h_ent_7 1 1.00
## h_ent_8 1 1.00
## h_ent_9 1 1.00
## h_ent_10 1 1.00
## h_ent_11 1 1.00
## h_ent_12 1 1.00
## h_ent_13 1 1.00
## h_ent_14 1 1.00
## h_ent_15 1 1.00
## h_ent_16 1 1.00
## h_ent_17 1 1.00
## h_ent_18 1 1.00
## h_ent_19 1 1.00
## h_ent_20 1 1.00
## h_ent_21 1 1.00
## h_ent_22 1 1.00
## h_ent_23 1 1.00
## Median Weight 1 1.00
## var_eartag 1 1.00
## var_error 1 1.00
## prp_var_eartag 1 1.00
## prp_var_error 1 1.00
## lp__ 1 1.01
##
## Multivariate psrf
##
## 1traplot(outp1,col =c("red1","blue4","purple3"))
denplot(outp1)
1.2. Summary Posterior Distribution
summary(outp1)##
## Iterations = 2001:12000
## Thinning interval = 1
## Number of chains = 3
## Sample size per chain = 10000
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## Loc1_t_1 1.336e+01 0.940354 5.429e-03 4.813e-03
## Loc1_t_2 7.126e+00 0.960096 5.543e-03 5.040e-03
## Loc1_t_3 1.013e+01 0.970803 5.605e-03 5.152e-03
## Loc1_t_4 8.176e+00 1.123613 6.487e-03 5.540e-03
## Loc1_t_5 9.009e+00 1.139739 6.580e-03 5.612e-03
## Loc1_t_6 4.870e+00 1.054594 6.089e-03 5.494e-03
## Loc1_t_7 1.097e+01 1.064899 6.148e-03 5.260e-03
## Loc2_t_1 1.041e+01 0.936948 5.409e-03 4.776e-03
## Loc2_t_2 7.952e+00 0.963802 5.565e-03 5.108e-03
## Loc2_t_3 1.461e+01 0.963323 5.562e-03 4.950e-03
## Loc2_t_4 6.817e+00 1.121261 6.474e-03 5.529e-03
## Loc2_t_5 9.736e+00 1.139676 6.580e-03 5.585e-03
## Loc2_t_6 6.814e+00 1.054841 6.090e-03 5.381e-03
## Loc2_t_7 8.368e+00 1.122435 6.480e-03 5.636e-03
## h_ent_1 2.237e-01 0.281532 1.625e-03 1.669e-03
## h_ent_2 1.972e-03 0.281479 1.625e-03 1.667e-03
## h_ent_3 -1.440e-01 0.283010 1.634e-03 1.625e-03
## h_ent_4 -3.344e-01 0.274906 1.587e-03 1.613e-03
## h_ent_5 -6.011e-01 0.250288 1.445e-03 1.481e-03
## h_ent_6 -5.964e-01 0.229110 1.323e-03 1.304e-03
## h_ent_7 -1.131e+00 0.218419 1.261e-03 1.273e-03
## h_ent_8 -2.308e+00 0.210991 1.218e-03 1.243e-03
## h_ent_9 -1.006e+00 0.215647 1.245e-03 1.263e-03
## h_ent_10 -1.058e-01 0.220283 1.272e-03 1.281e-03
## h_ent_11 3.966e-01 0.219543 1.268e-03 1.300e-03
## h_ent_12 6.892e-01 0.218775 1.263e-03 1.295e-03
## h_ent_13 4.033e-01 0.215989 1.247e-03 1.278e-03
## h_ent_14 5.503e-01 0.216492 1.250e-03 1.269e-03
## h_ent_15 8.020e-01 0.218997 1.264e-03 1.285e-03
## h_ent_16 1.368e+00 0.228050 1.317e-03 1.364e-03
## h_ent_17 1.724e+00 0.243090 1.403e-03 1.431e-03
## h_ent_18 1.226e+00 0.248779 1.436e-03 1.456e-03
## h_ent_19 7.743e-01 0.251046 1.449e-03 1.501e-03
## h_ent_20 4.285e-01 0.252459 1.458e-03 1.463e-03
## h_ent_21 2.528e-01 0.255056 1.473e-03 1.508e-03
## h_ent_22 -1.015e-01 0.251414 1.452e-03 1.481e-03
## h_ent_23 3.975e-01 0.264244 1.526e-03 1.517e-03
## Median Weight 1.250e-02 0.001691 9.765e-06 9.618e-06
## var_eartag 9.664e+00 1.298339 7.496e-03 7.694e-03
## var_error 4.305e+01 0.251428 1.452e-03 1.424e-03
## prp_var_eartag 1.828e-01 0.019921 1.150e-04 1.177e-04
## prp_var_error 8.172e-01 0.019921 1.150e-04 1.177e-04
## lp__ -1.389e+05 9.383089 5.417e-02 8.993e-02
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.151e+01 1.273e+01 1.336e+01 1.398e+01 1.521e+01
## Loc1_t_2 5.240e+00 6.478e+00 7.124e+00 7.781e+00 9.005e+00
## Loc1_t_3 8.238e+00 9.480e+00 1.013e+01 1.078e+01 1.204e+01
## Loc1_t_4 5.964e+00 7.428e+00 8.174e+00 8.919e+00 1.040e+01
## Loc1_t_5 6.758e+00 8.232e+00 9.022e+00 9.791e+00 1.122e+01
## Loc1_t_6 2.806e+00 4.164e+00 4.865e+00 5.567e+00 6.961e+00
## Loc1_t_7 8.863e+00 1.025e+01 1.097e+01 1.168e+01 1.304e+01
## Loc2_t_1 8.551e+00 9.767e+00 1.041e+01 1.104e+01 1.224e+01
## Loc2_t_2 6.040e+00 7.304e+00 7.953e+00 8.599e+00 9.838e+00
## Loc2_t_3 1.272e+01 1.395e+01 1.461e+01 1.526e+01 1.652e+01
## Loc2_t_4 4.615e+00 6.056e+00 6.820e+00 7.576e+00 9.004e+00
## Loc2_t_5 7.487e+00 8.975e+00 9.734e+00 1.050e+01 1.195e+01
## Loc2_t_6 4.737e+00 6.105e+00 6.812e+00 7.534e+00 8.871e+00
## Loc2_t_7 6.161e+00 7.613e+00 8.374e+00 9.119e+00 1.056e+01
## h_ent_1 -3.352e-01 3.602e-02 2.248e-01 4.140e-01 7.658e-01
## h_ent_2 -5.537e-01 -1.869e-01 2.911e-03 1.943e-01 5.529e-01
## h_ent_3 -7.007e-01 -3.318e-01 -1.453e-01 4.790e-02 4.112e-01
## h_ent_4 -8.745e-01 -5.178e-01 -3.355e-01 -1.505e-01 2.088e-01
## h_ent_5 -1.091e+00 -7.704e-01 -6.005e-01 -4.326e-01 -1.126e-01
## h_ent_6 -1.044e+00 -7.518e-01 -5.963e-01 -4.410e-01 -1.480e-01
## h_ent_7 -1.557e+00 -1.278e+00 -1.131e+00 -9.841e-01 -7.003e-01
## h_ent_8 -2.722e+00 -2.450e+00 -2.308e+00 -2.166e+00 -1.898e+00
## h_ent_9 -1.428e+00 -1.152e+00 -1.005e+00 -8.612e-01 -5.815e-01
## h_ent_10 -5.409e-01 -2.531e-01 -1.060e-01 4.210e-02 3.281e-01
## h_ent_11 -2.969e-02 2.485e-01 3.965e-01 5.451e-01 8.247e-01
## h_ent_12 2.612e-01 5.431e-01 6.889e-01 8.368e-01 1.123e+00
## h_ent_13 -1.632e-02 2.571e-01 4.034e-01 5.495e-01 8.267e-01
## h_ent_14 1.263e-01 4.041e-01 5.511e-01 6.976e-01 9.715e-01
## h_ent_15 3.726e-01 6.551e-01 8.016e-01 9.504e-01 1.228e+00
## h_ent_16 9.229e-01 1.214e+00 1.367e+00 1.523e+00 1.816e+00
## h_ent_17 1.250e+00 1.558e+00 1.722e+00 1.889e+00 2.202e+00
## h_ent_18 7.398e-01 1.059e+00 1.226e+00 1.395e+00 1.714e+00
## h_ent_19 2.838e-01 6.043e-01 7.759e-01 9.443e-01 1.261e+00
## h_ent_20 -6.921e-02 2.592e-01 4.285e-01 5.993e-01 9.224e-01
## h_ent_21 -2.469e-01 7.878e-02 2.536e-01 4.271e-01 7.521e-01
## h_ent_22 -5.918e-01 -2.708e-01 -1.010e-01 6.868e-02 3.900e-01
## h_ent_23 -1.153e-01 2.191e-01 3.977e-01 5.751e-01 9.138e-01
## Median Weight 9.156e-03 1.136e-02 1.251e-02 1.366e-02 1.580e-02
## var_eartag 7.458e+00 8.747e+00 9.555e+00 1.045e+01 1.253e+01
## var_error 4.256e+01 4.288e+01 4.305e+01 4.322e+01 4.354e+01
## prp_var_eartag 1.477e-01 1.688e-01 1.815e-01 1.954e-01 2.253e-01
## prp_var_error 7.747e-01 8.046e-01 8.185e-01 8.312e-01 8.523e-01
## lp__ -1.390e+05 -1.389e+05 -1.389e+05 -1.389e+05 -1.389e+05print(M160s.model)## Inference for Stan model: M1_Eartag_model.
## 3 chains, each with iter=12000; warmup=2000; thin=1;
## post-warmup draws per chain=10000, total post-warmup draws=30000.
##
## mean se_mean sd 2.5% 25% 50%
## beta[1] 13.36 0.00 0.94 11.51 12.73 13.36
## beta[2] 7.13 0.01 0.96 5.24 6.48 7.12
## beta[3] 10.13 0.01 0.97 8.24 9.48 10.13
## beta[4] 8.18 0.01 1.12 5.96 7.43 8.17
## beta[5] 9.01 0.01 1.14 6.76 8.23 9.02
## beta[6] 4.87 0.01 1.05 2.81 4.16 4.87
## beta[7] 10.97 0.01 1.06 8.86 10.25 10.97
## beta[8] 10.41 0.00 0.94 8.55 9.77 10.41
## beta[9] 7.95 0.01 0.96 6.04 7.30 7.95
## beta[10] 14.61 0.00 0.96 12.72 13.95 14.61
## beta[11] 6.82 0.01 1.12 4.61 6.06 6.82
## beta[12] 9.74 0.01 1.14 7.49 8.98 9.73
## beta[13] 6.81 0.01 1.05 4.74 6.11 6.81
## beta[14] 8.37 0.01 1.12 6.16 7.61 8.37
## beta[15] 0.22 0.00 0.28 -0.34 0.04 0.22
## beta[16] 0.00 0.00 0.28 -0.55 -0.19 0.00
## beta[17] -0.14 0.00 0.28 -0.70 -0.33 -0.15
## beta[18] -0.33 0.00 0.27 -0.87 -0.52 -0.34
## beta[19] -0.60 0.00 0.25 -1.09 -0.77 -0.60
## beta[20] -0.60 0.00 0.23 -1.04 -0.75 -0.60
## beta[21] -1.13 0.00 0.22 -1.56 -1.28 -1.13
## beta[22] -2.31 0.00 0.21 -2.72 -2.45 -2.31
## beta[23] -1.01 0.00 0.22 -1.43 -1.15 -1.00
## beta[24] -0.11 0.00 0.22 -0.54 -0.25 -0.11
## beta[25] 0.40 0.00 0.22 -0.03 0.25 0.40
## beta[26] 0.69 0.00 0.22 0.26 0.54 0.69
## beta[27] 0.40 0.00 0.22 -0.02 0.26 0.40
## beta[28] 0.55 0.00 0.22 0.13 0.40 0.55
## beta[29] 0.80 0.00 0.22 0.37 0.66 0.80
## beta[30] 1.37 0.00 0.23 0.92 1.21 1.37
## beta[31] 1.72 0.00 0.24 1.25 1.56 1.72
## beta[32] 1.23 0.00 0.25 0.74 1.06 1.23
## beta[33] 0.77 0.00 0.25 0.28 0.60 0.78
## beta[34] 0.43 0.00 0.25 -0.07 0.26 0.43
## beta[35] 0.25 0.00 0.26 -0.25 0.08 0.25
## beta[36] -0.10 0.00 0.25 -0.59 -0.27 -0.10
## beta[37] 0.40 0.00 0.26 -0.12 0.22 0.40
## beta[38] 0.01 0.00 0.00 0.01 0.01 0.01
## var_eartag 9.66 0.01 1.30 7.46 8.75 9.56
## var_error 43.05 0.00 0.25 42.56 42.88 43.05
## prp_var_eartag 0.18 0.00 0.02 0.15 0.17 0.18
## prp_var_error 0.82 0.00 0.02 0.77 0.80 0.82
## lp__ -138931.82 0.09 9.38 -138951.25 -138937.99 -138931.46
## 75% 97.5% n_eff Rhat
## beta[1] 13.98 15.21 39052 1
## beta[2] 7.78 9.00 35955 1
## beta[3] 10.78 12.04 34949 1
## beta[4] 8.92 10.40 40590 1
## beta[5] 9.79 11.22 41419 1
## beta[6] 5.57 6.96 36818 1
## beta[7] 11.68 13.04 40773 1
## beta[8] 11.04 12.24 37541 1
## beta[9] 8.60 9.84 35255 1
## beta[10] 15.26 16.52 37146 1
## beta[11] 7.58 9.00 40674 1
## beta[12] 10.50 11.95 41274 1
## beta[13] 7.53 8.87 38219 1
## beta[14] 9.12 10.56 39761 1
## beta[15] 0.41 0.77 28682 1
## beta[16] 0.19 0.55 28895 1
## beta[17] 0.05 0.41 30236 1
## beta[18] -0.15 0.21 28201 1
## beta[19] -0.43 -0.11 29555 1
## beta[20] -0.44 -0.15 28808 1
## beta[21] -0.98 -0.70 28551 1
## beta[22] -2.17 -1.90 28470 1
## beta[23] -0.86 -0.58 28937 1
## beta[24] 0.04 0.33 27943 1
## beta[25] 0.55 0.82 27850 1
## beta[26] 0.84 1.12 28511 1
## beta[27] 0.55 0.83 28026 1
## beta[28] 0.70 0.97 29044 1
## beta[29] 0.95 1.23 29128 1
## beta[30] 1.52 1.82 28463 1
## beta[31] 1.89 2.20 29102 1
## beta[32] 1.40 1.71 29176 1
## beta[33] 0.94 1.26 28463 1
## beta[34] 0.60 0.92 28335 1
## beta[35] 0.43 0.75 27772 1
## beta[36] 0.07 0.39 28824 1
## beta[37] 0.58 0.91 28310 1
## beta[38] 0.01 0.02 30474 1
## var_eartag 10.45 12.53 27409 1
## var_error 43.22 43.54 30989 1
## prp_var_eartag 0.20 0.23 27640 1
## prp_var_error 0.83 0.85 27640 1
## lp__ -138925.34 -138914.49 10241 1
##
## Samples were drawn using NUTS(diag_e) at Sat Jan 25 01:04:57 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).Posterior Correlation of model parameters
parcorplot(outp1,col = terrain.colors(15,0.5,T), cex.axis=0.6)
2. Mixed model: Location + Hours + Median wt + Eartag + Follower
## [1] "mcmc.list"2.1.Convergence Diagnostic
Check autorrelation, effective sample size, traceplot
ggs_autocorrelation(ggs(outp2)%>%filter(Parameter%in%lt1))
ggs_autocorrelation(ggs(outp2)%>%filter(Parameter%in%lt2))
ggs_autocorrelation(ggs(outp1)%>%filter(Parameter%in%hent1))
ggs_autocorrelation(ggs(outp1)%>%filter(Parameter%in%hent2))
ggs_autocorrelation(ggs(outp2)%>%filter(Parameter%in%c("Median Weight",
"var_eartag", "var_follower", "var_error",
"prp_var_eartag","prp_var_follower", "prp_var_error")))
autocorr.diag(outp2)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4 Loc1_t_5
## Lag 0 1.000000000 1.000000000 1.00000000 1.000000000 1.00000000
## Lag 1 0.354946556 0.420174172 0.41278114 0.356186197 0.36978083
## Lag 5 0.052707601 0.085746532 0.08675868 0.058781783 0.06683354
## Lag 10 0.004160664 0.008130075 0.02059384 0.002262731 -0.00295396
## Lag 50 0.001394410 0.002682890 0.01674743 -0.003336492 -0.01860511
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## Lag 0 1.0000000000 1.00000000 1.000000000 1.00000000 1.000000000
## Lag 1 0.4087740339 0.39022209 0.383634484 0.41386958 0.420128024
## Lag 5 0.0667217689 0.07202671 0.065580177 0.08488643 0.063779114
## Lag 10 -0.0003525985 0.01133235 0.011191437 0.02097682 0.015508413
## Lag 50 -0.0079839535 -0.01148909 -0.001487246 -0.00240930 0.002778221
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1 h_ent_2
## Lag 0 1.000000000 1.000000000 1.00000000 1.000000000 1.000000000 1.00000000
## Lag 1 0.373138664 0.341649453 0.40355418 0.366125728 0.138619928 0.11969717
## Lag 5 0.068201889 0.058613252 0.08081979 0.057394013 0.073372005 0.07292291
## Lag 10 0.009429183 0.007660883 0.01199418 0.010029691 0.003095651 0.01651861
## Lag 50 -0.015552940 0.002297262 0.00684543 -0.004315665 0.011522052 0.01110793
## h_ent_3 h_ent_4 h_ent_5 h_ent_6 h_ent_7 h_ent_8
## Lag 0 1.000000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000
## Lag 1 0.134988239 0.14117431 0.20846039 0.30107045 0.35573357 0.40621824
## Lag 5 0.068846735 0.07581485 0.08617644 0.10183888 0.10898193 0.11700368
## Lag 10 0.022010027 0.01684615 0.01416413 0.01570079 0.01626635 0.02151209
## Lag 50 0.005907581 0.02049565 0.01207416 0.01158604 0.01402996 0.01832043
## h_ent_9 h_ent_10 h_ent_11 h_ent_12 h_ent_13 h_ent_14
## Lag 0 1.00000000 1.000000000 1.000000000 1.00000000 1.00000000 1.00000000
## Lag 1 0.36779253 0.349915657 0.350448195 0.35056458 0.37279024 0.36952604
## Lag 5 0.11707084 0.110322774 0.110735690 0.10568015 0.10925494 0.11565759
## Lag 10 0.02239556 0.019545808 0.016561233 0.01842223 0.01307210 0.02046023
## Lag 50 0.01437657 0.009189227 0.006903503 0.01018360 0.01314191 0.01411713
## h_ent_15 h_ent_16 h_ent_17 h_ent_18 h_ent_19 h_ent_20
## Lag 0 1.00000000 1.00000000 1.00000000 1.000000000 1.00000000 1.000000000
## Lag 1 0.34917393 0.30335996 0.24438496 0.227397583 0.20047383 0.219375685
## Lag 5 0.11402462 0.10297237 0.08449800 0.086225761 0.08313746 0.086185645
## Lag 10 0.01679219 0.01920877 0.02532862 0.017455655 0.01638822 0.012300520
## Lag 50 0.01857943 0.01021250 0.01222905 0.003397212 0.01481565 0.009909304
## h_ent_21 h_ent_22 h_ent_23 Median Weight var_eartag
## Lag 0 1.00000000 1.0000000000 1.00000000 1.000000000 1.000000000
## Lag 1 0.18604255 0.1998501536 0.16938825 -0.235146813 -0.011772196
## Lag 5 0.07226201 0.0894882340 0.07318666 -0.004000513 0.023653401
## Lag 10 0.01037046 0.0078335218 0.01248590 -0.012395976 -0.003344268
## Lag 50 0.01122439 0.0005795794 0.01386453 0.003267863 0.002925730
## var_follower var_error prp_var_eartag prp_var_follower prp_var_error
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.014423876 -0.189805826 -0.019675522 0.011619886 -0.017901845
## Lag 5 0.015229931 0.002874876 0.023187127 0.015717596 0.023141418
## Lag 10 -0.002026357 0.001830530 -0.003113122 -0.001821770 -0.002964806
## Lag 50 0.000612375 -0.004361088 0.003565767 0.002820392 0.001191275
## lp__
## Lag 0 1.000000000
## Lag 1 0.505597393
## Lag 5 0.048425579
## Lag 10 0.001899543
## Lag 50 0.004276996effectiveSize(outp2)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## 14487.522 13243.222 12776.161 15369.030
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 14449.578 13434.012 13539.246 13462.784
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 12637.524 13062.744 15529.748 14719.492
## Loc2_t_6 Loc2_t_7 h_ent_1 h_ent_2
## 13318.972 14467.495 13889.468 14438.125
## h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 14280.807 14000.854 12745.524 11598.182
## h_ent_7 h_ent_8 h_ent_9 h_ent_10
## 11415.221 10387.376 10762.880 10985.316
## h_ent_11 h_ent_12 h_ent_13 h_ent_14
## 10968.327 11675.245 11413.933 10811.516
## h_ent_15 h_ent_16 h_ent_17 h_ent_18
## 10722.006 11283.256 12362.562 12545.914
## h_ent_19 h_ent_20 h_ent_21 h_ent_22
## 13619.736 12560.065 12907.514 12497.266
## h_ent_23 Median Weight var_eartag var_follower
## 14060.840 50279.023 23363.336 21808.414
## var_error prp_var_eartag prp_var_follower prp_var_error
## 41669.043 23444.721 22243.116 23594.620
## lp__
## 9729.388geweke.diag(outp2)## [[1]]
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## 0.47233 0.44003 -0.72566 -0.12693
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 0.25057 -0.51244 -0.48425 -0.32829
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## -0.53312 1.13292 0.73722 -1.34345
## Loc2_t_6 Loc2_t_7 h_ent_1 h_ent_2
## -0.08017 1.81882 -0.65347 -0.58133
## h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 0.14207 0.18395 -1.75092 -0.03210
## h_ent_7 h_ent_8 h_ent_9 h_ent_10
## -1.11711 -0.14110 -0.27958 -0.27009
## h_ent_11 h_ent_12 h_ent_13 h_ent_14
## -0.43584 0.53562 0.08414 0.10707
## h_ent_15 h_ent_16 h_ent_17 h_ent_18
## -0.27628 -0.24594 -0.10290 -0.93223
## h_ent_19 h_ent_20 h_ent_21 h_ent_22
## -0.40879 -0.87182 -1.28015 -0.87744
## h_ent_23 Median Weight var_eartag var_follower
## 1.23575 -0.04186 -0.61832 -0.55408
## var_error prp_var_eartag prp_var_follower prp_var_error
## -2.54676 -0.55256 -0.33899 0.63429
## lp__
## 1.01126
##
##
## [[2]]
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## -0.7745 -1.4543 -1.1280 -1.4199
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## -0.8618 -1.1173 -0.1851 0.2419
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 0.1817 0.6519 -0.1001 -1.4178
## Loc2_t_6 Loc2_t_7 h_ent_1 h_ent_2
## -0.2324 0.3390 1.5302 1.4059
## h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 1.5056 1.3537 1.2088 0.9628
## h_ent_7 h_ent_8 h_ent_9 h_ent_10
## 1.2660 1.3894 1.5893 1.1129
## h_ent_11 h_ent_12 h_ent_13 h_ent_14
## 1.1296 1.5277 1.0293 1.5996
## h_ent_15 h_ent_16 h_ent_17 h_ent_18
## 1.1780 1.3549 0.8358 1.6954
## h_ent_19 h_ent_20 h_ent_21 h_ent_22
## 1.3389 0.9825 0.9098 0.9161
## h_ent_23 Median Weight var_eartag var_follower
## 0.6050 -0.1970 -0.5501 -0.0692
## var_error prp_var_eartag prp_var_follower prp_var_error
## -0.8553 -0.5565 0.1107 0.5770
## lp__
## 0.3005
##
##
## [[3]]
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## 1.77911 0.82476 0.64853 -1.77476
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 0.02787 -0.96142 0.02544 0.53444
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## -0.81291 0.51938 -0.16591 -1.30450
## Loc2_t_6 Loc2_t_7 h_ent_1 h_ent_2
## -0.36965 1.54867 -0.89974 -0.90824
## h_ent_3 h_ent_4 h_ent_5 h_ent_6
## -0.78977 -1.20484 -0.75663 -0.88512
## h_ent_7 h_ent_8 h_ent_9 h_ent_10
## -0.64076 -0.59224 -0.86444 -0.81765
## h_ent_11 h_ent_12 h_ent_13 h_ent_14
## -0.64028 -0.56809 -0.80700 -0.86224
## h_ent_15 h_ent_16 h_ent_17 h_ent_18
## -0.60682 -0.67548 -1.31449 -0.77929
## h_ent_19 h_ent_20 h_ent_21 h_ent_22
## -0.88583 -0.46883 -0.59359 -0.66978
## h_ent_23 Median Weight var_eartag var_follower
## -0.40770 0.37037 -2.97658 -0.84081
## var_error prp_var_eartag prp_var_follower prp_var_error
## 0.05361 -2.40993 -0.39361 2.58350
## lp__
## 0.61265gelman.diag(outp2, transform = T)## Potential scale reduction factors:
##
## Point est. Upper C.I.
## Loc1_t_1 1 1
## Loc1_t_2 1 1
## Loc1_t_3 1 1
## Loc1_t_4 1 1
## Loc1_t_5 1 1
## Loc1_t_6 1 1
## Loc1_t_7 1 1
## Loc2_t_1 1 1
## Loc2_t_2 1 1
## Loc2_t_3 1 1
## Loc2_t_4 1 1
## Loc2_t_5 1 1
## Loc2_t_6 1 1
## Loc2_t_7 1 1
## h_ent_1 1 1
## h_ent_2 1 1
## h_ent_3 1 1
## h_ent_4 1 1
## h_ent_5 1 1
## h_ent_6 1 1
## h_ent_7 1 1
## h_ent_8 1 1
## h_ent_9 1 1
## h_ent_10 1 1
## h_ent_11 1 1
## h_ent_12 1 1
## h_ent_13 1 1
## h_ent_14 1 1
## h_ent_15 1 1
## h_ent_16 1 1
## h_ent_17 1 1
## h_ent_18 1 1
## h_ent_19 1 1
## h_ent_20 1 1
## h_ent_21 1 1
## h_ent_22 1 1
## h_ent_23 1 1
## Median Weight 1 1
## var_eartag 1 1
## var_follower 1 1
## var_error 1 1
## prp_var_eartag 1 1
## prp_var_follower 1 1
## prp_var_error 1 1
## lp__ 1 1
##
## Multivariate psrf
##
## 1traplot(outp2, col = c("red1","purple1","blue4"))
denplot(outp2,col = c("red1","purple1","blue4"))
## 2.2. Summary Posterior Distribution
summary(outp2)##
## Iterations = 2001:12000
## Thinning interval = 1
## Number of chains = 3
## Sample size per chain = 10000
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## Loc1_t_1 1.320e+01 1.003906 5.796e-03 9.983e-03
## Loc1_t_2 6.935e+00 1.022644 5.904e-03 1.113e-02
## Loc1_t_3 9.911e+00 1.011606 5.841e-03 1.099e-02
## Loc1_t_4 8.040e+00 1.196480 6.908e-03 1.161e-02
## Loc1_t_5 9.007e+00 1.193784 6.892e-03 1.180e-02
## Loc1_t_6 4.828e+00 1.115717 6.442e-03 1.167e-02
## Loc1_t_7 1.110e+01 1.121007 6.472e-03 1.164e-02
## Loc2_t_1 1.064e+01 0.998443 5.765e-03 1.020e-02
## Loc2_t_2 7.861e+00 1.040790 6.009e-03 1.128e-02
## Loc2_t_3 1.459e+01 1.022598 5.904e-03 1.071e-02
## Loc2_t_4 6.537e+00 1.200812 6.933e-03 1.242e-02
## Loc2_t_5 9.475e+00 1.208998 6.980e-03 1.169e-02
## Loc2_t_6 6.985e+00 1.112400 6.422e-03 1.187e-02
## Loc2_t_7 8.398e+00 1.210240 6.987e-03 1.219e-02
## h_ent_1 2.052e-01 0.277661 1.603e-03 2.612e-03
## h_ent_2 -1.122e-02 0.279109 1.611e-03 2.630e-03
## h_ent_3 -1.587e-01 0.281111 1.623e-03 2.594e-03
## h_ent_4 -4.318e-01 0.271701 1.569e-03 2.608e-03
## h_ent_5 -6.249e-01 0.248979 1.437e-03 2.532e-03
## h_ent_6 -5.291e-01 0.230706 1.332e-03 2.483e-03
## h_ent_7 -1.008e+00 0.218742 1.263e-03 2.431e-03
## h_ent_8 -2.162e+00 0.210878 1.218e-03 2.447e-03
## h_ent_9 -9.178e-01 0.215663 1.245e-03 2.455e-03
## h_ent_10 2.110e-02 0.218798 1.263e-03 2.446e-03
## h_ent_11 5.113e-01 0.219907 1.270e-03 2.493e-03
## h_ent_12 8.530e-01 0.218461 1.261e-03 2.408e-03
## h_ent_13 5.855e-01 0.215371 1.243e-03 2.403e-03
## h_ent_14 7.233e-01 0.216188 1.248e-03 2.446e-03
## h_ent_15 8.854e-01 0.218328 1.261e-03 2.446e-03
## h_ent_16 1.406e+00 0.226782 1.309e-03 2.472e-03
## h_ent_17 1.747e+00 0.242452 1.400e-03 2.530e-03
## h_ent_18 1.248e+00 0.247473 1.429e-03 2.526e-03
## h_ent_19 7.676e-01 0.252128 1.456e-03 2.517e-03
## h_ent_20 5.167e-01 0.247686 1.430e-03 2.521e-03
## h_ent_21 3.219e-01 0.253371 1.463e-03 2.528e-03
## h_ent_22 -2.831e-02 0.252268 1.456e-03 2.534e-03
## h_ent_23 4.449e-01 0.261541 1.510e-03 2.541e-03
## Median Weight 1.331e-02 0.001682 9.713e-06 7.684e-06
## var_eartag 9.591e+00 1.289144 7.443e-03 8.487e-03
## var_follower 1.297e+00 0.187430 1.082e-03 1.271e-03
## var_error 4.190e+01 0.242544 1.400e-03 1.207e-03
## prp_var_eartag 1.812e-01 0.019795 1.143e-04 1.304e-04
## prp_var_follower 2.457e-02 0.003511 2.027e-05 2.360e-05
## prp_var_error 7.942e-01 0.019405 1.120e-04 1.271e-04
## lp__ -1.382e+05 12.697657 7.331e-02 1.288e-01
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.123e+01 1.252e+01 1.321e+01 1.387e+01 1.519e+01
## Loc1_t_2 4.926e+00 6.245e+00 6.935e+00 7.624e+00 8.941e+00
## Loc1_t_3 7.920e+00 9.235e+00 9.914e+00 1.060e+01 1.189e+01
## Loc1_t_4 5.694e+00 7.238e+00 8.042e+00 8.846e+00 1.040e+01
## Loc1_t_5 6.658e+00 8.206e+00 8.996e+00 9.800e+00 1.136e+01
## Loc1_t_6 2.633e+00 4.090e+00 4.828e+00 5.561e+00 7.046e+00
## Loc1_t_7 8.924e+00 1.035e+01 1.109e+01 1.184e+01 1.331e+01
## Loc2_t_1 8.672e+00 9.969e+00 1.064e+01 1.130e+01 1.260e+01
## Loc2_t_2 5.822e+00 7.164e+00 7.854e+00 8.562e+00 9.896e+00
## Loc2_t_3 1.260e+01 1.391e+01 1.459e+01 1.527e+01 1.661e+01
## Loc2_t_4 4.153e+00 5.735e+00 6.531e+00 7.343e+00 8.898e+00
## Loc2_t_5 7.081e+00 8.657e+00 9.479e+00 1.029e+01 1.186e+01
## Loc2_t_6 4.818e+00 6.236e+00 6.987e+00 7.730e+00 9.174e+00
## Loc2_t_7 6.013e+00 7.582e+00 8.395e+00 9.207e+00 1.082e+01
## h_ent_1 -3.399e-01 1.758e-02 2.045e-01 3.922e-01 7.483e-01
## h_ent_2 -5.596e-01 -1.992e-01 -9.571e-03 1.772e-01 5.336e-01
## h_ent_3 -7.128e-01 -3.489e-01 -1.568e-01 3.036e-02 3.883e-01
## h_ent_4 -9.630e-01 -6.171e-01 -4.322e-01 -2.471e-01 9.799e-02
## h_ent_5 -1.111e+00 -7.932e-01 -6.236e-01 -4.571e-01 -1.327e-01
## h_ent_6 -9.801e-01 -6.840e-01 -5.285e-01 -3.737e-01 -7.360e-02
## h_ent_7 -1.441e+00 -1.155e+00 -1.008e+00 -8.602e-01 -5.859e-01
## h_ent_8 -2.577e+00 -2.305e+00 -2.162e+00 -2.018e+00 -1.751e+00
## h_ent_9 -1.345e+00 -1.063e+00 -9.182e-01 -7.714e-01 -5.002e-01
## h_ent_10 -4.076e-01 -1.271e-01 2.182e-02 1.705e-01 4.480e-01
## h_ent_11 7.407e-02 3.632e-01 5.127e-01 6.601e-01 9.407e-01
## h_ent_12 4.223e-01 7.058e-01 8.542e-01 1.000e+00 1.279e+00
## h_ent_13 1.550e-01 4.419e-01 5.866e-01 7.292e-01 1.005e+00
## h_ent_14 2.983e-01 5.789e-01 7.240e-01 8.689e-01 1.146e+00
## h_ent_15 4.556e-01 7.376e-01 8.870e-01 1.034e+00 1.310e+00
## h_ent_16 9.598e-01 1.254e+00 1.407e+00 1.560e+00 1.846e+00
## h_ent_17 1.272e+00 1.585e+00 1.746e+00 1.912e+00 2.222e+00
## h_ent_18 7.575e-01 1.083e+00 1.250e+00 1.413e+00 1.731e+00
## h_ent_19 2.701e-01 5.980e-01 7.676e-01 9.360e-01 1.259e+00
## h_ent_20 3.187e-02 3.493e-01 5.163e-01 6.846e-01 1.004e+00
## h_ent_21 -1.733e-01 1.507e-01 3.235e-01 4.928e-01 8.203e-01
## h_ent_22 -5.229e-01 -1.983e-01 -2.911e-02 1.421e-01 4.668e-01
## h_ent_23 -7.202e-02 2.682e-01 4.456e-01 6.212e-01 9.572e-01
## Median Weight 9.994e-03 1.218e-02 1.329e-02 1.443e-02 1.664e-02
## var_eartag 7.397e+00 8.676e+00 9.472e+00 1.038e+01 1.243e+01
## var_follower 9.803e-01 1.164e+00 1.280e+00 1.410e+00 1.710e+00
## var_error 4.143e+01 4.173e+01 4.190e+01 4.206e+01 4.237e+01
## prp_var_eartag 1.463e-01 1.673e-01 1.798e-01 1.937e-01 2.233e-01
## prp_var_follower 1.862e-02 2.207e-02 2.427e-02 2.669e-02 3.226e-02
## prp_var_error 7.529e-01 7.820e-01 7.955e-01 8.078e-01 8.286e-01
## lp__ -1.382e+05 -1.382e+05 -1.382e+05 -1.382e+05 -1.382e+05print(M260s.model)## Inference for Stan model: M2_EartagFoll_model.
## 3 chains, each with iter=12000; warmup=2000; thin=1;
## post-warmup draws per chain=10000, total post-warmup draws=30000.
##
## mean se_mean sd 2.5% 25% 50%
## beta[1] 13.20 0.01 1.00 11.23 12.52 13.21
## beta[2] 6.93 0.01 1.02 4.93 6.24 6.93
## beta[3] 9.91 0.01 1.01 7.92 9.24 9.91
## beta[4] 8.04 0.01 1.20 5.69 7.24 8.04
## beta[5] 9.01 0.01 1.19 6.66 8.21 9.00
## beta[6] 4.83 0.01 1.12 2.63 4.09 4.83
## beta[7] 11.10 0.01 1.12 8.92 10.35 11.09
## beta[8] 10.64 0.01 1.00 8.67 9.97 10.64
## beta[9] 7.86 0.01 1.04 5.82 7.16 7.85
## beta[10] 14.59 0.01 1.02 12.60 13.91 14.59
## beta[11] 6.54 0.01 1.20 4.15 5.73 6.53
## beta[12] 9.48 0.01 1.21 7.08 8.66 9.48
## beta[13] 6.99 0.01 1.11 4.82 6.24 6.99
## beta[14] 8.40 0.01 1.21 6.01 7.58 8.40
## beta[15] 0.21 0.00 0.28 -0.34 0.02 0.20
## beta[16] -0.01 0.00 0.28 -0.56 -0.20 -0.01
## beta[17] -0.16 0.00 0.28 -0.71 -0.35 -0.16
## beta[18] -0.43 0.00 0.27 -0.96 -0.62 -0.43
## beta[19] -0.62 0.00 0.25 -1.11 -0.79 -0.62
## beta[20] -0.53 0.00 0.23 -0.98 -0.68 -0.53
## beta[21] -1.01 0.00 0.22 -1.44 -1.15 -1.01
## beta[22] -2.16 0.00 0.21 -2.58 -2.31 -2.16
## beta[23] -0.92 0.00 0.22 -1.35 -1.06 -0.92
## beta[24] 0.02 0.00 0.22 -0.41 -0.13 0.02
## beta[25] 0.51 0.00 0.22 0.07 0.36 0.51
## beta[26] 0.85 0.00 0.22 0.42 0.71 0.85
## beta[27] 0.59 0.00 0.22 0.15 0.44 0.59
## beta[28] 0.72 0.00 0.22 0.30 0.58 0.72
## beta[29] 0.89 0.00 0.22 0.46 0.74 0.89
## beta[30] 1.41 0.00 0.23 0.96 1.25 1.41
## beta[31] 1.75 0.00 0.24 1.27 1.59 1.75
## beta[32] 1.25 0.00 0.25 0.76 1.08 1.25
## beta[33] 0.77 0.00 0.25 0.27 0.60 0.77
## beta[34] 0.52 0.00 0.25 0.03 0.35 0.52
## beta[35] 0.32 0.00 0.25 -0.17 0.15 0.32
## beta[36] -0.03 0.00 0.25 -0.52 -0.20 -0.03
## beta[37] 0.44 0.00 0.26 -0.07 0.27 0.45
## beta[38] 0.01 0.00 0.00 0.01 0.01 0.01
## var_eartag 9.59 0.01 1.29 7.40 8.68 9.47
## var_follower 1.30 0.00 0.19 0.98 1.16 1.28
## var_error 41.90 0.00 0.24 41.43 41.73 41.90
## prp_var_eartag 0.18 0.00 0.02 0.15 0.17 0.18
## prp_var_follower 0.02 0.00 0.00 0.02 0.02 0.02
## prp_var_error 0.79 0.00 0.02 0.75 0.78 0.80
## lp__ -138224.01 0.13 12.70 -138249.96 -138232.35 -138223.65
## 75% 97.5% n_eff Rhat
## beta[1] 13.87 15.19 10264 1
## beta[2] 7.62 8.94 8671 1
## beta[3] 10.60 11.89 8379 1
## beta[4] 8.85 10.40 10447 1
## beta[5] 9.80 11.36 9890 1
## beta[6] 5.56 7.05 9255 1
## beta[7] 11.84 13.31 9219 1
## beta[8] 11.30 12.60 9358 1
## beta[9] 8.56 9.90 8251 1
## beta[10] 15.27 16.61 8878 1
## beta[11] 7.34 8.90 9333 1
## beta[12] 10.29 11.86 10344 1
## beta[13] 7.73 9.17 7956 1
## beta[14] 9.21 10.82 9944 1
## beta[15] 0.39 0.75 11481 1
## beta[16] 0.18 0.53 11355 1
## beta[17] 0.03 0.39 11573 1
## beta[18] -0.25 0.10 11007 1
## beta[19] -0.46 -0.13 9605 1
## beta[20] -0.37 -0.07 8424 1
## beta[21] -0.86 -0.59 7914 1
## beta[22] -2.02 -1.75 7559 1
## beta[23] -0.77 -0.50 7649 1
## beta[24] 0.17 0.45 7937 1
## beta[25] 0.66 0.94 7939 1
## beta[26] 1.00 1.28 8099 1
## beta[27] 0.73 1.00 7962 1
## beta[28] 0.87 1.15 7706 1
## beta[29] 1.03 1.31 8006 1
## beta[30] 1.56 1.85 8373 1
## beta[31] 1.91 2.22 9317 1
## beta[32] 1.41 1.73 9524 1
## beta[33] 0.94 1.26 9930 1
## beta[34] 0.68 1.00 9483 1
## beta[35] 0.49 0.82 10026 1
## beta[36] 0.14 0.47 9941 1
## beta[37] 0.62 0.96 10689 1
## beta[38] 0.01 0.02 46639 1
## var_eartag 10.38 12.43 21550 1
## var_follower 1.41 1.71 21576 1
## var_error 42.06 42.37 40821 1
## prp_var_eartag 0.19 0.22 22008 1
## prp_var_follower 0.03 0.03 21772 1
## prp_var_error 0.81 0.83 21997 1
## lp__ -138215.31 -138200.06 9310 1
##
## Samples were drawn using NUTS(diag_e) at Fri Jan 24 17:37:54 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).Posterior Correlation of model parameters
parcorplot(outp2,col = terrain.colors(15,0.5,T), cex.axis=0.6)
3. Mixed model: Location + Hours + Median wt + Eartag + Follower + covariance between eartag and follower random effects
3.1.Convergence Diagnostic
Check autorrelation, effective sample size, traceplot
ggs_autocorrelation(ggs(outp3)%>%filter(Parameter%in%lt1))
ggs_autocorrelation(ggs(outp3)%>%filter(Parameter%in%lt2))
ggs_autocorrelation(ggs(outp1)%>%filter(Parameter%in%hent1))
ggs_autocorrelation(ggs(outp1)%>%filter(Parameter%in%hent2))
ggs_autocorrelation(ggs(outp3)%>%filter(Parameter%in%c("Median Weight",
"rho","var_eartag","var_follower", "var_error",
"prp_var_eartag","prp_var_follower", "prp_var_error")))
autocorr.diag(outp3)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4 Loc1_t_5 Loc1_t_6
## Lag 0 1.00000000 1.000000000 1.0000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.69479304 0.759026751 0.7600638 0.704895488 0.706219731 0.725027576
## Lag 5 0.21601234 0.288249094 0.3053916 0.217008901 0.220636595 0.244773474
## Lag 10 0.04367865 0.101359745 0.1123263 0.054482871 0.060325457 0.077094209
## Lag 50 -0.00243463 0.009332297 -0.0195713 0.002936573 0.008589115 0.006340119
## Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## Lag 0 1.0000000000 1.000000000 1.00000000 1.000000000 1.000000000
## Lag 1 0.7355349276 0.708027278 0.74056503 0.745239189 0.708945563
## Lag 5 0.2626135154 0.239095622 0.27772054 0.287823083 0.224772725
## Lag 10 0.0867461455 0.043465641 0.08564167 0.098728011 0.067600495
## Lag 50 0.0006814136 0.009080729 -0.01033292 -0.002967006 -0.006032725
## Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1 h_ent_2
## Lag 0 1.000000000 1.00000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.683282693 0.73951325 0.712739520 0.239272930 0.243721966
## Lag 5 0.180390757 0.26990590 0.232858640 0.189963276 0.199167660
## Lag 10 0.024679870 0.09090583 0.070681357 0.073835336 0.088530121
## Lag 50 0.007009968 0.01281563 0.001152849 -0.000582039 -0.008258083
## h_ent_3 h_ent_4 h_ent_5 h_ent_6 h_ent_7
## Lag 0 1.000000000 1.00000000 1.000000000 1.00000000 1.000000000
## Lag 1 0.238218992 0.26807244 0.352875788 0.45535012 0.543747020
## Lag 5 0.192685008 0.20686118 0.240324812 0.27915205 0.304525358
## Lag 10 0.079667975 0.08132021 0.105820452 0.11726159 0.129823900
## Lag 50 -0.009346956 -0.00189554 -0.009860122 -0.01066487 -0.008606763
## h_ent_8 h_ent_9 h_ent_10 h_ent_11 h_ent_12
## Lag 0 1.00000000 1.000000000 1.00000000 1.00000000 1.000000000
## Lag 1 0.61817941 0.565660743 0.54047758 0.53959183 0.549493433
## Lag 5 0.32567490 0.314834304 0.30714812 0.30328701 0.305090883
## Lag 10 0.13645484 0.129077108 0.12822258 0.12769729 0.127624423
## Lag 50 -0.01122603 -0.007591824 -0.01110623 -0.00676963 -0.009771402
## h_ent_13 h_ent_14 h_ent_15 h_ent_16 h_ent_17
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.574348863 0.563875248 0.541351660 0.467633085 0.376645969
## Lag 5 0.313190406 0.310694917 0.306021327 0.282984421 0.249468446
## Lag 10 0.129647015 0.127949628 0.131321757 0.113688887 0.104304784
## Lag 50 -0.009614678 -0.007994781 -0.006786078 -0.006998523 -0.007512659
## h_ent_18 h_ent_19 h_ent_20 h_ent_21 h_ent_22
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.364266737 0.341534756 0.359524677 0.334482471 0.332717930
## Lag 5 0.241718954 0.230253508 0.230376149 0.231401815 0.227079301
## Lag 10 0.104227208 0.098167210 0.097292680 0.093644584 0.106029910
## Lag 50 -0.003408158 -0.002803259 -0.006064036 0.002343389 -0.005184507
## h_ent_23 Median Weight rho var_eartag var_follower
## Lag 0 1.00000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.30311632 -0.300877818 0.070130369 0.049825609 0.087643369
## Lag 5 0.22150244 -0.001905226 0.021977362 0.035126115 0.025565319
## Lag 10 0.09413428 0.001396727 0.004519305 0.009297866 0.004447461
## Lag 50 -0.01179503 -0.001497396 -0.004300655 0.008359921 0.006846733
## var_error prp_var_eartag prp_var_follower prp_var_error lp__
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 -0.194371080 0.039937349 0.079421188 0.047223470 0.505489085
## Lag 5 -0.005528333 0.034236102 0.024405482 0.035496044 0.033853762
## Lag 10 0.005295735 0.009540629 0.003832443 0.009375113 0.002584933
## Lag 50 0.007407015 0.008854242 0.006166096 0.009329413 -0.012575070effectiveSize(outp3)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## 4488.362 3708.454 3562.211 4765.400
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 4555.143 4305.945 4067.592 4289.031
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 3937.598 3760.792 4613.665 5145.578
## Loc2_t_6 Loc2_t_7 h_ent_1 h_ent_2
## 3817.377 4449.361 5475.407 5044.148
## h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 5533.424 5254.928 4303.494 3809.655
## h_ent_7 h_ent_8 h_ent_9 h_ent_10
## 3631.922 3327.873 3441.734 3548.584
## h_ent_11 h_ent_12 h_ent_13 h_ent_14
## 3698.468 3557.886 3458.791 3526.690
## h_ent_15 h_ent_16 h_ent_17 h_ent_18
## 3518.449 3766.474 4334.894 4463.943
## h_ent_19 h_ent_20 h_ent_21 h_ent_22
## 4523.097 4529.109 4636.105 4566.657
## h_ent_23 Median Weight rho var_eartag
## 4781.232 55853.647 18789.098 17455.847
## var_follower var_error prp_var_eartag prp_var_follower
## 18944.506 45249.703 17801.160 19262.562
## prp_var_error lp__
## 17482.308 9650.367geweke.diag(outp3)## [[1]]
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## -0.70302 -1.15894 0.76079 1.64129
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## -1.80280 1.08724 -1.71000 -0.92352
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 0.55813 -0.54096 -0.82344 -0.05195
## Loc2_t_6 Loc2_t_7 h_ent_1 h_ent_2
## -0.73606 -0.09409 1.15255 1.78154
## h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 1.48696 1.28102 1.48331 1.50907
## h_ent_7 h_ent_8 h_ent_9 h_ent_10
## 1.42820 1.35816 1.32576 1.19059
## h_ent_11 h_ent_12 h_ent_13 h_ent_14
## 1.44529 1.31713 1.16236 1.24862
## h_ent_15 h_ent_16 h_ent_17 h_ent_18
## 1.45832 1.24774 1.12913 1.22540
## h_ent_19 h_ent_20 h_ent_21 h_ent_22
## 1.55812 1.30542 1.22318 1.44808
## h_ent_23 Median Weight rho var_eartag
## 1.55191 0.78403 1.30135 0.94832
## var_follower var_error prp_var_eartag prp_var_follower
## -1.25319 -1.50149 0.98316 -1.43180
## prp_var_error lp__
## -0.79688 -0.17807
##
##
## [[2]]
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## -1.43102 0.85434 0.32774 0.33484
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 1.95068 -0.87705 0.93229 -0.14771
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## -1.29937 -0.74321 -0.02265 0.72483
## Loc2_t_6 Loc2_t_7 h_ent_1 h_ent_2
## 0.82936 -0.39979 0.04059 -0.24891
## h_ent_3 h_ent_4 h_ent_5 h_ent_6
## -0.09990 -0.42627 -0.40976 -0.17948
## h_ent_7 h_ent_8 h_ent_9 h_ent_10
## -0.06993 -0.27219 -0.03957 -0.33290
## h_ent_11 h_ent_12 h_ent_13 h_ent_14
## -0.34379 -0.09260 -0.37484 -0.09933
## h_ent_15 h_ent_16 h_ent_17 h_ent_18
## -0.24476 -0.24284 -0.43252 -0.37948
## h_ent_19 h_ent_20 h_ent_21 h_ent_22
## -0.10062 -0.19386 -0.45219 -0.41563
## h_ent_23 Median Weight rho var_eartag
## -0.31236 -0.42004 0.89749 -0.23039
## var_follower var_error prp_var_eartag prp_var_follower
## 0.01075 0.04672 -0.32181 0.04480
## prp_var_error lp__
## 0.30103 -1.29947
##
##
## [[3]]
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## -1.682705 -0.788013 0.821439 -1.326979
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## -0.029656 -1.167014 -0.433153 0.003489
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## -0.403848 0.642222 -0.703551 -1.984867
## Loc2_t_6 Loc2_t_7 h_ent_1 h_ent_2
## -1.653162 -0.138327 1.899027 1.573001
## h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 2.003738 1.325827 1.965339 1.705772
## h_ent_7 h_ent_8 h_ent_9 h_ent_10
## 1.686357 1.760215 1.777563 1.669288
## h_ent_11 h_ent_12 h_ent_13 h_ent_14
## 1.589723 1.751426 1.846475 1.671786
## h_ent_15 h_ent_16 h_ent_17 h_ent_18
## 1.824138 1.669849 1.993321 1.272222
## h_ent_19 h_ent_20 h_ent_21 h_ent_22
## 1.622646 1.465840 1.906419 1.599902
## h_ent_23 Median Weight rho var_eartag
## 1.600461 0.321383 0.285526 -0.179324
## var_follower var_error prp_var_eartag prp_var_follower
## 0.161055 -0.185482 -0.135582 0.194856
## prp_var_error lp__
## 0.103855 0.757753gelman.diag(outp3, transform = T)## Potential scale reduction factors:
##
## Point est. Upper C.I.
## Loc1_t_1 1 1.01
## Loc1_t_2 1 1.00
## Loc1_t_3 1 1.00
## Loc1_t_4 1 1.00
## Loc1_t_5 1 1.00
## Loc1_t_6 1 1.00
## Loc1_t_7 1 1.00
## Loc2_t_1 1 1.00
## Loc2_t_2 1 1.00
## Loc2_t_3 1 1.00
## Loc2_t_4 1 1.00
## Loc2_t_5 1 1.01
## Loc2_t_6 1 1.00
## Loc2_t_7 1 1.00
## h_ent_1 1 1.00
## h_ent_2 1 1.00
## h_ent_3 1 1.00
## h_ent_4 1 1.00
## h_ent_5 1 1.00
## h_ent_6 1 1.00
## h_ent_7 1 1.00
## h_ent_8 1 1.00
## h_ent_9 1 1.00
## h_ent_10 1 1.00
## h_ent_11 1 1.00
## h_ent_12 1 1.00
## h_ent_13 1 1.00
## h_ent_14 1 1.00
## h_ent_15 1 1.00
## h_ent_16 1 1.00
## h_ent_17 1 1.00
## h_ent_18 1 1.00
## h_ent_19 1 1.00
## h_ent_20 1 1.00
## h_ent_21 1 1.00
## h_ent_22 1 1.00
## h_ent_23 1 1.00
## Median Weight 1 1.00
## rho 1 1.00
## var_eartag 1 1.00
## var_follower 1 1.00
## var_error 1 1.00
## prp_var_eartag 1 1.00
## prp_var_follower 1 1.00
## prp_var_error 1 1.00
## lp__ 1 1.00
##
## Multivariate psrf
##
## 1.01traplot(outp3,col =c("red1","blue4","purple3"))
denplot(outp3,col = c("red1","blue4","purple3"))
3.2. Summary Posterior Distribution
summary(outp3)##
## Iterations = 2001:12000
## Thinning interval = 1
## Number of chains = 3
## Sample size per chain = 10000
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## Loc1_t_1 1.322e+01 1.038676 5.997e-03 1.557e-02
## Loc1_t_2 6.937e+00 1.060302 6.122e-03 1.746e-02
## Loc1_t_3 9.890e+00 1.062783 6.136e-03 1.788e-02
## Loc1_t_4 8.062e+00 1.220253 7.045e-03 1.780e-02
## Loc1_t_5 8.987e+00 1.276659 7.371e-03 1.895e-02
## Loc1_t_6 4.831e+00 1.163798 6.719e-03 1.782e-02
## Loc1_t_7 1.110e+01 1.184088 6.836e-03 1.866e-02
## Loc2_t_1 1.067e+01 1.021613 5.898e-03 1.563e-02
## Loc2_t_2 7.861e+00 1.056328 6.099e-03 1.686e-02
## Loc2_t_3 1.459e+01 1.071952 6.189e-03 1.753e-02
## Loc2_t_4 6.550e+00 1.234128 7.125e-03 1.831e-02
## Loc2_t_5 9.484e+00 1.262917 7.291e-03 1.765e-02
## Loc2_t_6 6.976e+00 1.194326 6.895e-03 1.941e-02
## Loc2_t_7 8.434e+00 1.250480 7.220e-03 1.902e-02
## h_ent_1 2.029e-01 0.278798 1.610e-03 3.787e-03
## h_ent_2 -1.189e-02 0.281928 1.628e-03 3.989e-03
## h_ent_3 -1.596e-01 0.284473 1.642e-03 3.856e-03
## h_ent_4 -4.372e-01 0.274078 1.582e-03 3.816e-03
## h_ent_5 -6.283e-01 0.249058 1.438e-03 3.832e-03
## h_ent_6 -5.324e-01 0.230952 1.333e-03 3.774e-03
## h_ent_7 -1.010e+00 0.219450 1.267e-03 3.671e-03
## h_ent_8 -2.164e+00 0.211541 1.221e-03 3.699e-03
## h_ent_9 -9.196e-01 0.217094 1.253e-03 3.739e-03
## h_ent_10 2.039e-02 0.219304 1.266e-03 3.718e-03
## h_ent_11 5.092e-01 0.219689 1.268e-03 3.645e-03
## h_ent_12 8.508e-01 0.218539 1.262e-03 3.703e-03
## h_ent_13 5.835e-01 0.215653 1.245e-03 3.694e-03
## h_ent_14 7.219e-01 0.215967 1.247e-03 3.687e-03
## h_ent_15 8.808e-01 0.219765 1.269e-03 3.748e-03
## h_ent_16 1.402e+00 0.227980 1.316e-03 3.741e-03
## h_ent_17 1.745e+00 0.242803 1.402e-03 3.724e-03
## h_ent_18 1.247e+00 0.249018 1.438e-03 3.765e-03
## h_ent_19 7.652e-01 0.251939 1.455e-03 3.795e-03
## h_ent_20 5.146e-01 0.250298 1.445e-03 3.762e-03
## h_ent_21 3.192e-01 0.254380 1.469e-03 3.764e-03
## h_ent_22 -2.860e-02 0.252921 1.460e-03 3.796e-03
## h_ent_23 4.408e-01 0.263773 1.523e-03 3.863e-03
## Median Weight 1.333e-02 0.001673 9.659e-06 7.080e-06
## rho 1.217e-01 0.095867 5.535e-04 7.004e-04
## var_eartag 9.697e+00 1.313979 7.586e-03 9.956e-03
## var_follower 1.312e+00 0.188871 1.090e-03 1.377e-03
## var_error 4.190e+01 0.246180 1.421e-03 1.162e-03
## prp_var_eartag 1.828e-01 0.020063 1.158e-04 1.505e-04
## prp_var_follower 2.480e-02 0.003524 2.035e-05 2.551e-05
## prp_var_error 7.924e-01 0.019694 1.137e-04 1.491e-04
## lp__ -1.382e+05 12.768147 7.372e-02 1.300e-01
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.115e+01 1.252e+01 1.322e+01 1.392e+01 1.524e+01
## Loc1_t_2 4.859e+00 6.210e+00 6.947e+00 7.659e+00 8.991e+00
## Loc1_t_3 7.808e+00 9.187e+00 9.888e+00 1.060e+01 1.199e+01
## Loc1_t_4 5.676e+00 7.243e+00 8.057e+00 8.882e+00 1.044e+01
## Loc1_t_5 6.449e+00 8.132e+00 8.992e+00 9.860e+00 1.146e+01
## Loc1_t_6 2.510e+00 4.065e+00 4.840e+00 5.611e+00 7.073e+00
## Loc1_t_7 8.783e+00 1.030e+01 1.109e+01 1.189e+01 1.342e+01
## Loc2_t_1 8.674e+00 9.979e+00 1.068e+01 1.135e+01 1.266e+01
## Loc2_t_2 5.823e+00 7.145e+00 7.837e+00 8.566e+00 9.971e+00
## Loc2_t_3 1.250e+01 1.386e+01 1.460e+01 1.532e+01 1.669e+01
## Loc2_t_4 4.145e+00 5.726e+00 6.555e+00 7.379e+00 8.957e+00
## Loc2_t_5 6.979e+00 8.640e+00 9.496e+00 1.033e+01 1.193e+01
## Loc2_t_6 4.630e+00 6.190e+00 6.983e+00 7.768e+00 9.315e+00
## Loc2_t_7 5.979e+00 7.603e+00 8.435e+00 9.264e+00 1.088e+01
## h_ent_1 -3.478e-01 1.565e-02 2.039e-01 3.920e-01 7.500e-01
## h_ent_2 -5.736e-01 -1.992e-01 -1.060e-02 1.775e-01 5.307e-01
## h_ent_3 -7.228e-01 -3.518e-01 -1.595e-01 3.519e-02 3.949e-01
## h_ent_4 -9.731e-01 -6.249e-01 -4.377e-01 -2.513e-01 9.960e-02
## h_ent_5 -1.122e+00 -7.956e-01 -6.275e-01 -4.606e-01 -1.413e-01
## h_ent_6 -9.873e-01 -6.884e-01 -5.297e-01 -3.757e-01 -8.282e-02
## h_ent_7 -1.446e+00 -1.158e+00 -1.007e+00 -8.599e-01 -5.873e-01
## h_ent_8 -2.580e+00 -2.308e+00 -2.161e+00 -2.019e+00 -1.755e+00
## h_ent_9 -1.345e+00 -1.066e+00 -9.171e-01 -7.699e-01 -5.006e-01
## h_ent_10 -4.186e-01 -1.262e-01 2.321e-02 1.694e-01 4.415e-01
## h_ent_11 7.714e-02 3.612e-01 5.098e-01 6.588e-01 9.312e-01
## h_ent_12 4.164e-01 7.048e-01 8.543e-01 9.995e-01 1.272e+00
## h_ent_13 1.571e-01 4.394e-01 5.859e-01 7.309e-01 1.000e+00
## h_ent_14 2.928e-01 5.765e-01 7.245e-01 8.701e-01 1.140e+00
## h_ent_15 4.470e-01 7.333e-01 8.825e-01 1.033e+00 1.302e+00
## h_ent_16 9.533e-01 1.249e+00 1.404e+00 1.558e+00 1.843e+00
## h_ent_17 1.272e+00 1.580e+00 1.747e+00 1.910e+00 2.219e+00
## h_ent_18 7.558e-01 1.081e+00 1.248e+00 1.416e+00 1.725e+00
## h_ent_19 2.663e-01 5.949e-01 7.676e-01 9.369e-01 1.255e+00
## h_ent_20 1.924e-02 3.483e-01 5.151e-01 6.853e-01 1.003e+00
## h_ent_21 -1.807e-01 1.473e-01 3.212e-01 4.944e-01 8.078e-01
## h_ent_22 -5.304e-01 -1.988e-01 -2.657e-02 1.411e-01 4.627e-01
## h_ent_23 -7.787e-02 2.646e-01 4.412e-01 6.163e-01 9.611e-01
## Median Weight 1.008e-02 1.220e-02 1.331e-02 1.446e-02 1.664e-02
## rho -6.956e-02 5.728e-02 1.227e-01 1.873e-01 3.073e-01
## var_eartag 7.468e+00 8.764e+00 9.584e+00 1.049e+01 1.262e+01
## var_follower 9.899e-01 1.178e+00 1.297e+00 1.428e+00 1.723e+00
## var_error 4.142e+01 4.173e+01 4.190e+01 4.206e+01 4.238e+01
## prp_var_eartag 1.474e-01 1.686e-01 1.815e-01 1.954e-01 2.260e-01
## prp_var_follower 1.878e-02 2.230e-02 2.453e-02 2.699e-02 3.243e-02
## prp_var_error 7.500e-01 7.801e-01 7.936e-01 8.062e-01 8.273e-01
## lp__ -1.383e+05 -1.382e+05 -1.382e+05 -1.382e+05 -1.382e+05print(M360s.model)## Inference for Stan model: M3_corEartagFoll_model.
## 3 chains, each with iter=12000; warmup=2000; thin=1;
## post-warmup draws per chain=10000, total post-warmup draws=30000.
##
## mean se_mean sd 2.5% 25% 50%
## beta[1] 13.22 0.02 1.04 11.15 12.52 13.22
## beta[2] 6.94 0.02 1.06 4.86 6.21 6.95
## beta[3] 9.89 0.02 1.06 7.81 9.19 9.89
## beta[4] 8.06 0.02 1.22 5.68 7.24 8.06
## beta[5] 8.99 0.02 1.28 6.45 8.13 8.99
## beta[6] 4.83 0.02 1.16 2.51 4.07 4.84
## beta[7] 11.10 0.02 1.18 8.78 10.30 11.09
## beta[8] 10.67 0.02 1.02 8.67 9.98 10.68
## beta[9] 7.86 0.02 1.06 5.82 7.15 7.84
## beta[10] 14.59 0.02 1.07 12.50 13.86 14.60
## beta[11] 6.55 0.02 1.23 4.14 5.73 6.55
## beta[12] 9.48 0.02 1.26 6.98 8.64 9.50
## beta[13] 6.98 0.02 1.19 4.63 6.19 6.98
## beta[14] 8.43 0.02 1.25 5.98 7.60 8.44
## beta[15] 0.20 0.00 0.28 -0.35 0.02 0.20
## beta[16] -0.01 0.00 0.28 -0.57 -0.20 -0.01
## beta[17] -0.16 0.00 0.28 -0.72 -0.35 -0.16
## beta[18] -0.44 0.00 0.27 -0.97 -0.62 -0.44
## beta[19] -0.63 0.00 0.25 -1.12 -0.80 -0.63
## beta[20] -0.53 0.00 0.23 -0.99 -0.69 -0.53
## beta[21] -1.01 0.00 0.22 -1.45 -1.16 -1.01
## beta[22] -2.16 0.00 0.21 -2.58 -2.31 -2.16
## beta[23] -0.92 0.00 0.22 -1.34 -1.07 -0.92
## beta[24] 0.02 0.00 0.22 -0.42 -0.13 0.02
## beta[25] 0.51 0.00 0.22 0.08 0.36 0.51
## beta[26] 0.85 0.00 0.22 0.42 0.70 0.85
## beta[27] 0.58 0.00 0.22 0.16 0.44 0.59
## beta[28] 0.72 0.00 0.22 0.29 0.58 0.72
## beta[29] 0.88 0.00 0.22 0.45 0.73 0.88
## beta[30] 1.40 0.00 0.23 0.95 1.25 1.40
## beta[31] 1.75 0.00 0.24 1.27 1.58 1.75
## beta[32] 1.25 0.00 0.25 0.76 1.08 1.25
## beta[33] 0.77 0.00 0.25 0.27 0.59 0.77
## beta[34] 0.51 0.00 0.25 0.02 0.35 0.52
## beta[35] 0.32 0.00 0.25 -0.18 0.15 0.32
## beta[36] -0.03 0.00 0.25 -0.53 -0.20 -0.03
## beta[37] 0.44 0.00 0.26 -0.08 0.26 0.44
## beta[38] 0.01 0.00 0.00 0.01 0.01 0.01
## rho 0.12 0.00 0.10 -0.07 0.06 0.12
## var_eartag 9.70 0.01 1.31 7.47 8.76 9.58
## var_follower 1.31 0.00 0.19 0.99 1.18 1.30
## var_error 41.90 0.00 0.25 41.42 41.73 41.90
## prp_var_eartag 0.18 0.00 0.02 0.15 0.17 0.18
## prp_var_follower 0.02 0.00 0.00 0.02 0.02 0.02
## prp_var_error 0.79 0.00 0.02 0.75 0.78 0.79
## lp__ -138224.63 0.13 12.77 -138250.58 -138233.04 -138224.30
## 75% 97.5% n_eff Rhat
## beta[1] 13.92 15.24 4655 1
## beta[2] 7.66 8.99 3554 1
## beta[3] 10.60 11.99 3319 1
## beta[4] 8.88 10.44 4567 1
## beta[5] 9.86 11.46 4262 1
## beta[6] 5.61 7.07 4178 1
## beta[7] 11.89 13.42 3781 1
## beta[8] 11.35 12.66 4498 1
## beta[9] 8.57 9.97 3727 1
## beta[10] 15.32 16.69 3618 1
## beta[11] 7.38 8.96 4202 1
## beta[12] 10.33 11.93 5308 1
## beta[13] 7.77 9.31 3692 1
## beta[14] 9.26 10.88 4191 1
## beta[15] 0.39 0.75 5473 1
## beta[16] 0.18 0.53 5132 1
## beta[17] 0.04 0.39 5380 1
## beta[18] -0.25 0.10 5127 1
## beta[19] -0.46 -0.14 4277 1
## beta[20] -0.38 -0.08 3822 1
## beta[21] -0.86 -0.59 3506 1
## beta[22] -2.02 -1.76 3269 1
## beta[23] -0.77 -0.50 3414 1
## beta[24] 0.17 0.44 3430 1
## beta[25] 0.66 0.93 3569 1
## beta[26] 1.00 1.27 3411 1
## beta[27] 0.73 1.00 3367 1
## beta[28] 0.87 1.14 3476 1
## beta[29] 1.03 1.30 3468 1
## beta[30] 1.56 1.84 3718 1
## beta[31] 1.91 2.22 4196 1
## beta[32] 1.42 1.72 4358 1
## beta[33] 0.94 1.25 4315 1
## beta[34] 0.69 1.00 4456 1
## beta[35] 0.49 0.81 4563 1
## beta[36] 0.14 0.46 4510 1
## beta[37] 0.62 0.96 4719 1
## beta[38] 0.01 0.02 54836 1
## rho 0.19 0.31 18486 1
## var_eartag 10.49 12.62 16810 1
## var_follower 1.43 1.72 18213 1
## var_error 42.06 42.38 44734 1
## prp_var_eartag 0.20 0.23 17098 1
## prp_var_follower 0.03 0.03 18656 1
## prp_var_error 0.81 0.83 16700 1
## lp__ -138215.91 -138200.39 9484 1
##
## Samples were drawn using NUTS(diag_e) at Fri Jan 24 02:10:00 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).Posterior Correlation of model parameters
parcorplot(outp3,col = terrain.colors(15,0.5,T), cex.axis=0.6)