Bayesian estimating variance components visit length without observations influential
\(Results\ bayesian\ estimating\ of\ variance\ components\ (proportion\ of\ variance)\ with\ Stan\ program,\\ on\ 6256\ records\ of\ visit\ length\ time\ at\ the\ feeder\ when\ the\ next\ visit\ was\ greater\ than\ or\ equal\ to\ 600\ sc,\\ from\ 7\ trials,\ including\ locations\ (2\ per\ trial),\ median\ weight\ and\ hour\ entry\ at\ the\ feeder\ as\ fixed\ effects\ and\ Eartag (135\ individuals)\\ and\ followers\ (135)\ as\ random\ effects\ in\ the\ mixed\ models.\)
\(iter = 12000,\ chain= 3,\ burn-in = 2000,\ Thin=1.\)
\(For\ the\ fixed\ parameters\ in\ {\beta},\ flat\ priors\ were\ assumed,\ thus\ {\beta}\ {\sim} U(-\infty,+\infty),\\the\ priors\ distributions\ for\ covariance\ components\ {\sigma}_d^2,\ {\sigma}_f^2\ {\sim }\ U(0,100),\\ {\rho} {\sim}\ U(-1,1)\ and\ the\ prior\ distribution\ for\ the\ error\ variance\ was\ {\sigma}_e^2\ {\sim}\ U(0,\infty).\)
1. Mixed model: Location + Hour entry + 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 1.00000000 1.000000000 1.000000e+00
## Lag 1 0.032317076 0.171862289 0.17290786 0.173419492 8.382228e-02
## Lag 5 0.007594170 0.020539440 0.02664658 0.030295648 1.392313e-02
## Lag 10 -0.005964634 0.007284470 0.01847445 0.013005371 4.261394e-05
## Lag 50 -0.003991416 -0.007420851 -0.00393944 -0.006365782 -5.582876e-03
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.235611783 0.065663918 -0.011815915 0.190252521 0.098119297
## Lag 5 0.040138234 0.012897131 0.006223333 0.022863407 0.012898621
## Lag 10 -0.006447768 0.003272335 -0.009142906 -0.006187258 -0.003193445
## Lag 50 0.006763836 -0.015157812 0.008301603 -0.001930715 -0.004986896
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.140359437 0.101958913 0.199151961 0.092688423 0.071818719
## Lag 5 0.008377404 0.022646838 0.016758689 0.021703649 0.009623258
## Lag 10 0.001773929 0.008176926 0.004497025 0.002381532 -0.006998040
## Lag 50 0.009307403 -0.004000204 0.009287156 -0.004877969 -0.010088675
## 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 0.082644223 0.090255213 0.084067428 0.066007411 0.020575532
## Lag 5 0.015517780 0.009966112 0.015532494 0.013461827 0.015703371
## Lag 10 0.004034988 0.002126194 -0.006638037 -0.005633435 -0.007391047
## Lag 50 -0.007713072 -0.013821786 -0.017460082 -0.004328144 0.001502623
## 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 -0.010480757 -0.040584322 -0.036985437 -0.0178648866 -0.045133042
## Lag 5 0.009246406 0.002266243 0.005001878 0.0061607385 0.004727194
## Lag 10 -0.007556119 -0.008150471 0.006062985 -0.0004727051 -0.011488792
## Lag 50 -0.009114125 -0.005362952 -0.002892456 -0.0028272904 -0.003380911
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## Lag 0 1.000000000 1.000000000 1.0000000000 1.000000000 1.000000000
## Lag 1 -0.079504102 -0.102219900 -0.0896003814 -0.048370171 -0.014689132
## Lag 5 0.002738672 0.008150409 0.0011869950 0.003991343 0.001177437
## Lag 10 0.002452105 -0.002443321 -0.0009514697 0.005938357 -0.001105398
## Lag 50 -0.002362321 -0.006837222 -0.0003255614 0.001367088 -0.007209241
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.031562135 0.051679559 0.061603025 0.043167263 0.074722520
## Lag 5 0.011427214 0.010689270 0.011679985 0.002738735 0.011195016
## Lag 10 0.003456335 0.001353124 0.001880711 -0.001396069 -0.003750659
## Lag 50 0.010160395 -0.009545043 -0.014874937 -0.007497557 -0.007580281
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## Lag 0 1.0000000000 1.000000000 1.000000000 1.000000000 1.0000000000
## Lag 1 0.0608862389 0.074617972 -0.162905847 -0.054646216 -0.1029568308
## Lag 5 0.0061901213 0.007491730 0.005334696 0.011894229 0.0041211424
## Lag 10 -0.0004624895 -0.003136279 0.003752044 0.004920860 0.0003978744
## Lag 50 -0.0135698581 -0.012163970 -0.002467470 0.001775151 0.0007223106
## prp_var_eartag prp_var_error lp__
## Lag 0 1.000000000 1.000000000 1.000000000
## Lag 1 -0.058336679 -0.058336679 0.491720323
## Lag 5 0.013060845 0.013060845 0.048636915
## Lag 10 0.006245814 0.006245814 -0.001257806
## Lag 50 0.001303194 0.001303194 -0.003418071effectiveSize(outp1)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4 Loc1_t_5
## 29225.36 24064.34 21695.46 22378.05 26316.77
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## 20286.23 28452.84 31774.57 21552.25 26465.78
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## 24474.01 26126.20 21551.31 26819.13 21489.85
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 20837.03 20448.97 21095.98 21748.77 24369.41
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## 25435.49 27664.83 27363.30 25242.41 28044.06
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## 31798.55 36401.03 33066.30 28166.43 25568.13
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## 23367.85 22567.85 22795.74 22983.01 21695.10
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## 22538.32 21804.96 40117.93 27690.18 38240.40
## prp_var_eartag prp_var_error lp__
## 28103.01 28103.01 9987.65geweke.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
## -0.37601 -0.17594 -0.37078 -0.51642 0.13984
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## -0.30298 -1.51042 0.40623 -0.74091 0.46248
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## 1.20389 -0.14595 -0.71805 -0.76348 -0.56470
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 0.62236 1.10680 0.19535 1.55041 1.10451
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## 0.69091 -0.67607 0.76514 -0.39692 -0.55737
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## 0.69767 -0.20696 -1.26711 0.39805 1.43539
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## 0.08478 0.11589 1.34500 0.16410 1.58075
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## 0.50324 0.13823 -0.59374 -0.26883 0.90268
## prp_var_eartag prp_var_error lp__
## -0.41999 0.41999 0.64953
##
##
## [[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
## 0.441519 -0.255206 -0.236302 -2.622354 0.008657
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## -0.547949 -0.638825 0.554469 -2.343600 0.017996
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## -1.854848 -0.521692 -1.287317 -0.506338 0.493666
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 0.929672 -0.297015 0.312323 1.342032 -0.158958
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## -0.899264 1.345202 1.175080 -0.062740 0.989060
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## 0.248160 0.143340 1.901262 2.150841 0.193593
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## 0.460397 0.557520 0.893724 0.613529 0.894159
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## 0.952410 0.949703 1.623540 1.907862 -0.261375
## prp_var_eartag prp_var_error lp__
## 1.922077 -1.922077 -0.536019
##
##
## [[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
## 0.76871 -0.87932 0.36453 0.93400 -0.87697
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## -0.18546 -2.01667 -0.17233 -0.68705 1.07604
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## 0.88177 1.13810 -0.41259 0.82416 0.77358
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 1.03333 1.19352 0.65710 0.72467 0.22952
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## 0.56883 0.17005 0.70806 1.71731 0.66807
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## 0.23363 1.84546 1.14458 0.73836 0.96187
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## 0.61287 0.59285 1.16076 0.44214 1.15018
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## 0.09726 0.45617 0.01708 1.88544 -0.82110
## prp_var_eartag prp_var_error lp__
## 1.93732 -1.93732 -0.80728gelman.diag(outp1,transform = T,multivariate = F)## 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_error 1 1
## prp_var_eartag 1 1
## prp_var_error 1 1
## lp__ 1 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 1.644e+01 1.217581 7.030e-03 8.273e-03
## Loc1_t_2 1.152e+01 1.170136 6.756e-03 9.282e-03
## Loc1_t_3 1.249e+01 1.177108 6.796e-03 9.467e-03
## Loc1_t_4 1.111e+01 1.312454 7.577e-03 1.042e-02
## Loc1_t_5 1.256e+01 1.341915 7.748e-03 9.515e-03
## Loc1_t_6 8.455e+00 1.248212 7.207e-03 1.027e-02
## Loc1_t_7 1.274e+01 1.326677 7.660e-03 9.527e-03
## Loc2_t_1 1.604e+01 1.249573 7.214e-03 8.176e-03
## Loc2_t_2 1.157e+01 1.153511 6.660e-03 9.197e-03
## Loc2_t_3 1.917e+01 1.191919 6.882e-03 8.682e-03
## Loc2_t_4 1.215e+01 1.317657 7.607e-03 1.004e-02
## Loc2_t_5 1.262e+01 1.339119 7.731e-03 9.970e-03
## Loc2_t_6 1.052e+01 1.244858 7.187e-03 9.857e-03
## Loc2_t_7 1.258e+01 1.346196 7.772e-03 9.850e-03
## h_ent_1 -1.315e-01 0.445386 2.571e-03 3.272e-03
## h_ent_2 -8.528e-01 0.444320 2.565e-03 3.305e-03
## h_ent_3 -7.923e-01 0.442568 2.555e-03 3.303e-03
## h_ent_4 -7.231e-01 0.451127 2.605e-03 3.326e-03
## h_ent_5 -1.076e+00 0.480352 2.773e-03 3.463e-03
## h_ent_6 -1.162e+00 0.524965 3.031e-03 3.538e-03
## h_ent_7 -7.476e-01 0.641648 3.705e-03 4.080e-03
## h_ent_8 -1.942e+00 0.752350 4.344e-03 4.562e-03
## h_ent_9 -2.040e-01 0.710063 4.100e-03 4.321e-03
## h_ent_10 9.261e-01 0.657000 3.793e-03 4.177e-03
## h_ent_11 3.002e-01 0.783972 4.526e-03 4.707e-03
## h_ent_12 1.899e+00 1.044730 6.032e-03 5.862e-03
## h_ent_13 1.196e-01 1.512732 8.734e-03 7.969e-03
## h_ent_14 -1.525e+00 1.225220 7.074e-03 6.756e-03
## h_ent_15 2.865e+00 0.763940 4.411e-03 4.564e-03
## h_ent_16 2.692e+00 0.593437 3.426e-03 3.818e-03
## h_ent_17 1.700e+00 0.512390 2.958e-03 3.519e-03
## h_ent_18 4.526e-01 0.488411 2.820e-03 3.457e-03
## h_ent_19 4.928e-01 0.479737 2.770e-03 3.373e-03
## h_ent_20 2.162e-02 0.483367 2.791e-03 3.353e-03
## h_ent_21 3.005e-01 0.464919 2.684e-03 3.357e-03
## h_ent_22 5.786e-01 0.458927 2.650e-03 3.242e-03
## h_ent_23 -3.731e-01 0.457438 2.641e-03 3.308e-03
## Median Weight -2.976e-02 0.005129 2.961e-05 2.682e-05
## var_eartag 1.151e+01 1.751274 1.011e-02 1.054e-02
## var_error 4.350e+01 0.784429 4.529e-03 4.136e-03
## prp_var_eartag 2.084e-01 0.025088 1.448e-04 1.500e-04
## prp_var_error 7.916e-01 0.025088 1.448e-04 1.500e-04
## lp__ -1.516e+04 9.653844 5.574e-02 9.663e-02
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.404e+01 1.562e+01 1.645e+01 1.725e+01 1.882e+01
## Loc1_t_2 9.216e+00 1.073e+01 1.153e+01 1.231e+01 1.380e+01
## Loc1_t_3 1.020e+01 1.169e+01 1.248e+01 1.328e+01 1.480e+01
## Loc1_t_4 8.551e+00 1.023e+01 1.111e+01 1.198e+01 1.371e+01
## Loc1_t_5 9.922e+00 1.167e+01 1.256e+01 1.346e+01 1.520e+01
## Loc1_t_6 6.014e+00 7.613e+00 8.456e+00 9.283e+00 1.092e+01
## Loc1_t_7 1.016e+01 1.184e+01 1.273e+01 1.363e+01 1.537e+01
## Loc2_t_1 1.356e+01 1.520e+01 1.604e+01 1.688e+01 1.849e+01
## Loc2_t_2 9.297e+00 1.079e+01 1.157e+01 1.236e+01 1.384e+01
## Loc2_t_3 1.685e+01 1.836e+01 1.917e+01 1.997e+01 2.151e+01
## Loc2_t_4 9.565e+00 1.126e+01 1.214e+01 1.304e+01 1.474e+01
## Loc2_t_5 1.001e+01 1.172e+01 1.262e+01 1.351e+01 1.526e+01
## Loc2_t_6 8.082e+00 9.678e+00 1.053e+01 1.136e+01 1.297e+01
## Loc2_t_7 9.937e+00 1.168e+01 1.258e+01 1.348e+01 1.522e+01
## h_ent_1 -1.006e+00 -4.327e-01 -1.330e-01 1.697e-01 7.476e-01
## h_ent_2 -1.724e+00 -1.148e+00 -8.518e-01 -5.562e-01 2.434e-02
## h_ent_3 -1.664e+00 -1.087e+00 -7.939e-01 -4.931e-01 7.597e-02
## h_ent_4 -1.601e+00 -1.027e+00 -7.241e-01 -4.175e-01 1.637e-01
## h_ent_5 -2.017e+00 -1.401e+00 -1.072e+00 -7.487e-01 -1.454e-01
## h_ent_6 -2.194e+00 -1.517e+00 -1.163e+00 -8.089e-01 -1.356e-01
## h_ent_7 -2.009e+00 -1.176e+00 -7.491e-01 -3.148e-01 5.151e-01
## h_ent_8 -3.423e+00 -2.453e+00 -1.941e+00 -1.430e+00 -4.647e-01
## h_ent_9 -1.589e+00 -6.816e-01 -2.075e-01 2.809e-01 1.193e+00
## h_ent_10 -3.503e-01 4.799e-01 9.265e-01 1.377e+00 2.207e+00
## h_ent_11 -1.230e+00 -2.315e-01 2.989e-01 8.313e-01 1.839e+00
## h_ent_12 -1.593e-01 1.199e+00 1.903e+00 2.604e+00 3.933e+00
## h_ent_13 -2.823e+00 -9.062e-01 1.144e-01 1.148e+00 3.073e+00
## h_ent_14 -3.933e+00 -2.345e+00 -1.524e+00 -7.065e-01 8.921e-01
## h_ent_15 1.370e+00 2.349e+00 2.861e+00 3.381e+00 4.361e+00
## h_ent_16 1.533e+00 2.291e+00 2.690e+00 3.094e+00 3.854e+00
## h_ent_17 6.987e-01 1.355e+00 1.696e+00 2.043e+00 2.709e+00
## h_ent_18 -5.160e-01 1.268e-01 4.577e-01 7.780e-01 1.410e+00
## h_ent_19 -4.428e-01 1.683e-01 4.936e-01 8.158e-01 1.431e+00
## h_ent_20 -9.270e-01 -3.021e-01 1.963e-02 3.451e-01 9.743e-01
## h_ent_21 -6.143e-01 -1.405e-02 3.036e-01 6.147e-01 1.211e+00
## h_ent_22 -3.221e-01 2.698e-01 5.843e-01 8.902e-01 1.472e+00
## h_ent_23 -1.275e+00 -6.832e-01 -3.686e-01 -6.588e-02 5.253e-01
## Median Weight -3.982e-02 -3.325e-02 -2.978e-02 -2.628e-02 -1.979e-02
## var_eartag 8.515e+00 1.029e+01 1.134e+01 1.257e+01 1.541e+01
## var_error 4.199e+01 4.297e+01 4.349e+01 4.403e+01 4.507e+01
## prp_var_eartag 1.635e-01 1.911e-01 2.068e-01 2.244e-01 2.621e-01
## prp_var_error 7.379e-01 7.756e-01 7.932e-01 8.089e-01 8.365e-01
## lp__ -1.518e+04 -1.516e+04 -1.516e+04 -1.515e+04 -1.514e+04print(M1600swo.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% 75%
## beta[1] 16.44 0.01 1.22 14.04 15.62 16.45 17.25
## beta[2] 11.52 0.01 1.17 9.22 10.73 11.53 12.31
## beta[3] 12.49 0.01 1.18 10.20 11.69 12.48 13.28
## beta[4] 11.11 0.01 1.31 8.55 10.23 11.11 11.98
## beta[5] 12.56 0.01 1.34 9.92 11.67 12.56 13.46
## beta[6] 8.45 0.01 1.25 6.01 7.61 8.46 9.28
## beta[7] 12.74 0.01 1.33 10.16 11.84 12.73 13.63
## beta[8] 16.04 0.01 1.25 13.56 15.20 16.04 16.88
## beta[9] 11.57 0.01 1.15 9.30 10.79 11.57 12.36
## beta[10] 19.17 0.01 1.19 16.85 18.36 19.17 19.97
## beta[11] 12.15 0.01 1.32 9.57 11.26 12.14 13.04
## beta[12] 12.62 0.01 1.34 10.01 11.72 12.62 13.51
## beta[13] 10.52 0.01 1.24 8.08 9.68 10.53 11.36
## beta[14] 12.58 0.01 1.35 9.94 11.68 12.58 13.48
## beta[15] -0.13 0.00 0.45 -1.01 -0.43 -0.13 0.17
## beta[16] -0.85 0.00 0.44 -1.72 -1.15 -0.85 -0.56
## beta[17] -0.79 0.00 0.44 -1.66 -1.09 -0.79 -0.49
## beta[18] -0.72 0.00 0.45 -1.60 -1.03 -0.72 -0.42
## beta[19] -1.08 0.00 0.48 -2.02 -1.40 -1.07 -0.75
## beta[20] -1.16 0.00 0.52 -2.19 -1.52 -1.16 -0.81
## beta[21] -0.75 0.00 0.64 -2.01 -1.18 -0.75 -0.31
## beta[22] -1.94 0.00 0.75 -3.42 -2.45 -1.94 -1.43
## beta[23] -0.20 0.00 0.71 -1.59 -0.68 -0.21 0.28
## beta[24] 0.93 0.00 0.66 -0.35 0.48 0.93 1.38
## beta[25] 0.30 0.00 0.78 -1.23 -0.23 0.30 0.83
## beta[26] 1.90 0.01 1.04 -0.16 1.20 1.90 2.60
## beta[27] 0.12 0.01 1.51 -2.82 -0.91 0.11 1.15
## beta[28] -1.52 0.01 1.23 -3.93 -2.34 -1.52 -0.71
## beta[29] 2.87 0.00 0.76 1.37 2.35 2.86 3.38
## beta[30] 2.69 0.00 0.59 1.53 2.29 2.69 3.09
## beta[31] 1.70 0.00 0.51 0.70 1.35 1.70 2.04
## beta[32] 0.45 0.00 0.49 -0.52 0.13 0.46 0.78
## beta[33] 0.49 0.00 0.48 -0.44 0.17 0.49 0.82
## beta[34] 0.02 0.00 0.48 -0.93 -0.30 0.02 0.35
## beta[35] 0.30 0.00 0.46 -0.61 -0.01 0.30 0.61
## beta[36] 0.58 0.00 0.46 -0.32 0.27 0.58 0.89
## beta[37] -0.37 0.00 0.46 -1.27 -0.68 -0.37 -0.07
## beta[38] -0.03 0.00 0.01 -0.04 -0.03 -0.03 -0.03
## var_eartag 11.51 0.01 1.75 8.52 10.29 11.34 12.57
## var_error 43.50 0.00 0.78 41.99 42.97 43.49 44.03
## prp_var_eartag 0.21 0.00 0.03 0.16 0.19 0.21 0.22
## prp_var_error 0.79 0.00 0.03 0.74 0.78 0.79 0.81
## lp__ -15156.44 0.10 9.65 -15176.17 -15162.73 -15156.09 -15149.71
## 97.5% n_eff Rhat
## beta[1] 18.82 21161 1
## beta[2] 13.80 15577 1
## beta[3] 14.80 13577 1
## beta[4] 13.71 14644 1
## beta[5] 15.20 19758 1
## beta[6] 10.92 14799 1
## beta[7] 15.37 19158 1
## beta[8] 18.49 23066 1
## beta[9] 13.84 15905 1
## beta[10] 21.51 19421 1
## beta[11] 14.74 17210 1
## beta[12] 15.26 17870 1
## beta[13] 12.97 15859 1
## beta[14] 15.22 18681 1
## beta[15] 0.75 18887 1
## beta[16] 0.02 18536 1
## beta[17] 0.08 18614 1
## beta[18] 0.16 19198 1
## beta[19] -0.15 19375 1
## beta[20] -0.14 22390 1
## beta[21] 0.52 24963 1
## beta[22] -0.46 27475 1
## beta[23] 1.19 26568 1
## beta[24] 2.21 24881 1
## beta[25] 1.84 27808 1
## beta[26] 3.93 31602 1
## beta[27] 3.07 34289 1
## beta[28] 0.89 32438 1
## beta[29] 4.36 28194 1
## beta[30] 3.85 23577 1
## beta[31] 2.71 21817 1
## beta[32] 1.41 20046 1
## beta[33] 1.43 20234 1
## beta[34] 0.97 21342 1
## beta[35] 1.21 19105 1
## beta[36] 1.47 20777 1
## beta[37] 0.53 19429 1
## beta[38] -0.02 36346 1
## var_eartag 15.41 26161 1
## var_error 45.07 34922 1
## prp_var_eartag 0.26 26304 1
## prp_var_error 0.84 26304 1
## lp__ -15138.59 9813 1
##
## Samples were drawn using NUTS(diag_e) at Wed Apr 15 13:47:51 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 + Median wt + Eartag + Follower
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 1.000000e+00 1.000000000 1.00000000 1.00000000 1.0000000000
## Lag 1 3.462713e-01 0.489319953 0.48002013 0.48064112 0.4444614206
## Lag 5 9.360588e-02 0.133017944 0.12628298 0.12506742 0.1069347185
## Lag 10 2.902841e-02 0.034078299 0.05169494 0.04699485 0.0243776383
## Lag 50 8.326783e-05 -0.007402082 -0.00292322 -0.02453315 0.0005452484
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.00000000
## Lag 1 0.516432891 0.402409066 0.338829047 0.503439657 0.42109885
## Lag 5 0.150608533 0.080753784 0.068479373 0.136773542 0.09211896
## Lag 10 0.041655519 0.023541334 0.029444240 0.041925276 0.02524378
## Lag 50 0.001287226 -0.006135255 0.002114597 0.007855289 -0.01541622
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 Hour_entry_1
## Lag 0 1.000000000 1.00000000 1.000000000 1.000000000 1.0000000000
## Lag 1 0.473006835 0.44119397 0.505704072 0.425461531 0.2286177025
## Lag 5 0.099473522 0.09516446 0.121932783 0.098378034 0.0965137034
## Lag 10 0.010005946 0.02739956 0.019383530 0.026754261 0.0178957024
## Lag 50 -0.005955548 -0.01015994 -0.001043349 0.002797538 0.0001363101
## Hour_entry_2 Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.215114983 0.213518062 0.217553437 0.183225480 0.123133141
## Lag 5 0.100430209 0.093524862 0.096268044 0.089120946 0.070679402
## Lag 10 0.026880668 0.026917727 0.029782692 0.026612431 0.021687072
## Lag 50 0.005855998 0.007978268 -0.008020943 -0.008351162 -0.006219995
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10 Hour_entry_11
## Lag 0 1.000000000 1.0000000000 1.000000000 1.0000000000 1.000000000
## Lag 1 0.052071469 -0.0052976139 0.025908435 0.0291345212 -0.015916188
## Lag 5 0.047832551 0.0282310241 0.048554438 0.0439340906 0.033687059
## Lag 10 0.019121435 0.0133397363 0.020252967 0.0120013987 0.003980624
## Lag 50 -0.004427651 -0.0004785678 -0.004507968 -0.0006464399 0.003157832
## Hour_entry_12 Hour_entry_13 Hour_entry_14 Hour_entry_15 Hour_entry_16
## Lag 0 1.000000000 1.0000000000 1.000000000 1.000000000 1.000000000
## Lag 1 -0.030692771 -0.0659006664 -0.073203394 -0.005919196 0.074407776
## Lag 5 0.011949733 0.0115302597 0.016478096 0.032891220 0.061190287
## Lag 10 0.006502753 0.0136322699 0.005833426 0.014983907 0.010118917
## Lag 50 0.003870261 -0.0004107566 0.000212800 0.006588445 0.002143138
## Hour_entry_17 Hour_entry_18 Hour_entry_19 Hour_entry_20 Hour_entry_21
## Lag 0 1.000000000 1.00000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.138653106 0.15807961 0.181720384 0.175669655 0.198043482
## Lag 5 0.077896525 0.09088482 0.084282983 0.065822080 0.085540620
## Lag 10 0.029713690 0.03997862 0.023261247 0.022538384 0.019008792
## Lag 50 0.002941933 -0.00343321 -0.007587961 -0.001595903 0.003360355
## Hour_entry_22 Hour_entry_23 Median Weight var_eartag var_follower
## Lag 0 1.000000000 1.000000000 1.0000000000 1.000000000 1.0000000
## Lag 1 0.204438512 0.210494824 0.0943340772 0.032687497 0.9308918
## Lag 5 0.091499609 0.085972477 0.0141807106 0.025885186 0.8130918
## Lag 10 0.027766390 0.027361383 0.0006947571 -0.001197172 0.7020291
## Lag 50 -0.006867652 0.009038946 -0.0008726796 -0.009071016 0.3444240
## var_error prp_var_eartag prp_var_follower prp_var_error lp__
## Lag 0 1.0000000000 1.000000000 1.0000000 1.0000000000 1.0000000
## Lag 1 -0.0826067720 0.028330942 0.9287295 0.0307409947 0.9838090
## Lag 5 -0.0080599855 0.024861883 0.8116770 0.0268962738 0.9402095
## Lag 10 0.0006396106 -0.002613062 0.7011444 -0.0006900149 0.8969798
## Lag 50 -0.0062565873 -0.009842405 0.3440528 -0.0085413943 0.6321063effectiveSize(outp2)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## 9120.1580 6977.1212 7028.9107 7196.7979
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 7588.3113 6224.3939 8995.5993 10360.4615
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 6578.9537 8660.6542 8162.9531 8100.9329
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## 7189.8189 8796.2610 9204.7259 9098.9406
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## 8932.0306 9128.1977 9574.0666 11584.8779
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## 14515.4436 17501.9935 15601.2743 15274.4632
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## 19687.2601 24135.0839 27004.9790 24443.7321
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## 17941.1269 12930.6855 10955.8788 9571.5093
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## 10276.7953 10499.2049 9716.9687 9618.2700
## Hour_entry_23 Median Weight var_eartag var_follower
## 9350.3381 20412.1136 20052.6258 326.3599
## var_error prp_var_eartag prp_var_follower prp_var_error
## 34802.5190 19905.4304 327.4938 19604.2813
## lp__
## 143.4183geweke.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
## -0.08892 -1.08520 0.46060 -0.02752
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## -1.69846 -0.45895 -0.41607 -1.08032
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## -0.01894 0.43969 -0.24823 -1.43758
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## -1.46276 -2.28986 -0.53848 -0.91161
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## 0.31796 -0.85105 -0.49905 -0.69015
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## 0.91957 -0.36866 -0.57107 0.53728
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## 0.97763 0.01536 0.48511 0.16362
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## 0.26811 -0.47776 -0.41000 -0.24985
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## -0.38188 -0.79593 -0.80543 -0.86289
## Hour_entry_23 Median Weight var_eartag var_follower
## -1.26420 1.61259 0.08670 -1.52094
## var_error prp_var_eartag prp_var_follower prp_var_error
## -1.36582 0.29038 -1.60270 0.13688
## lp__
## 1.04323
##
##
## [[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
## 1.13216 -0.33719 1.52640 0.66070
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## -0.29653 -0.09120 1.45360 1.04589
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 1.04390 1.11053 1.73993 1.24158
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## 0.26860 -0.34183 -0.76145 -0.56516
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## -0.82216 -0.30878 -0.42370 -0.80120
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## -0.25285 0.29562 -0.23607 -0.18646
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## -0.17302 -0.14541 0.30288 -0.27277
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## -1.55290 -0.13627 -0.98537 -0.57678
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## -0.33664 -1.01929 -1.55590 -0.25482
## Hour_entry_23 Median Weight var_eartag var_follower
## -0.47130 -1.50638 -0.09044 2.32018
## var_error prp_var_eartag prp_var_follower prp_var_error
## -0.82463 -0.29143 2.32745 -0.67436
## lp__
## -2.46445
##
##
## [[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
## -0.685607 -0.382926 -1.492802 1.026212
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## -0.589401 -0.166018 -0.346268 0.711673
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 0.807888 -0.561120 -0.678906 -2.196146
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## -0.422091 0.743847 0.402442 -0.071215
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## 0.805831 0.195330 -0.021143 0.838201
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## 0.648755 0.616514 -0.119824 -0.009258
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## 0.087118 0.775716 0.813799 1.020925
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## -0.049003 0.575402 0.342039 0.072193
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## 0.387533 0.111073 0.539970 0.207018
## Hour_entry_23 Median Weight var_eartag var_follower
## 1.060468 0.027922 -1.274053 -0.900077
## var_error prp_var_eartag prp_var_follower prp_var_error
## -1.030191 -1.099822 -1.111926 1.308874
## lp__
## 0.567009gelman.diag(outp2, transform = T, multivariate = F)## Potential scale reduction factors:
##
## Point est. Upper C.I.
## Loc1_t_1 1.00 1.00
## Loc1_t_2 1.00 1.00
## Loc1_t_3 1.00 1.00
## Loc1_t_4 1.00 1.00
## Loc1_t_5 1.00 1.00
## Loc1_t_6 1.00 1.00
## Loc1_t_7 1.00 1.00
## Loc2_t_1 1.00 1.00
## Loc2_t_2 1.00 1.00
## Loc2_t_3 1.00 1.00
## Loc2_t_4 1.00 1.00
## Loc2_t_5 1.00 1.00
## Loc2_t_6 1.00 1.00
## Loc2_t_7 1.00 1.00
## Hour_entry_1 1.00 1.00
## Hour_entry_2 1.00 1.00
## Hour_entry_3 1.00 1.00
## Hour_entry_4 1.00 1.00
## Hour_entry_5 1.00 1.00
## Hour_entry_6 1.00 1.00
## Hour_entry_7 1.00 1.00
## Hour_entry_8 1.00 1.00
## Hour_entry_9 1.00 1.00
## Hour_entry_10 1.00 1.00
## Hour_entry_11 1.00 1.00
## Hour_entry_12 1.00 1.00
## Hour_entry_13 1.00 1.00
## Hour_entry_14 1.00 1.00
## Hour_entry_15 1.00 1.00
## Hour_entry_16 1.00 1.00
## Hour_entry_17 1.00 1.00
## Hour_entry_18 1.00 1.00
## Hour_entry_19 1.00 1.00
## Hour_entry_20 1.00 1.00
## Hour_entry_21 1.00 1.00
## Hour_entry_22 1.00 1.00
## Hour_entry_23 1.00 1.00
## Median Weight 1.00 1.00
## var_eartag 1.00 1.00
## var_follower 1.02 1.06
## var_error 1.00 1.00
## prp_var_eartag 1.00 1.00
## prp_var_follower 1.03 1.07
## prp_var_error 1.00 1.00
## lp__ 1.02 1.06traplot(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 1.647e+01 1.222220 7.056e-03 1.328e-02
## Loc1_t_2 1.156e+01 1.150591 6.643e-03 1.414e-02
## Loc1_t_3 1.248e+01 1.180609 6.816e-03 1.454e-02
## Loc1_t_4 1.118e+01 1.310498 7.566e-03 1.597e-02
## Loc1_t_5 1.257e+01 1.352227 7.807e-03 1.587e-02
## Loc1_t_6 8.456e+00 1.251803 7.227e-03 1.634e-02
## Loc1_t_7 1.276e+01 1.332132 7.691e-03 1.420e-02
## Loc2_t_1 1.606e+01 1.238531 7.151e-03 1.266e-02
## Loc2_t_2 1.157e+01 1.147421 6.625e-03 1.454e-02
## Loc2_t_3 1.921e+01 1.190535 6.874e-03 1.344e-02
## Loc2_t_4 1.216e+01 1.333713 7.700e-03 1.541e-02
## Loc2_t_5 1.263e+01 1.353790 7.816e-03 1.532e-02
## Loc2_t_6 1.054e+01 1.256837 7.256e-03 1.529e-02
## Loc2_t_7 1.260e+01 1.336674 7.717e-03 1.496e-02
## Hour_entry_1 -1.505e-01 0.446730 2.579e-03 4.706e-03
## Hour_entry_2 -8.697e-01 0.443877 2.563e-03 4.738e-03
## Hour_entry_3 -8.035e-01 0.444595 2.567e-03 4.754e-03
## Hour_entry_4 -7.346e-01 0.454086 2.622e-03 4.794e-03
## Hour_entry_5 -1.085e+00 0.475389 2.745e-03 4.902e-03
## Hour_entry_6 -1.173e+00 0.531264 3.067e-03 4.989e-03
## Hour_entry_7 -7.539e-01 0.642633 3.710e-03 5.394e-03
## Hour_entry_8 -1.956e+00 0.751887 4.341e-03 5.722e-03
## Hour_entry_9 -2.186e-01 0.713293 4.118e-03 5.794e-03
## Hour_entry_10 9.302e-01 0.658492 3.802e-03 5.346e-03
## Hour_entry_11 2.941e-01 0.784562 4.530e-03 5.633e-03
## Hour_entry_12 1.865e+00 1.029902 5.946e-03 6.676e-03
## Hour_entry_13 1.057e-01 1.525966 8.810e-03 9.409e-03
## Hour_entry_14 -1.542e+00 1.226261 7.080e-03 7.901e-03
## Hour_entry_15 2.854e+00 0.763434 4.408e-03 5.733e-03
## Hour_entry_16 2.685e+00 0.590690 3.410e-03 5.221e-03
## Hour_entry_17 1.693e+00 0.514193 2.969e-03 4.988e-03
## Hour_entry_18 4.418e-01 0.490931 2.834e-03 5.059e-03
## Hour_entry_19 4.846e-01 0.483968 2.794e-03 4.826e-03
## Hour_entry_20 1.308e-02 0.483603 2.792e-03 4.786e-03
## Hour_entry_21 2.978e-01 0.463695 2.677e-03 4.743e-03
## Hour_entry_22 5.696e-01 0.458031 2.644e-03 4.740e-03
## Hour_entry_23 -3.898e-01 0.455362 2.629e-03 4.762e-03
## Median Weight -2.989e-02 0.005095 2.942e-05 3.687e-05
## var_eartag 1.149e+01 1.759269 1.016e-02 1.262e-02
## var_follower 6.509e-02 0.071832 4.147e-04 4.015e-03
## var_error 4.347e+01 0.809048 4.671e-03 4.368e-03
## prp_var_eartag 2.080e-01 0.025248 1.458e-04 1.809e-04
## prp_var_follower 1.183e-03 0.001305 7.536e-06 7.283e-05
## prp_var_error 7.908e-01 0.025246 1.458e-04 1.824e-04
## lp__ -1.499e+04 95.295618 5.502e-01 8.166e+00
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.406e+01 1.565e+01 1.648e+01 1.729e+01 1.886e+01
## Loc1_t_2 9.305e+00 1.078e+01 1.155e+01 1.233e+01 1.383e+01
## Loc1_t_3 1.019e+01 1.169e+01 1.248e+01 1.328e+01 1.479e+01
## Loc1_t_4 8.600e+00 1.031e+01 1.118e+01 1.205e+01 1.374e+01
## Loc1_t_5 9.909e+00 1.166e+01 1.257e+01 1.346e+01 1.520e+01
## Loc1_t_6 5.986e+00 7.613e+00 8.459e+00 9.289e+00 1.091e+01
## Loc1_t_7 1.011e+01 1.187e+01 1.277e+01 1.366e+01 1.535e+01
## Loc2_t_1 1.364e+01 1.522e+01 1.606e+01 1.690e+01 1.848e+01
## Loc2_t_2 9.299e+00 1.080e+01 1.156e+01 1.234e+01 1.384e+01
## Loc2_t_3 1.689e+01 1.840e+01 1.921e+01 2.001e+01 2.157e+01
## Loc2_t_4 9.536e+00 1.127e+01 1.215e+01 1.305e+01 1.478e+01
## Loc2_t_5 9.976e+00 1.173e+01 1.262e+01 1.354e+01 1.531e+01
## Loc2_t_6 8.057e+00 9.693e+00 1.055e+01 1.138e+01 1.301e+01
## Loc2_t_7 9.964e+00 1.171e+01 1.260e+01 1.349e+01 1.522e+01
## Hour_entry_1 -1.017e+00 -4.511e-01 -1.539e-01 1.467e-01 7.267e-01
## Hour_entry_2 -1.740e+00 -1.173e+00 -8.689e-01 -5.698e-01 -1.340e-03
## Hour_entry_3 -1.672e+00 -1.106e+00 -8.022e-01 -5.006e-01 6.525e-02
## Hour_entry_4 -1.637e+00 -1.040e+00 -7.321e-01 -4.243e-01 1.518e-01
## Hour_entry_5 -2.020e+00 -1.404e+00 -1.086e+00 -7.592e-01 -1.512e-01
## Hour_entry_6 -2.219e+00 -1.527e+00 -1.171e+00 -8.159e-01 -1.260e-01
## Hour_entry_7 -2.023e+00 -1.187e+00 -7.515e-01 -3.166e-01 4.989e-01
## Hour_entry_8 -3.415e+00 -2.469e+00 -1.955e+00 -1.445e+00 -4.832e-01
## Hour_entry_9 -1.599e+00 -7.026e-01 -2.192e-01 2.659e-01 1.182e+00
## Hour_entry_10 -3.557e-01 4.869e-01 9.312e-01 1.371e+00 2.226e+00
## Hour_entry_11 -1.238e+00 -2.375e-01 2.939e-01 8.320e-01 1.832e+00
## Hour_entry_12 -1.443e-01 1.172e+00 1.865e+00 2.563e+00 3.884e+00
## Hour_entry_13 -2.872e+00 -9.283e-01 1.028e-01 1.142e+00 3.121e+00
## Hour_entry_14 -3.929e+00 -2.368e+00 -1.539e+00 -7.160e-01 8.582e-01
## Hour_entry_15 1.379e+00 2.331e+00 2.852e+00 3.368e+00 4.362e+00
## Hour_entry_16 1.535e+00 2.286e+00 2.682e+00 3.082e+00 3.849e+00
## Hour_entry_17 6.747e-01 1.347e+00 1.696e+00 2.036e+00 2.697e+00
## Hour_entry_18 -5.313e-01 1.108e-01 4.435e-01 7.774e-01 1.403e+00
## Hour_entry_19 -4.788e-01 1.629e-01 4.876e-01 8.144e-01 1.422e+00
## Hour_entry_20 -9.406e-01 -3.113e-01 1.510e-02 3.401e-01 9.474e-01
## Hour_entry_21 -6.183e-01 -1.538e-02 3.016e-01 6.068e-01 1.210e+00
## Hour_entry_22 -3.201e-01 2.615e-01 5.697e-01 8.799e-01 1.461e+00
## Hour_entry_23 -1.282e+00 -6.955e-01 -3.887e-01 -8.436e-02 5.045e-01
## Median Weight -3.979e-02 -3.329e-02 -2.988e-02 -2.649e-02 -1.985e-02
## var_eartag 8.484e+00 1.025e+01 1.134e+01 1.256e+01 1.534e+01
## var_follower 1.136e-03 1.275e-02 4.092e-02 9.288e-02 2.615e-01
## var_error 4.193e+01 4.292e+01 4.346e+01 4.401e+01 4.510e+01
## prp_var_eartag 1.625e-01 1.903e-01 2.066e-01 2.240e-01 2.612e-01
## prp_var_follower 2.071e-05 2.321e-04 7.453e-04 1.689e-03 4.773e-03
## prp_var_error 7.376e-01 7.747e-01 7.922e-01 8.085e-01 8.364e-01
## lp__ -1.513e+04 -1.506e+04 -1.501e+04 -1.493e+04 -1.477e+04print(M2600swo.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] 16.47 0.01 1.22 14.06 15.65 16.48
## beta[2] 11.56 0.01 1.15 9.31 10.78 11.55
## beta[3] 12.48 0.02 1.18 10.19 11.69 12.48
## beta[4] 11.18 0.02 1.31 8.60 10.31 11.18
## beta[5] 12.57 0.02 1.35 9.91 11.66 12.57
## beta[6] 8.46 0.02 1.25 5.99 7.61 8.46
## beta[7] 12.76 0.01 1.33 10.11 11.87 12.77
## beta[8] 16.06 0.01 1.24 13.64 15.22 16.06
## beta[9] 11.57 0.02 1.15 9.30 10.80 11.56
## beta[10] 19.21 0.01 1.19 16.89 18.40 19.21
## beta[11] 12.16 0.02 1.33 9.54 11.27 12.15
## beta[12] 12.63 0.02 1.35 9.98 11.73 12.62
## beta[13] 10.54 0.02 1.26 8.06 9.69 10.55
## beta[14] 12.60 0.02 1.34 9.96 11.71 12.60
## beta[15] -0.15 0.00 0.45 -1.02 -0.45 -0.15
## beta[16] -0.87 0.00 0.44 -1.74 -1.17 -0.87
## beta[17] -0.80 0.00 0.44 -1.67 -1.11 -0.80
## beta[18] -0.73 0.00 0.45 -1.64 -1.04 -0.73
## beta[19] -1.08 0.00 0.48 -2.02 -1.40 -1.09
## beta[20] -1.17 0.01 0.53 -2.22 -1.53 -1.17
## beta[21] -0.75 0.01 0.64 -2.02 -1.19 -0.75
## beta[22] -1.96 0.01 0.75 -3.41 -2.47 -1.95
## beta[23] -0.22 0.01 0.71 -1.60 -0.70 -0.22
## beta[24] 0.93 0.01 0.66 -0.36 0.49 0.93
## beta[25] 0.29 0.01 0.78 -1.24 -0.24 0.29
## beta[26] 1.86 0.01 1.03 -0.14 1.17 1.86
## beta[27] 0.11 0.01 1.53 -2.87 -0.93 0.10
## beta[28] -1.54 0.01 1.23 -3.93 -2.37 -1.54
## beta[29] 2.85 0.01 0.76 1.38 2.33 2.85
## beta[30] 2.69 0.01 0.59 1.53 2.29 2.68
## beta[31] 1.69 0.00 0.51 0.67 1.35 1.70
## beta[32] 0.44 0.01 0.49 -0.53 0.11 0.44
## beta[33] 0.48 0.00 0.48 -0.48 0.16 0.49
## beta[34] 0.01 0.00 0.48 -0.94 -0.31 0.02
## beta[35] 0.30 0.00 0.46 -0.62 -0.02 0.30
## beta[36] 0.57 0.00 0.46 -0.32 0.26 0.57
## beta[37] -0.39 0.00 0.46 -1.28 -0.70 -0.39
## beta[38] -0.03 0.00 0.01 -0.04 -0.03 -0.03
## var_eartag 11.49 0.01 1.76 8.48 10.25 11.34
## var_follower 0.07 0.01 0.07 0.00 0.01 0.04
## var_error 43.47 0.00 0.81 41.93 42.92 43.46
## prp_var_eartag 0.21 0.00 0.03 0.16 0.19 0.21
## prp_var_follower 0.00 0.00 0.00 0.00 0.00 0.00
## prp_var_error 0.79 0.00 0.03 0.74 0.77 0.79
## lp__ -14988.10 11.22 95.30 -15126.30 -15060.64 -15007.21
## 75% 97.5% n_eff Rhat
## beta[1] 17.29 18.86 8357 1.00
## beta[2] 12.33 13.83 6356 1.00
## beta[3] 13.28 14.79 5942 1.00
## beta[4] 12.05 13.74 6170 1.00
## beta[5] 13.46 15.20 7165 1.00
## beta[6] 9.29 10.91 5915 1.00
## beta[7] 13.66 15.35 7914 1.00
## beta[8] 16.90 18.48 9288 1.00
## beta[9] 12.34 13.84 5760 1.00
## beta[10] 20.01 21.57 7701 1.00
## beta[11] 13.05 14.78 7429 1.00
## beta[12] 13.54 15.31 7435 1.00
## beta[13] 11.38 13.01 6734 1.00
## beta[14] 13.49 15.22 7335 1.00
## beta[15] 0.15 0.73 8924 1.00
## beta[16] -0.57 0.00 8708 1.00
## beta[17] -0.50 0.07 8853 1.00
## beta[18] -0.42 0.15 8793 1.00
## beta[19] -0.76 -0.15 9311 1.00
## beta[20] -0.82 -0.13 11188 1.00
## beta[21] -0.32 0.50 13909 1.00
## beta[22] -1.45 -0.48 16612 1.00
## beta[23] 0.27 1.18 15563 1.00
## beta[24] 1.37 2.23 15053 1.00
## beta[25] 0.83 1.83 19378 1.00
## beta[26] 2.56 3.88 23388 1.00
## beta[27] 1.14 3.12 26026 1.00
## beta[28] -0.72 0.86 23744 1.00
## beta[29] 3.37 4.36 16985 1.00
## beta[30] 3.08 3.85 13003 1.00
## beta[31] 2.04 2.70 10636 1.00
## beta[32] 0.78 1.40 9542 1.00
## beta[33] 0.81 1.42 9917 1.00
## beta[34] 0.34 0.95 9818 1.00
## beta[35] 0.61 1.21 9382 1.00
## beta[36] 0.88 1.46 9247 1.00
## beta[37] -0.08 0.50 8910 1.00
## beta[38] -0.03 -0.02 18646 1.00
## var_eartag 12.56 15.34 18552 1.00
## var_follower 0.09 0.26 204 1.02
## var_error 44.01 45.10 33153 1.00
## prp_var_eartag 0.22 0.26 18844 1.00
## prp_var_follower 0.00 0.00 204 1.02
## prp_var_error 0.81 0.84 18048 1.00
## lp__ -14930.05 -14770.00 72 1.05
##
## Samples were drawn using NUTS(diag_e) at Wed Apr 15 14:02:05 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 + 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 1.000000000 1.00000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.371071089 0.50756765 0.516938854 0.509795755 0.459121398 0.552218308
## Lag 5 0.056044722 0.11092871 0.132353962 0.108120692 0.079543248 0.132228622
## Lag 10 0.012926511 0.01691798 0.024786315 0.014788714 0.019944965 0.025596855
## Lag 50 -0.006884289 0.01531142 0.006215045 0.001246645 0.001604593 -0.005852995
## Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## Lag 0 1.00000000 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.41225474 0.345635231 0.534794272 0.469096412 0.533809176 0.464038531
## Lag 5 0.07839617 0.059557630 0.118245304 0.084474315 0.127502287 0.090135673
## Lag 10 0.01374573 0.010912234 0.027730629 0.014072225 0.014876929 0.004063156
## Lag 50 0.01971763 -0.003651896 -0.002487584 0.001552361 0.006829465 0.001043656
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2 Hour_entry_3
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.523752150 0.476244100 0.205927467 0.199450817 0.219960069
## Lag 5 0.121270396 0.091161351 0.098025280 0.085419622 0.087619529
## Lag 10 0.024451525 0.015019594 0.023190015 0.014281113 0.024408962
## Lag 50 -0.001832313 0.008469057 -0.002992633 -0.000112622 -0.008675866
## Hour_entry_4 Hour_entry_5 Hour_entry_6 Hour_entry_7 Hour_entry_8
## Lag 0 1.00000000 1.000000000 1.00000000 1.000000000 1.000000000
## Lag 1 0.19810086 0.158421153 0.11053980 0.027948646 -0.012165921
## Lag 5 0.09226445 0.075041736 0.06452865 0.048341429 0.022054694
## Lag 10 0.02569384 0.016712726 0.01658468 0.014720839 0.020581462
## Lag 50 -0.00157993 -0.007181712 -0.00769922 0.003120612 0.003649965
## Hour_entry_9 Hour_entry_10 Hour_entry_11 Hour_entry_12 Hour_entry_13
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.020270548 0.017673705 -0.035186579 -0.026328344 -0.087323151
## Lag 5 0.040987269 0.042453656 0.030063255 0.029541249 0.008592241
## Lag 10 0.003677876 -0.004894595 0.011582031 0.007549562 0.009213990
## Lag 50 -0.003608068 -0.004930263 -0.000571103 -0.003585046 0.001875011
## Hour_entry_14 Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## Lag 0 1.0000000000 1.0000000000 1.000000000 1.000000000 1.000000000
## Lag 1 -0.0767778460 -0.0068531217 0.049593832 0.101920088 0.146960651
## Lag 5 0.0265976680 0.0321749766 0.050131081 0.058586328 0.074564860
## Lag 10 0.0040193415 0.0061541610 0.012137413 0.021142203 0.020959776
## Lag 50 -0.0002261705 -0.0008516742 -0.003848898 -0.005486291 -0.003765592
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22 Hour_entry_23
## Lag 0 1.000000000 1.000000000 1.0000000000 1.00000000 1.0000000000
## Lag 1 0.142972013 0.148514759 0.1812986071 0.18953288 0.1839491034
## Lag 5 0.069370713 0.070437083 0.0842638488 0.07741746 0.0798454781
## Lag 10 0.018944016 0.023064756 0.0279285193 0.02125727 0.0151160603
## Lag 50 -0.008344305 -0.008995188 0.0005195099 -0.00605548 0.0001686177
## Median Weight rho var_eartag var_follower var_error
## Lag 0 1.0000000000 1.00000000 1.000000000 1.0000000 1.000000000
## Lag 1 0.0900098405 0.85542609 0.039105743 0.9158816 -0.130969479
## Lag 5 0.0039033223 0.58341980 0.020372459 0.7895721 -0.001009669
## Lag 10 0.0015329158 0.40676993 0.015784567 0.6752453 0.011412156
## Lag 50 -0.0007821554 0.09582785 -0.007962437 0.2567443 -0.002354143
## prp_var_eartag prp_var_follower prp_var_error lp__
## Lag 0 1.000000000 1.0000000 1.000000000 1.0000000
## Lag 1 0.034803292 0.9155479 0.035770965 0.9744357
## Lag 5 0.020591471 0.7887412 0.021884923 0.9046948
## Lag 10 0.015701365 0.6738643 0.017338004 0.8313970
## Lag 50 -0.007976017 0.2559308 -0.006326578 0.3917122effectiveSize(outp3)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## 10709.7707 7597.9473 6830.4075 7413.7143
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 8752.3691 6645.8665 9179.5292 10498.7497
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 7094.8018 8572.6932 6863.6963 8413.8551
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## 7090.4325 8195.1957 9694.7660 10141.3865
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## 9680.9392 9778.3050 10874.2376 12603.2103
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## 14652.4680 17609.9707 16837.4526 16269.9282
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## 19832.7938 21358.6998 26956.9507 23683.5995
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## 17375.2900 15016.1173 11810.8594 11099.6520
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## 11284.7239 11104.5452 9597.1422 9729.0297
## Hour_entry_23 Median Weight rho var_eartag
## 10057.0527 21508.0970 1242.0060 18820.1727
## var_follower var_error prp_var_eartag prp_var_follower
## 409.5447 33816.7254 18898.3456 409.5436
## prp_var_error lp__
## 18598.8772 266.2777geweke.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
## 0.892654 -0.595528 -0.081341 -0.365771
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## -0.036324 -0.790584 -0.771891 -1.445514
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## -1.029715 -0.031835 -0.828687 -0.856433
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## 0.559689 -1.432239 -0.245912 0.364281
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## 0.882407 0.511440 0.007401 1.074428
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## 0.809064 0.199351 0.248783 -0.760006
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## 0.430755 0.677693 0.322903 0.418748
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## 0.852837 -0.250636 1.157830 0.033204
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## 1.082200 0.281171 0.338297 -0.361834
## Hour_entry_23 Median Weight rho var_eartag
## 0.317523 0.900476 0.099291 1.284692
## var_follower var_error prp_var_eartag prp_var_follower
## 0.739526 -0.340308 1.218401 0.735634
## prp_var_error lp__
## -1.395813 -1.666603
##
##
## [[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
## 0.42710 0.95249 1.43389 0.36092
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## -0.05805 -0.50498 -0.07515 -1.03968
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 1.31256 -0.25562 -1.41117 1.05850
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## -0.14800 0.66421 -0.21861 -0.63556
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## -0.82993 -1.08606 -0.51509 -0.66459
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## -0.04942 -1.10257 -0.42571 -0.51814
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## -0.06622 -0.84045 0.37335 1.57677
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## -0.27108 -0.05516 -0.36940 -0.60487
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## -0.52513 0.23042 -0.06119 -1.05239
## Hour_entry_23 Median Weight rho var_eartag
## -0.45816 -1.28097 0.95329 1.11284
## var_follower var_error prp_var_eartag prp_var_follower
## 0.35420 0.30473 1.03267 0.35020
## prp_var_error lp__
## -1.15371 -0.45119
##
##
## [[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
## 0.030353 -0.617381 -1.332178 -1.187946
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 0.659947 0.005489 -0.127276 1.318433
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## -0.177653 -0.383154 -0.082132 -0.965945
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## -0.637647 -1.441603 -0.669073 -0.383936
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## -0.766082 -0.996737 -0.434246 -0.841938
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## -1.205636 -0.426889 -1.548319 -0.967537
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## -1.605753 0.092962 -1.215328 -0.715399
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## -0.675256 0.314651 -1.220768 -0.555602
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## -0.389652 -0.930631 -0.703689 -0.373660
## Hour_entry_23 Median Weight rho var_eartag
## -0.289754 1.203997 1.301745 -0.144282
## var_follower var_error prp_var_eartag prp_var_follower
## -0.311271 0.657251 -0.162000 -0.349698
## prp_var_error lp__
## 0.257898 -0.013699gelman.diag(outp3, transform = T,multivariate = F)## Potential scale reduction factors:
##
## Point est. Upper C.I.
## Loc1_t_1 1.00 1.00
## Loc1_t_2 1.00 1.01
## Loc1_t_3 1.00 1.00
## Loc1_t_4 1.00 1.00
## Loc1_t_5 1.00 1.00
## Loc1_t_6 1.00 1.00
## Loc1_t_7 1.00 1.00
## Loc2_t_1 1.00 1.00
## Loc2_t_2 1.00 1.00
## Loc2_t_3 1.00 1.00
## Loc2_t_4 1.00 1.01
## Loc2_t_5 1.00 1.00
## Loc2_t_6 1.00 1.00
## Loc2_t_7 1.00 1.00
## Hour_entry_1 1.00 1.01
## Hour_entry_2 1.00 1.00
## Hour_entry_3 1.00 1.01
## Hour_entry_4 1.00 1.01
## Hour_entry_5 1.00 1.00
## Hour_entry_6 1.00 1.01
## Hour_entry_7 1.00 1.00
## Hour_entry_8 1.00 1.00
## Hour_entry_9 1.00 1.00
## Hour_entry_10 1.00 1.00
## Hour_entry_11 1.00 1.00
## Hour_entry_12 1.00 1.00
## Hour_entry_13 1.00 1.00
## Hour_entry_14 1.00 1.00
## Hour_entry_15 1.00 1.00
## Hour_entry_16 1.00 1.00
## Hour_entry_17 1.00 1.00
## Hour_entry_18 1.00 1.00
## Hour_entry_19 1.00 1.00
## Hour_entry_20 1.00 1.00
## Hour_entry_21 1.00 1.00
## Hour_entry_22 1.00 1.00
## Hour_entry_23 1.00 1.01
## Median Weight 1.00 1.00
## rho 1.01 1.03
## var_eartag 1.00 1.00
## var_follower 1.02 1.06
## var_error 1.00 1.00
## prp_var_eartag 1.00 1.00
## prp_var_follower 1.02 1.06
## prp_var_error 1.00 1.00
## lp__ 1.02 1.07traplot(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 1.647e+01 1.220656 7.047e-03 1.204e-02
## Loc1_t_2 1.156e+01 1.134642 6.551e-03 1.342e-02
## Loc1_t_3 1.249e+01 1.174634 6.782e-03 1.438e-02
## Loc1_t_4 1.112e+01 1.308835 7.557e-03 1.540e-02
## Loc1_t_5 1.257e+01 1.332991 7.696e-03 1.448e-02
## Loc1_t_6 8.453e+00 1.231102 7.108e-03 1.529e-02
## Loc1_t_7 1.276e+01 1.315659 7.596e-03 1.379e-02
## Loc2_t_1 1.605e+01 1.245894 7.193e-03 1.230e-02
## Loc2_t_2 1.158e+01 1.146382 6.619e-03 1.380e-02
## Loc2_t_3 1.919e+01 1.185182 6.843e-03 1.305e-02
## Loc2_t_4 1.216e+01 1.327095 7.662e-03 1.615e-02
## Loc2_t_5 1.260e+01 1.336057 7.714e-03 1.488e-02
## Loc2_t_6 1.052e+01 1.222950 7.061e-03 1.499e-02
## Loc2_t_7 1.256e+01 1.354917 7.823e-03 1.507e-02
## Hour_entry_1 -1.243e-01 0.445194 2.570e-03 4.614e-03
## Hour_entry_2 -8.423e-01 0.443415 2.560e-03 4.488e-03
## Hour_entry_3 -7.806e-01 0.442511 2.555e-03 4.582e-03
## Hour_entry_4 -7.109e-01 0.448262 2.588e-03 4.616e-03
## Hour_entry_5 -1.063e+00 0.476872 2.753e-03 4.671e-03
## Hour_entry_6 -1.151e+00 0.526698 3.041e-03 4.800e-03
## Hour_entry_7 -7.351e-01 0.635818 3.671e-03 5.429e-03
## Hour_entry_8 -1.924e+00 0.765330 4.419e-03 5.894e-03
## Hour_entry_9 -2.030e-01 0.709825 4.098e-03 5.507e-03
## Hour_entry_10 9.410e-01 0.658569 3.802e-03 5.187e-03
## Hour_entry_11 3.182e-01 0.780108 4.504e-03 5.576e-03
## Hour_entry_12 1.886e+00 1.023363 5.908e-03 7.172e-03
## Hour_entry_13 1.165e-01 1.523683 8.797e-03 9.391e-03
## Hour_entry_14 -1.508e+00 1.219376 7.040e-03 7.953e-03
## Hour_entry_15 2.873e+00 0.768656 4.438e-03 5.858e-03
## Hour_entry_16 2.712e+00 0.598088 3.453e-03 4.979e-03
## Hour_entry_17 1.719e+00 0.512758 2.960e-03 4.908e-03
## Hour_entry_18 4.618e-01 0.492995 2.846e-03 4.766e-03
## Hour_entry_19 5.054e-01 0.479434 2.768e-03 4.589e-03
## Hour_entry_20 3.152e-02 0.485552 2.803e-03 4.650e-03
## Hour_entry_21 3.163e-01 0.459343 2.652e-03 4.784e-03
## Hour_entry_22 5.904e-01 0.457229 2.640e-03 4.706e-03
## Hour_entry_23 -3.655e-01 0.458319 2.646e-03 4.652e-03
## Median Weight -2.997e-02 0.005076 2.931e-05 3.496e-05
## rho -1.033e-01 0.448477 2.589e-03 1.280e-02
## var_eartag 1.153e+01 1.764618 1.019e-02 1.294e-02
## var_follower 6.463e-02 0.061535 3.553e-04 3.040e-03
## var_error 4.347e+01 0.794372 4.586e-03 4.335e-03
## prp_var_eartag 2.087e-01 0.025270 1.459e-04 1.863e-04
## prp_var_follower 1.174e-03 0.001116 6.444e-06 5.514e-05
## prp_var_error 7.901e-01 0.025267 1.459e-04 1.883e-04
## lp__ -1.499e+04 70.990996 4.099e-01 4.363e+00
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.408e+01 1.564e+01 1.646e+01 1.729e+01 1.886e+01
## Loc1_t_2 9.327e+00 1.080e+01 1.156e+01 1.232e+01 1.378e+01
## Loc1_t_3 1.021e+01 1.168e+01 1.248e+01 1.329e+01 1.482e+01
## Loc1_t_4 8.570e+00 1.024e+01 1.112e+01 1.199e+01 1.373e+01
## Loc1_t_5 9.921e+00 1.167e+01 1.256e+01 1.345e+01 1.517e+01
## Loc1_t_6 6.043e+00 7.637e+00 8.458e+00 9.279e+00 1.087e+01
## Loc1_t_7 1.015e+01 1.187e+01 1.277e+01 1.364e+01 1.534e+01
## Loc2_t_1 1.360e+01 1.522e+01 1.604e+01 1.687e+01 1.848e+01
## Loc2_t_2 9.309e+00 1.081e+01 1.158e+01 1.234e+01 1.382e+01
## Loc2_t_3 1.687e+01 1.839e+01 1.919e+01 1.998e+01 2.152e+01
## Loc2_t_4 9.549e+00 1.127e+01 1.216e+01 1.304e+01 1.475e+01
## Loc2_t_5 9.965e+00 1.171e+01 1.260e+01 1.349e+01 1.522e+01
## Loc2_t_6 8.115e+00 9.694e+00 1.051e+01 1.135e+01 1.293e+01
## Loc2_t_7 9.899e+00 1.166e+01 1.255e+01 1.348e+01 1.519e+01
## Hour_entry_1 -9.900e-01 -4.263e-01 -1.293e-01 1.774e-01 7.560e-01
## Hour_entry_2 -1.706e+00 -1.140e+00 -8.419e-01 -5.468e-01 2.639e-02
## Hour_entry_3 -1.652e+00 -1.079e+00 -7.788e-01 -4.794e-01 7.555e-02
## Hour_entry_4 -1.586e+00 -1.018e+00 -7.124e-01 -4.111e-01 1.729e-01
## Hour_entry_5 -1.991e+00 -1.386e+00 -1.066e+00 -7.405e-01 -1.326e-01
## Hour_entry_6 -2.189e+00 -1.506e+00 -1.148e+00 -7.951e-01 -1.094e-01
## Hour_entry_7 -1.976e+00 -1.168e+00 -7.316e-01 -3.058e-01 4.998e-01
## Hour_entry_8 -3.433e+00 -2.438e+00 -1.925e+00 -1.410e+00 -4.288e-01
## Hour_entry_9 -1.590e+00 -6.886e-01 -2.041e-01 2.741e-01 1.194e+00
## Hour_entry_10 -3.346e-01 4.929e-01 9.371e-01 1.379e+00 2.243e+00
## Hour_entry_11 -1.219e+00 -2.027e-01 3.234e-01 8.426e-01 1.845e+00
## Hour_entry_12 -1.294e-01 1.202e+00 1.884e+00 2.571e+00 3.897e+00
## Hour_entry_13 -2.871e+00 -9.118e-01 1.093e-01 1.139e+00 3.115e+00
## Hour_entry_14 -3.908e+00 -2.327e+00 -1.500e+00 -6.837e-01 8.791e-01
## Hour_entry_15 1.387e+00 2.351e+00 2.876e+00 3.393e+00 4.384e+00
## Hour_entry_16 1.542e+00 2.304e+00 2.715e+00 3.116e+00 3.882e+00
## Hour_entry_17 7.186e-01 1.373e+00 1.717e+00 2.064e+00 2.722e+00
## Hour_entry_18 -4.973e-01 1.319e-01 4.610e-01 7.912e-01 1.431e+00
## Hour_entry_19 -4.395e-01 1.822e-01 5.054e-01 8.318e-01 1.444e+00
## Hour_entry_20 -9.141e-01 -2.967e-01 2.798e-02 3.612e-01 9.747e-01
## Hour_entry_21 -5.726e-01 3.201e-03 3.154e-01 6.256e-01 1.219e+00
## Hour_entry_22 -3.056e-01 2.804e-01 5.929e-01 8.951e-01 1.484e+00
## Hour_entry_23 -1.258e+00 -6.733e-01 -3.656e-01 -5.404e-02 5.258e-01
## Median Weight -4.006e-02 -3.336e-02 -2.996e-02 -2.655e-02 -2.003e-02
## rho -9.039e-01 -4.381e-01 -1.160e-01 2.184e-01 7.876e-01
## var_eartag 8.548e+00 1.027e+01 1.137e+01 1.262e+01 1.539e+01
## var_follower 1.092e-02 2.173e-02 4.312e-02 8.552e-02 2.318e-01
## var_error 4.195e+01 4.293e+01 4.346e+01 4.400e+01 4.506e+01
## prp_var_eartag 1.639e-01 1.909e-01 2.072e-01 2.250e-01 2.617e-01
## prp_var_follower 1.987e-04 3.949e-04 7.810e-04 1.554e-03 4.218e-03
## prp_var_error 7.371e-01 7.738e-01 7.916e-01 8.080e-01 8.349e-01
## lp__ -1.512e+04 -1.505e+04 -1.500e+04 -1.494e+04 -1.484e+04print(M3600swo.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] 16.47 0.01 1.22 14.08 15.64 16.46
## beta[2] 11.56 0.01 1.13 9.33 10.80 11.56
## beta[3] 12.49 0.01 1.17 10.21 11.68 12.48
## beta[4] 11.12 0.02 1.31 8.57 10.24 11.12
## beta[5] 12.57 0.01 1.33 9.92 11.67 12.56
## beta[6] 8.45 0.02 1.23 6.04 7.64 8.46
## beta[7] 12.76 0.01 1.32 10.15 11.87 12.77
## beta[8] 16.05 0.01 1.25 13.60 15.22 16.04
## beta[9] 11.58 0.01 1.15 9.31 10.81 11.58
## beta[10] 19.19 0.01 1.19 16.87 18.39 19.19
## beta[11] 12.16 0.02 1.33 9.55 11.27 12.16
## beta[12] 12.60 0.01 1.34 9.96 11.71 12.60
## beta[13] 10.52 0.01 1.22 8.12 9.69 10.51
## beta[14] 12.56 0.02 1.35 9.90 11.66 12.55
## beta[15] -0.12 0.00 0.45 -0.99 -0.43 -0.13
## beta[16] -0.84 0.00 0.44 -1.71 -1.14 -0.84
## beta[17] -0.78 0.00 0.44 -1.65 -1.08 -0.78
## beta[18] -0.71 0.01 0.45 -1.59 -1.02 -0.71
## beta[19] -1.06 0.00 0.48 -1.99 -1.39 -1.07
## beta[20] -1.15 0.01 0.53 -2.19 -1.51 -1.15
## beta[21] -0.74 0.01 0.64 -1.98 -1.17 -0.73
## beta[22] -1.92 0.01 0.77 -3.43 -2.44 -1.92
## beta[23] -0.20 0.01 0.71 -1.59 -0.69 -0.20
## beta[24] 0.94 0.01 0.66 -0.33 0.49 0.94
## beta[25] 0.32 0.01 0.78 -1.22 -0.20 0.32
## beta[26] 1.89 0.01 1.02 -0.13 1.20 1.88
## beta[27] 0.12 0.01 1.52 -2.87 -0.91 0.11
## beta[28] -1.51 0.01 1.22 -3.91 -2.33 -1.50
## beta[29] 2.87 0.01 0.77 1.39 2.35 2.88
## beta[30] 2.71 0.01 0.60 1.54 2.30 2.71
## beta[31] 1.72 0.00 0.51 0.72 1.37 1.72
## beta[32] 0.46 0.01 0.49 -0.50 0.13 0.46
## beta[33] 0.51 0.00 0.48 -0.44 0.18 0.51
## beta[34] 0.03 0.00 0.49 -0.91 -0.30 0.03
## beta[35] 0.32 0.01 0.46 -0.57 0.00 0.32
## beta[36] 0.59 0.00 0.46 -0.31 0.28 0.59
## beta[37] -0.37 0.00 0.46 -1.26 -0.67 -0.37
## beta[38] -0.03 0.00 0.01 -0.04 -0.03 -0.03
## rho -0.10 0.02 0.45 -0.90 -0.44 -0.12
## var_eartag 11.53 0.01 1.76 8.55 10.27 11.37
## var_follower 0.06 0.00 0.06 0.01 0.02 0.04
## var_error 43.47 0.00 0.79 41.95 42.93 43.46
## prp_var_eartag 0.21 0.00 0.03 0.16 0.19 0.21
## prp_var_follower 0.00 0.00 0.00 0.00 0.00 0.00
## prp_var_error 0.79 0.00 0.03 0.74 0.77 0.79
## lp__ -14993.50 4.37 70.99 -15117.60 -15046.47 -14995.64
## 75% 97.5% n_eff Rhat
## beta[1] 17.29 18.86 9342 1.00
## beta[2] 12.32 13.78 7200 1.00
## beta[3] 13.29 14.82 6591 1.00
## beta[4] 11.99 13.73 6881 1.00
## beta[5] 13.45 15.17 8121 1.00
## beta[6] 9.28 10.87 6458 1.00
## beta[7] 13.64 15.34 8453 1.00
## beta[8] 16.87 18.48 10147 1.00
## beta[9] 12.34 13.82 6540 1.00
## beta[10] 19.98 21.52 7798 1.00
## beta[11] 13.04 14.75 6129 1.00
## beta[12] 13.49 15.22 8276 1.00
## beta[13] 11.35 12.93 6704 1.00
## beta[14] 13.48 15.19 7444 1.00
## beta[15] 0.18 0.76 9027 1.00
## beta[16] -0.55 0.03 8420 1.00
## beta[17] -0.48 0.08 8184 1.00
## beta[18] -0.41 0.17 7978 1.00
## beta[19] -0.74 -0.13 9647 1.00
## beta[20] -0.80 -0.11 10833 1.00
## beta[21] -0.31 0.50 13374 1.00
## beta[22] -1.41 -0.43 15860 1.00
## beta[23] 0.27 1.19 15742 1.00
## beta[24] 1.38 2.24 16140 1.00
## beta[25] 0.84 1.84 17636 1.00
## beta[26] 2.57 3.90 19956 1.00
## beta[27] 1.14 3.11 25408 1.00
## beta[28] -0.68 0.88 24306 1.00
## beta[29] 3.39 4.38 16772 1.00
## beta[30] 3.12 3.88 12592 1.00
## beta[31] 2.06 2.72 10587 1.00
## beta[32] 0.79 1.43 9710 1.00
## beta[33] 0.83 1.44 9917 1.00
## beta[34] 0.36 0.97 9745 1.00
## beta[35] 0.63 1.22 8436 1.00
## beta[36] 0.90 1.48 8781 1.00
## beta[37] -0.05 0.53 8707 1.00
## beta[38] -0.03 -0.02 21052 1.00
## rho 0.22 0.79 777 1.00
## var_eartag 12.62 15.39 16644 1.00
## var_follower 0.09 0.23 419 1.01
## var_error 44.00 45.06 33033 1.00
## prp_var_eartag 0.22 0.26 16614 1.00
## prp_var_follower 0.00 0.00 420 1.01
## prp_var_error 0.81 0.83 16041 1.00
## lp__ -14944.49 -14843.69 264 1.01
##
## Samples were drawn using NUTS(diag_e) at Wed Apr 15 14:48:56 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)