Bayesian Analysis visit length
Results bayesian estimating of variance components (proportion variance) with Stan program, on 50.652 records of visit length time at the feeder when the next visit was less than or equal to 60 sc, from 6 trials, including locations (2 per trial), median weight as fixed effects and Eartag (118) and followers (118) as random effects in the models. iter = 12000, chain= 3, burn-in = 2000, Thin=1.
1. Mixed model: Location + 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%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 1.0000000000
## Lag 1 -0.053520258 -0.026699057 -0.014540080 -0.106724350 -0.1031963576
## Lag 5 0.001912211 0.006751670 -0.001425002 -0.004764342 0.0002281415
## Lag 10 -0.004219859 -0.005566081 -0.003052252 -0.002097684 0.0065955717
## Lag 50 -0.002862487 0.006692880 0.003148512 0.005422867 -0.0022644799
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.0000000000
## Lag 1 -0.052864110 -0.062506923 -0.035828054 -0.058568008 -0.0816098781
## Lag 5 -0.010122011 -0.008026948 -0.002173820 0.008026601 -0.0054999953
## Lag 10 0.001729631 0.003461891 -0.004464009 -0.004365728 0.0020364902
## Lag 50 -0.010867604 -0.007486873 -0.003710631 0.001711360 -0.0002447055
## Loc2_t_5 Loc2_t_6 Median Weight var_eartag var_error
## Lag 0 1.0000000000 1.0000000000 1.0000000000 1.000000000 1.000000000
## Lag 1 -0.1078918601 -0.0630542963 -0.0240560196 0.040477671 -0.029523640
## Lag 5 -0.0046690647 -0.0106300812 -0.0056101527 0.008217066 0.007306181
## Lag 10 -0.0006233047 0.0007291921 -0.0007126617 0.005068373 -0.002467750
## Lag 50 0.0047798070 0.0044880138 0.0042085058 0.006887534 0.004261828
## prp_var_eartag prp_var_error lp__
## Lag 0 1.000000000 1.000000000 1.000000000
## Lag 1 0.035519546 0.035519546 0.484270060
## Lag 5 0.008115665 0.008115665 0.031489292
## Lag 10 0.005656528 0.005656528 -0.011538117
## Lag 50 0.006046834 0.006046834 -0.004943733effectiveSize(outp1)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4 Loc1_t_5
## 31772.48 30990.20 30722.21 35205.96 36318.47
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## 32043.86 33997.60 31364.11 32984.14 34253.98
## Loc2_t_5 Loc2_t_6 Median Weight var_eartag var_error
## 35860.91 33086.11 32293.40 25590.69 33186.42
## prp_var_eartag prp_var_error lp__
## 25969.98 25969.98 10683.10geweke.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
## 0.5524 0.1605 1.2579 -0.3541 1.3996
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## -1.8086 1.8697 -0.7270 -0.7338 0.7833
## Loc2_t_5 Loc2_t_6 Median Weight var_eartag var_error
## -0.6753 0.7579 -0.5933 -0.6769 -0.7365
## prp_var_eartag prp_var_error lp__
## -0.6981 0.6981 -0.7321
##
##
## [[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
## 0.521652 0.257457 -0.132030 -0.313235 1.450455
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## -1.344776 2.081424 1.096200 0.267589 -0.260193
## Loc2_t_5 Loc2_t_6 Median Weight var_eartag var_error
## -1.034951 0.357642 -0.720075 -0.069250 -0.618758
## prp_var_eartag prp_var_error lp__
## -0.007772 0.007772 -0.257783
##
##
## [[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
## -0.74415 0.66401 0.04275 -1.52141 0.23677
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## -1.00319 0.29206 1.78139 1.64796 -0.76271
## Loc2_t_5 Loc2_t_6 Median Weight var_eartag var_error
## 1.59985 1.62973 -0.65397 0.82819 -0.39917
## prp_var_eartag prp_var_error lp__
## 0.69576 -0.69576 0.37153#gelman.diag(outp1)
traplot(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 1.312e+01 0.913084 5.272e-03 5.134e-03
## Loc1_t_2 6.873e+00 0.937390 5.412e-03 5.344e-03
## Loc1_t_3 1.003e+01 0.932175 5.382e-03 5.398e-03
## Loc1_t_4 7.950e+00 1.093682 6.314e-03 5.835e-03
## Loc1_t_5 8.798e+00 1.112973 6.426e-03 5.854e-03
## Loc1_t_6 4.615e+00 1.018996 5.883e-03 5.732e-03
## Loc2_t_1 1.004e+01 0.905182 5.226e-03 4.937e-03
## Loc2_t_2 7.698e+00 0.927600 5.356e-03 5.283e-03
## Loc2_t_3 1.449e+01 0.929405 5.366e-03 5.163e-03
## Loc2_t_4 6.638e+00 1.097447 6.336e-03 5.931e-03
## Loc2_t_5 9.357e+00 1.097559 6.337e-03 5.798e-03
## Loc2_t_6 6.649e+00 1.032631 5.962e-03 5.716e-03
## Median Weight 1.498e-02 0.001799 1.039e-05 1.003e-05
## var_eartag 9.351e+00 1.341264 7.744e-03 8.396e-03
## var_error 4.281e+01 0.271617 1.568e-03 1.492e-03
## prp_var_eartag 1.787e-01 0.020855 1.204e-04 1.296e-04
## prp_var_error 8.213e-01 0.020855 1.204e-04 1.296e-04
## lp__ -1.207e+05 8.224933 4.749e-02 7.960e-02
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.133e+01 1.250e+01 1.312e+01 1.373e+01 1.490e+01
## Loc1_t_2 5.037e+00 6.247e+00 6.868e+00 7.496e+00 8.717e+00
## Loc1_t_3 8.194e+00 9.412e+00 1.003e+01 1.066e+01 1.187e+01
## Loc1_t_4 5.813e+00 7.223e+00 7.952e+00 8.675e+00 1.011e+01
## Loc1_t_5 6.617e+00 8.059e+00 8.797e+00 9.550e+00 1.097e+01
## Loc1_t_6 2.629e+00 3.921e+00 4.618e+00 5.304e+00 6.621e+00
## Loc2_t_1 8.249e+00 9.434e+00 1.004e+01 1.065e+01 1.181e+01
## Loc2_t_2 5.848e+00 7.077e+00 7.707e+00 8.320e+00 9.518e+00
## Loc2_t_3 1.266e+01 1.387e+01 1.450e+01 1.511e+01 1.631e+01
## Loc2_t_4 4.476e+00 5.895e+00 6.645e+00 7.386e+00 8.767e+00
## Loc2_t_5 7.200e+00 8.616e+00 9.350e+00 1.010e+01 1.151e+01
## Loc2_t_6 4.612e+00 5.944e+00 6.649e+00 7.348e+00 8.668e+00
## Median Weight 1.146e-02 1.376e-02 1.500e-02 1.621e-02 1.846e-02
## var_eartag 7.088e+00 8.409e+00 9.227e+00 1.017e+01 1.232e+01
## var_error 4.228e+01 4.263e+01 4.281e+01 4.299e+01 4.335e+01
## prp_var_eartag 1.420e-01 1.642e-01 1.773e-01 1.919e-01 2.236e-01
## prp_var_error 7.764e-01 8.081e-01 8.227e-01 8.358e-01 8.580e-01
## lp__ -1.207e+05 -1.207e+05 -1.207e+05 -1.206e+05 -1.206e+05print(Et60.model)## Inference for Stan model: Eartagtrp_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] 13.12 0.01 0.91 11.33 12.50 13.12
## beta[2] 6.87 0.01 0.94 5.04 6.25 6.87
## beta[3] 10.03 0.01 0.93 8.19 9.41 10.03
## beta[4] 7.95 0.01 1.09 5.81 7.22 7.95
## beta[5] 8.80 0.01 1.11 6.62 8.06 8.80
## beta[6] 4.62 0.01 1.02 2.63 3.92 4.62
## beta[7] 10.04 0.00 0.91 8.25 9.43 10.04
## beta[8] 7.70 0.01 0.93 5.85 7.08 7.71
## beta[9] 14.49 0.01 0.93 12.66 13.87 14.50
## beta[10] 6.64 0.01 1.10 4.48 5.89 6.64
## beta[11] 9.36 0.01 1.10 7.20 8.62 9.35
## beta[12] 6.65 0.01 1.03 4.61 5.94 6.65
## beta[13] 0.01 0.00 0.00 0.01 0.01 0.01
## var_eartag 9.35 0.01 1.34 7.09 8.41 9.23
## var_error 42.81 0.00 0.27 42.28 42.63 42.81
## prp_var_eartag 0.18 0.00 0.02 0.14 0.16 0.18
## prp_var_error 0.82 0.00 0.02 0.78 0.81 0.82
## lp__ -120655.46 0.08 8.22 -120672.53 -120660.77 -120655.12
## 75% 97.5% n_eff Rhat
## beta[1] 13.73 14.90 31526 1
## beta[2] 7.50 8.72 30667 1
## beta[3] 10.66 11.87 29390 1
## beta[4] 8.67 10.11 35019 1
## beta[5] 9.55 10.97 35375 1
## beta[6] 5.30 6.62 30992 1
## beta[7] 10.65 11.81 33783 1
## beta[8] 8.32 9.52 30511 1
## beta[9] 15.11 16.31 33269 1
## beta[10] 7.39 8.77 34025 1
## beta[11] 10.10 11.51 35436 1
## beta[12] 7.35 8.67 32428 1
## beta[13] 0.02 0.02 31489 1
## var_eartag 10.17 12.32 25270 1
## var_error 42.99 43.35 31893 1
## prp_var_eartag 0.19 0.22 25585 1
## prp_var_error 0.84 0.86 25585 1
## lp__ -120649.73 -120640.29 10425 1
##
## Samples were drawn using NUTS(diag_e) at Sun Sep 29 04:28:54 2019.
## 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
## [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(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 1.000000000 1.000000000 1.000000000
## Lag 1 0.377117880 0.453263694 0.427486047 0.375352826 0.369683801
## Lag 5 0.055756685 0.096934275 0.076770262 0.058160031 0.064573861
## Lag 10 0.017395144 0.027381864 0.014469473 0.019143553 0.015307764
## Lag 50 -0.008731512 -0.006140862 0.004252904 -0.009703487 0.001107061
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.426314049 0.390124248 0.441244537 0.427401625 0.407438645
## Lag 5 0.078738380 0.057413925 0.078059044 0.076684062 0.056706058
## Lag 10 0.016968271 0.006250382 0.006915195 0.025973166 0.005953313
## Lag 50 0.008991662 -0.002644904 -0.004490229 -0.002711335 0.016301553
## Loc2_t_5 Loc2_t_6 Median Weight var_eartag var_follower
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.0000000000
## Lag 1 0.363303856 0.433689538 -0.237711952 -0.009679289 -0.0027234557
## Lag 5 0.050667922 0.073877380 -0.018429534 0.013833812 0.0147671353
## Lag 10 0.012552248 0.007815358 0.006212836 0.009174978 -0.0006653534
## Lag 50 0.008497186 -0.006701009 0.001694136 -0.007489232 0.0063146359
## var_error prp_var_eartag prp_var_follower prp_var_error
## Lag 0 1.0000000000 1.000000000 1.000000000 1.000000000
## Lag 1 -0.2075573300 -0.017736747 -0.001748862 -0.019776420
## Lag 5 -0.0081777182 0.013664086 0.016245786 0.011592696
## Lag 10 0.0003269274 0.008406133 -0.001055915 0.008540258
## Lag 50 0.0003319606 -0.007813497 0.006121308 -0.008043339
## lp__
## Lag 0 1.000000000
## Lag 1 0.508824253
## Lag 5 0.035082500
## Lag 10 -0.002597973
## Lag 50 -0.001954400effectiveSize(outp2)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## 13060.774 10630.067 11566.723 13254.020
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## 12957.775 11022.102 12577.363 11078.210
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## 11550.935 11786.698 13268.711 11436.613
## Median Weight var_eartag var_follower var_error
## 49276.419 24373.682 24582.324 46096.070
## prp_var_eartag prp_var_follower prp_var_error lp__
## 24885.395 23950.323 25324.460 9765.314geweke.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
## 0.70356 0.08103 0.73264 1.26423
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## 0.50454 0.57848 -0.11711 0.01697
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## -0.67500 0.14421 0.23861 -2.05708
## Median Weight var_eartag var_follower var_error
## -0.61733 -0.76319 0.12699 0.01774
## prp_var_eartag prp_var_follower prp_var_error lp__
## -0.76253 0.27133 0.84928 -1.38319
##
##
## [[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
## -1.23121 0.90463 2.76037 0.55138
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## -0.55219 0.13998 0.23249 -0.02847
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## 0.46894 -0.67786 0.56023 1.50323
## Median Weight var_eartag var_follower var_error
## 2.67679 -0.53389 0.14650 0.99022
## prp_var_eartag prp_var_follower prp_var_error lp__
## -0.53996 0.23139 0.50965 -0.57114
##
##
## [[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
## 1.1391 0.2436 0.8825 -1.0724
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## 0.3234 -1.0836 1.2353 1.5316
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## 0.4733 -0.6425 -1.3802 1.5064
## Median Weight var_eartag var_follower var_error
## -0.4329 0.3880 -0.7080 -0.6170
## prp_var_eartag prp_var_follower prp_var_error lp__
## 0.4170 -0.7531 -0.2925 1.0022#gelman.diag(outp2)
traplot(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 1.309e+01 0.971747 5.610e-03 9.752e-03
## Loc1_t_2 6.782e+00 0.985517 5.690e-03 1.094e-02
## Loc1_t_3 9.917e+00 0.982857 5.675e-03 1.043e-02
## Loc1_t_4 7.945e+00 1.135793 6.558e-03 1.124e-02
## Loc1_t_5 8.915e+00 1.164037 6.721e-03 1.152e-02
## Loc1_t_6 4.672e+00 1.087614 6.279e-03 1.157e-02
## Loc2_t_1 1.041e+01 0.949926 5.484e-03 9.447e-03
## Loc2_t_2 7.722e+00 0.979697 5.656e-03 1.083e-02
## Loc2_t_3 1.457e+01 0.976955 5.640e-03 1.041e-02
## Loc2_t_4 6.507e+00 1.139368 6.578e-03 1.181e-02
## Loc2_t_5 9.234e+00 1.161044 6.703e-03 1.147e-02
## Loc2_t_6 6.985e+00 1.070987 6.183e-03 1.147e-02
## Median Weight 1.540e-02 0.001781 1.028e-05 8.024e-06
## var_eartag 9.152e+00 1.306253 7.542e-03 8.487e-03
## var_follower 1.192e+00 0.185264 1.070e-03 1.193e-03
## var_error 4.175e+01 0.260801 1.506e-03 1.216e-03
## prp_var_eartag 1.752e-01 0.020474 1.182e-04 1.316e-04
## prp_var_follower 2.289e-02 0.003523 2.034e-05 2.286e-05
## prp_var_error 8.019e-01 0.020088 1.160e-04 1.285e-04
## lp__ -1.201e+05 11.452101 6.612e-02 1.159e-01
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.119e+01 1.243e+01 1.309e+01 1.374e+01 1.501e+01
## Loc1_t_2 4.843e+00 6.111e+00 6.790e+00 7.442e+00 8.711e+00
## Loc1_t_3 7.973e+00 9.259e+00 9.915e+00 1.058e+01 1.186e+01
## Loc1_t_4 5.706e+00 7.185e+00 7.942e+00 8.713e+00 1.016e+01
## Loc1_t_5 6.659e+00 8.134e+00 8.912e+00 9.685e+00 1.120e+01
## Loc1_t_6 2.519e+00 3.941e+00 4.678e+00 5.408e+00 6.792e+00
## Loc2_t_1 8.522e+00 9.781e+00 1.042e+01 1.105e+01 1.226e+01
## Loc2_t_2 5.812e+00 7.056e+00 7.728e+00 8.382e+00 9.632e+00
## Loc2_t_3 1.262e+01 1.392e+01 1.457e+01 1.522e+01 1.646e+01
## Loc2_t_4 4.269e+00 5.741e+00 6.507e+00 7.269e+00 8.737e+00
## Loc2_t_5 6.981e+00 8.442e+00 9.235e+00 1.003e+01 1.147e+01
## Loc2_t_6 4.888e+00 6.257e+00 6.989e+00 7.709e+00 9.076e+00
## Median Weight 1.187e-02 1.419e-02 1.540e-02 1.659e-02 1.889e-02
## var_eartag 6.938e+00 8.230e+00 9.022e+00 9.948e+00 1.203e+01
## var_follower 8.800e-01 1.061e+00 1.175e+00 1.305e+00 1.604e+00
## var_error 4.124e+01 4.157e+01 4.175e+01 4.193e+01 4.226e+01
## prp_var_eartag 1.390e-01 1.608e-01 1.736e-01 1.881e-01 2.191e-01
## prp_var_follower 1.687e-02 2.040e-02 2.258e-02 2.506e-02 3.069e-02
## prp_var_error 7.592e-01 7.889e-01 8.034e-01 8.161e-01 8.374e-01
## lp__ -1.201e+05 -1.201e+05 -1.201e+05 -1.201e+05 -1.201e+05print(Follower.model)## Inference for Stan model: EFtrp_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] 13.09 0.01 0.97 11.19 12.43 13.09
## beta[2] 6.78 0.01 0.99 4.84 6.11 6.79
## beta[3] 9.92 0.01 0.98 7.97 9.26 9.91
## beta[4] 7.94 0.01 1.14 5.71 7.19 7.94
## beta[5] 8.92 0.01 1.16 6.66 8.13 8.91
## beta[6] 4.67 0.01 1.09 2.52 3.94 4.68
## beta[7] 10.41 0.01 0.95 8.52 9.78 10.42
## beta[8] 7.72 0.01 0.98 5.81 7.06 7.73
## beta[9] 14.57 0.01 0.98 12.62 13.92 14.57
## beta[10] 6.51 0.01 1.14 4.27 5.74 6.51
## beta[11] 9.23 0.01 1.16 6.98 8.44 9.24
## beta[12] 6.98 0.01 1.07 4.89 6.26 6.99
## beta[13] 0.02 0.00 0.00 0.01 0.01 0.02
## var_eartag 9.15 0.01 1.31 6.94 8.23 9.02
## var_follower 1.19 0.00 0.19 0.88 1.06 1.18
## var_error 41.75 0.00 0.26 41.24 41.57 41.75
## prp_var_eartag 0.18 0.00 0.02 0.14 0.16 0.17
## prp_var_follower 0.02 0.00 0.00 0.02 0.02 0.02
## prp_var_error 0.80 0.00 0.02 0.76 0.79 0.80
## lp__ -120088.62 0.12 11.45 -120112.00 -120096.20 -120088.31
## 75% 97.5% n_eff Rhat
## beta[1] 13.74 15.01 9730 1
## beta[2] 7.44 8.71 7082 1
## beta[3] 10.58 11.86 8772 1
## beta[4] 8.71 10.16 9006 1
## beta[5] 9.68 11.20 9687 1
## beta[6] 5.41 6.79 8109 1
## beta[7] 11.05 12.26 9828 1
## beta[8] 8.38 9.63 8452 1
## beta[9] 15.22 16.46 8197 1
## beta[10] 7.27 8.74 9806 1
## beta[11] 10.03 11.47 10177 1
## beta[12] 7.71 9.08 8650 1
## beta[13] 0.02 0.02 50193 1
## var_eartag 9.95 12.03 23579 1
## var_follower 1.30 1.60 22935 1
## var_error 41.93 42.26 46738 1
## prp_var_eartag 0.19 0.22 24028 1
## prp_var_follower 0.03 0.03 22929 1
## prp_var_error 0.82 0.84 24017 1
## lp__ -120080.69 -120067.18 9828 1
##
## Samples were drawn using NUTS(diag_e) at Sun Sep 29 00:23:57 2019.
## 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(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
## Lag 0 1.000000000 1.00000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.168130534 0.26903839 0.266627418 0.152903352 0.153772285
## Lag 5 0.026400353 0.03258695 0.040566404 0.018737280 0.006553161
## Lag 10 0.003959782 -0.00678998 -0.002915155 -0.004489188 -0.008857719
## Lag 50 0.001144777 -0.01656762 -0.012533959 0.004660287 0.004533442
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.250295014 0.194558746 0.248695259 0.275141406 0.197986858
## Lag 5 0.030377042 0.032770954 0.028296171 0.035202781 0.025810052
## Lag 10 -0.007155641 0.007228013 -0.005074405 0.007872586 0.015711364
## Lag 50 -0.010870764 0.002217106 0.005040667 0.015899293 0.002586386
## Loc2_t_5 Loc2_t_6 Median Weight rho var_eartag
## Lag 0 1.000000000 1.000000000 1.0000000000 1.0000000000 1.000000000
## Lag 1 0.132597542 0.222101039 -0.0938128372 -0.0487818622 -0.017833739
## Lag 5 0.023198654 0.019674625 -0.0003264389 -0.0005144541 0.006316356
## Lag 10 -0.002164482 0.001340779 -0.0005038793 -0.0001617244 0.006135414
## Lag 50 -0.001363070 0.005242995 -0.0043491407 0.0104301372 -0.001753063
## var_follower var_error prp_var_eartag prp_var_follower
## Lag 0 1.000000000 1.0000000000 1.000000000 1.000000000
## Lag 1 -0.008166733 -0.0868910001 -0.023865249 -0.008241664
## Lag 5 0.016810847 0.0002127597 0.006875355 0.017967816
## Lag 10 -0.000216908 -0.0020724564 0.006670404 0.001749950
## Lag 50 -0.012025465 -0.0013802112 -0.001751193 -0.011367186
## prp_var_error lp__
## Lag 0 1.000000000 1.0000000000
## Lag 1 -0.024484309 0.4936763054
## Lag 5 0.005837479 0.0335236818
## Lag 10 0.004125365 -0.0040603061
## Lag 50 -0.002601158 -0.0006830644effectiveSize(outp3)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## 21624.44 17750.62 17870.99 23709.58
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## 23110.20 18682.25 19471.02 18439.59
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## 17146.43 21287.36 24563.02 20123.25
## Median Weight rho var_eartag var_follower
## 38007.38 30184.60 28680.60 25870.22
## var_error prp_var_eartag prp_var_follower prp_var_error
## 37877.26 28967.27 25981.53 29072.10
## lp__
## 10014.85traplot(outp3,col =c("red1","blue4","purple3"))
geweke.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
## -1.1703 -0.3475 -1.3908 0.9851
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## -0.9116 -1.4209 -0.5475 -0.8801
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## 1.1797 -1.3497 -1.1651 -0.5686
## Median Weight rho var_eartag var_follower
## 0.3488 1.5646 0.5015 0.5061
## var_error prp_var_eartag prp_var_follower prp_var_error
## -0.3350 0.5256 0.4369 -0.6180
## lp__
## 0.9248
##
##
## [[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
## 0.70524 -0.03717 1.33995 0.92621
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## 1.22781 0.25841 -0.22075 -0.15434
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## -0.33871 1.56975 1.22530 -0.49539
## Median Weight rho var_eartag var_follower
## 0.01062 0.99905 -0.57156 0.14814
## var_error prp_var_eartag prp_var_follower prp_var_error
## 0.88104 -0.66111 0.27311 0.62586
## lp__
## -2.06380
##
##
## [[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
## 0.3195 1.0096 -1.7538 0.2336
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## 1.9619 0.2364 -0.4832 -1.5188
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## -2.6167 -0.4848 -0.6498 -2.7052
## Median Weight rho var_eartag var_follower
## 0.2125 -1.1743 0.6832 -2.3846
## var_error prp_var_eartag prp_var_follower prp_var_error
## -0.3239 0.7700 -2.5137 -0.4066
## lp__
## 0.1487gelman.diag(outp3)## 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
## 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 1.01
## 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
##
## 1denplot(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 1.308e+01 0.978454 5.649e-03 7.637e-03
## Loc1_t_2 6.798e+00 1.005698 5.806e-03 8.373e-03
## Loc1_t_3 9.946e+00 1.002927 5.790e-03 8.669e-03
## Loc1_t_4 7.947e+00 1.174178 6.779e-03 8.786e-03
## Loc1_t_5 8.927e+00 1.175839 6.789e-03 8.759e-03
## Loc1_t_6 4.664e+00 1.107966 6.397e-03 9.234e-03
## Loc2_t_1 1.044e+01 0.977253 5.642e-03 7.942e-03
## Loc2_t_2 7.731e+00 0.993977 5.739e-03 8.278e-03
## Loc2_t_3 1.457e+01 1.002283 5.787e-03 8.654e-03
## Loc2_t_4 6.524e+00 1.170760 6.759e-03 9.168e-03
## Loc2_t_5 9.235e+00 1.179620 6.811e-03 8.958e-03
## Loc2_t_6 7.010e+00 1.112924 6.425e-03 9.101e-03
## Median Weight 1.539e-02 0.001785 1.031e-05 9.447e-06
## rho 6.096e-02 0.104055 6.008e-04 6.033e-04
## var_eartag 9.230e+00 1.318650 7.613e-03 7.837e-03
## var_follower 1.207e+00 0.187968 1.085e-03 1.173e-03
## var_error 4.175e+01 0.263514 1.521e-03 1.404e-03
## prp_var_eartag 1.763e-01 0.020574 1.188e-04 1.216e-04
## prp_var_follower 2.313e-02 0.003559 2.055e-05 2.215e-05
## prp_var_error 8.005e-01 0.020220 1.167e-04 1.193e-04
## lp__ -1.201e+05 11.538696 6.662e-02 1.153e-01
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.116e+01 1.243e+01 1.309e+01 1.375e+01 1.501e+01
## Loc1_t_2 4.812e+00 6.130e+00 6.805e+00 7.465e+00 8.790e+00
## Loc1_t_3 7.979e+00 9.266e+00 9.942e+00 1.063e+01 1.189e+01
## Loc1_t_4 5.635e+00 7.165e+00 7.935e+00 8.733e+00 1.027e+01
## Loc1_t_5 6.631e+00 8.133e+00 8.929e+00 9.720e+00 1.123e+01
## Loc1_t_6 2.494e+00 3.916e+00 4.666e+00 5.410e+00 6.836e+00
## Loc2_t_1 8.535e+00 9.776e+00 1.044e+01 1.109e+01 1.236e+01
## Loc2_t_2 5.776e+00 7.068e+00 7.738e+00 8.400e+00 9.667e+00
## Loc2_t_3 1.258e+01 1.390e+01 1.458e+01 1.525e+01 1.651e+01
## Loc2_t_4 4.214e+00 5.735e+00 6.531e+00 7.308e+00 8.812e+00
## Loc2_t_5 6.912e+00 8.436e+00 9.234e+00 1.003e+01 1.153e+01
## Loc2_t_6 4.835e+00 6.263e+00 7.011e+00 7.762e+00 9.179e+00
## Median Weight 1.189e-02 1.420e-02 1.539e-02 1.661e-02 1.886e-02
## rho -1.435e-01 -9.268e-03 6.184e-02 1.322e-01 2.622e-01
## var_eartag 6.989e+00 8.301e+00 9.104e+00 1.002e+01 1.216e+01
## var_follower 8.876e-01 1.073e+00 1.190e+00 1.322e+00 1.619e+00
## var_error 4.124e+01 4.157e+01 4.175e+01 4.193e+01 4.227e+01
## prp_var_eartag 1.399e-01 1.620e-01 1.749e-01 1.891e-01 2.207e-01
## prp_var_follower 1.707e-02 2.061e-02 2.283e-02 2.531e-02 3.093e-02
## prp_var_error 7.571e-01 7.879e-01 8.019e-01 8.146e-01 8.367e-01
## lp__ -1.201e+05 -1.201e+05 -1.201e+05 -1.201e+05 -1.201e+05print(covEartfoll.model)## Inference for Stan model: covEartFolltrp_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] 13.08 0.01 0.98 11.16 12.43 13.09
## beta[2] 6.80 0.01 1.01 4.81 6.13 6.80
## beta[3] 9.95 0.01 1.00 7.98 9.27 9.94
## beta[4] 7.95 0.01 1.17 5.63 7.16 7.93
## beta[5] 8.93 0.01 1.18 6.63 8.13 8.93
## beta[6] 4.66 0.01 1.11 2.49 3.92 4.67
## beta[7] 10.44 0.01 0.98 8.53 9.78 10.44
## beta[8] 7.73 0.01 0.99 5.78 7.07 7.74
## beta[9] 14.57 0.01 1.00 12.58 13.90 14.58
## beta[10] 6.52 0.01 1.17 4.21 5.74 6.53
## beta[11] 9.23 0.01 1.18 6.91 8.44 9.23
## beta[12] 7.01 0.01 1.11 4.84 6.26 7.01
## beta[13] 0.02 0.00 0.00 0.01 0.01 0.02
## rho 0.06 0.00 0.10 -0.14 -0.01 0.06
## var_eartag 9.23 0.01 1.32 6.99 8.30 9.10
## var_follower 1.21 0.00 0.19 0.89 1.07 1.19
## var_error 41.75 0.00 0.26 41.24 41.57 41.75
## prp_var_eartag 0.18 0.00 0.02 0.14 0.16 0.17
## prp_var_follower 0.02 0.00 0.00 0.02 0.02 0.02
## prp_var_error 0.80 0.00 0.02 0.76 0.79 0.80
## lp__ -120089.69 0.12 11.54 -120113.25 -120097.27 -120089.38
## 75% 97.5% n_eff Rhat
## beta[1] 13.75 15.01 15998 1
## beta[2] 7.46 8.79 14409 1
## beta[3] 10.63 11.89 13401 1
## beta[4] 8.73 10.27 17746 1
## beta[5] 9.72 11.23 18276 1
## beta[6] 5.41 6.84 14506 1
## beta[7] 11.09 12.36 14859 1
## beta[8] 8.40 9.67 14353 1
## beta[9] 15.25 16.51 12894 1
## beta[10] 7.31 8.81 15922 1
## beta[11] 10.03 11.53 17348 1
## beta[12] 7.76 9.18 15254 1
## beta[13] 0.02 0.02 35357 1
## rho 0.13 0.26 29567 1
## var_eartag 10.02 12.16 27455 1
## var_follower 1.32 1.62 25350 1
## var_error 41.93 42.27 35185 1
## prp_var_eartag 0.19 0.22 27834 1
## prp_var_follower 0.03 0.03 25471 1
## prp_var_error 0.81 0.84 27959 1
## lp__ -120081.66 -120068.21 10011 1
##
## Samples were drawn using NUTS(diag_e) at Sun Sep 29 02:30:54 2019.
## 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)