Results of bayesian estimating of variance components on visit length at the when the median weight is included in the model. iter = 82000, burn-in = 2000, thin = 5.

1. Mixed Model: visit length ~ Location + wt + Eartag

1.1. Check Autocorrelation and convergence diagnostic

autocorr.plot(m1.chain)

autocorr.diag(m1.chain)
##        Locat_eff[1] Locat_eff[2]    deviance    eff_wt  var_Eartag
## Lag 0     1.0000000    1.0000000 1.000000000 1.0000000 1.000000000
## Lag 1     0.9496372    0.9597228 0.036518567 0.9626936 0.095671888
## Lag 5     0.7841315    0.8152752 0.023886078 0.8259834 0.047438338
## Lag 10    0.6290632    0.6701756 0.018859057 0.6842909 0.018870483
## Lag 50    0.1723512    0.1616493 0.003588325 0.1758652 0.003503853
##                var_e
## Lag 0   1.0000000000
## Lag 1  -0.0001785449
## Lag 5   0.0014752814
## Lag 10 -0.0090181487
## Lag 50  0.0076006735
effectiveSize(m1.chain)
## Locat_eff[1] Locat_eff[2]     deviance       eff_wt   var_Eartag 
##     1608.298     1603.076    45659.019     1482.587    37025.462 
##        var_e 
##    78000.000
geweke.diag(m1.chain)
## [[1]]
## 
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5 
## 
## Locat_eff[1] Locat_eff[2]     deviance       eff_wt   var_Eartag 
##       0.7820       0.7908       1.3090      -0.7934      -0.1526 
##        var_e 
##       2.1667
traplot(m1.chain, col = "darkblue")

denplot(m1.chain, col = "darkblue")

# DIC and pD
bugs.log("Trial_1_covariate_OpenBugs/log.txt")
## $stats
##                    mean      sd   val2.5pc     median  val97.5pc sample
## Locat_eff[1]  2.084e+01 1.71900    17.4600  2.084e+01  2.419e+01  78000
## Locat_eff[2]  1.889e+01 1.72100    15.5100  1.888e+01  2.223e+01  78000
## deviance      3.556e+04 7.25500 35550.0000  3.556e+04  3.557e+04  78000
## eff_wt       -8.048e-02 0.01496    -0.1101 -8.047e-02 -5.094e-02  78000
## var_Eartag    1.396e+01 4.92500     7.3000  1.301e+01  2.618e+01  78000
## var_e         6.797e+01 1.36000    65.3600  6.796e+01  7.070e+01  78000
## 
## $DIC
##        Dbar  Dhat   DIC    pD
## y     35560 35530 35580 25.47
## total 35560 35530 35580 25.47

1.2.Summary posterior distribution

summary(m1.chain)
## 
## Iterations = 2001:80000
## Thinning interval = 1 
## Number of chains = 1 
## Sample size per chain = 78000 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                    Mean      SD  Naive SE Time-series SE
## Locat_eff[1]  2.084e+01 1.71930 6.156e-03      0.0428714
## Locat_eff[2]  1.889e+01 1.72081 6.161e-03      0.0429789
## deviance      3.556e+04 7.80844 2.796e-02      0.0365428
## eff_wt       -8.048e-02 0.01496 5.357e-05      0.0003886
## var_Eartag    1.396e+01 4.92464 1.763e-02      0.0255932
## var_e         6.797e+01 1.36000 4.870e-03      0.0048696
## 
## 2. Quantiles for each variable:
## 
##                   2.5%        25%        50%        75%     97.5%
## Locat_eff[1]    17.470  1.969e+01  2.084e+01  2.201e+01    24.190
## Locat_eff[2]    15.500  1.773e+01  1.889e+01  2.005e+01    22.260
## deviance     35550.000  3.555e+04  3.556e+04  3.556e+04 35570.000
## eff_wt          -0.110 -9.041e-02 -8.051e-02 -7.048e-02    -0.051
## var_Eartag       7.295  1.055e+01  1.301e+01  1.630e+01    26.190
## var_e           65.370  6.704e+01  6.796e+01  6.888e+01    70.710

###Plot of posterior correlations between model parameters from MCMC simulation

parcorplot(m1.chain,col = terrain.colors(15,0.5,T), cex.axis=0.5)

2. Mixed Model: visit length ~ Location + wt + Eartag + Folower

2.1. Check autocorrelation and convergence diagnostics

autocorr.plot(m2.mcmc.chain)

autocorr.diag(m2.mcmc.chain)
##        Locat_eff[1] Locat_eff[2]    deviance    eff_wt   var_Eartag
## Lag 0     1.0000000    1.0000000 1.000000000 1.0000000 1.0000000000
## Lag 1     0.9525238    0.9627597 0.018662328 0.9635699 0.0964459207
## Lag 5     0.7860085    0.8250976 0.012560780 0.8320887 0.0471363831
## Lag 10    0.6285846    0.6825646 0.009299299 0.6896681 0.0214178082
## Lag 50    0.1336372    0.1446004 0.001759626 0.1346878 0.0003951272
##        var_Follower         var_e
## Lag 0   1.000000000  1.000000e+00
## Lag 1   0.052651045 -3.703953e-03
## Lag 5  -0.000123366 -8.685499e-05
## Lag 10  0.001758632  5.173715e-03
## Lag 50 -0.003681747 -3.405970e-03
effectiveSize(m2.mcmc.chain)
## Locat_eff[1] Locat_eff[2]     deviance       eff_wt   var_Eartag 
##     1777.990     1533.230    55168.210     1484.222    34341.811 
## var_Follower        var_e 
##    69980.694    80000.000
geweke.diag(m2.mcmc.chain)
## [[1]]
## 
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5 
## 
## Locat_eff[1] Locat_eff[2]     deviance       eff_wt   var_Eartag 
##      -0.5640      -1.5043      -0.2517       1.2326       0.9062 
## var_Follower        var_e 
##      -0.1036      -0.3596
traplot(m2.mcmc.chain, col = "darkslateblue")

denplot(m2.mcmc.chain, col = "darkslateblue")

bugs.log("Trial_1_covariate_OpenBugs/Model_EF_wt_covariate/log.txt")
## $stats
##                    mean      sd   val2.5pc     median  val97.5pc sample
## Locat_eff[1]  2.104e+01 1.75900    17.5700  2.103e+01  2.446e+01  80000
## Locat_eff[2]  1.935e+01 1.77900    15.9100  1.936e+01  2.277e+01  80000
## deviance      3.545e+04 9.62300 35430.0000  3.545e+04  3.547e+04  80000
## eff_wt       -8.168e-02 0.01507    -0.1107 -8.179e-02 -5.179e-02  80000
## var_Eartag    1.380e+01 4.87800     7.2600  1.285e+01  2.573e+01  80000
## var_Follower  1.390e+00 0.56500     0.6283  1.280e+00  2.793e+00  80000
## var_e         6.653e+01 1.33200    64.0000  6.651e+01  6.920e+01  80000
## 
## $DIC
##        Dbar  Dhat   DIC    pD
## y     35450 35410 35490 43.08
## total 35450 35410 35490 43.08

2.2. Summary posterior distribution

summary(m2.mcmc.chain)
## 
## Iterations = 2001:82000
## Thinning interval = 1 
## Number of chains = 1 
## Sample size per chain = 80000 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                    Mean       SD  Naive SE Time-series SE
## Locat_eff[1]  2.104e+01  1.75860 6.218e-03      0.0417065
## Locat_eff[2]  1.935e+01  1.77899 6.290e-03      0.0454328
## deviance      3.545e+04 10.04023 3.550e-02      0.0427464
## eff_wt       -8.168e-02  0.01507 5.327e-05      0.0003911
## var_Eartag    1.380e+01  4.87780 1.725e-02      0.0263216
## var_Follower  1.390e+00  0.56496 1.997e-03      0.0021356
## var_e         6.653e+01  1.33215 4.710e-03      0.0047098
## 
## 2. Quantiles for each variable:
## 
##                    2.5%        25%        50%        75%      97.5%
## Locat_eff[1]    17.5200    19.8800  2.104e+01  2.222e+01    24.4600
## Locat_eff[2]    15.8697    18.1600  1.936e+01  2.056e+01    22.7700
## deviance     35430.0000 35440.0000  3.545e+04  3.546e+04 35470.0000
## eff_wt          -0.1105    -0.0920 -8.172e-02 -7.153e-02    -0.0517
## var_Eartag       7.2530    10.4300  1.285e+01  1.609e+01    25.7900
## var_Follower     0.6285     0.9995  1.280e+00  1.656e+00     2.7980
## var_e           63.9900    65.6300  6.651e+01  6.742e+01    69.2000

Plot of posterior correlations between model parameters from MCMC simulation

parcorplot(m1.chain,col = terrain.colors(15,0.5,T), cex.axis=0.5)

3. Mixed Model: visit length ~ Location + wt + Eartag + Folower + cov(eartag,follower)

3.1. Check autocorrelation and convergence diagnostics

autocorr.plot(m3.mcmc.chain)

autocorr.diag(m3.mcmc.chain)
##        Locat_eff[1] Locat_eff[2]      deviance    eff_wt     rho_ef
## Lag 0     1.0000000    1.0000000  1.0000000000 1.0000000 1.00000000
## Lag 1     0.9533172    0.9628283  0.0298971515 0.9628320 0.85314522
## Lag 5     0.7940939    0.8294131  0.0166336360 0.8271444 0.46601322
## Lag 10    0.6400047    0.6871541  0.0033106558 0.6837801 0.23614759
## Lag 50    0.1389541    0.1792229 -0.0006441587 0.1562898 0.01244334
##        var_Eartag var_Follower        var_e
## Lag 0  1.00000000  1.000000000  1.000000000
## Lag 1  0.82709940  0.358445126 -0.002670875
## Lag 5  0.47151913  0.033674681 -0.003854224
## Lag 10 0.25887238  0.009985289  0.002850645
## Lag 50 0.01294272 -0.002489581  0.003356217
effectiveSize(m3.mcmc.chain)
## Locat_eff[1] Locat_eff[2]     deviance       eff_wt       rho_ef 
##     1728.512     1515.008    56487.289     1514.854     5751.884 
##   var_Eartag var_Follower        var_e 
##     5313.879    32129.247    80384.053
geweke.diag(m3.mcmc.chain)
## [[1]]
## 
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5 
## 
## Locat_eff[1] Locat_eff[2]     deviance       eff_wt       rho_ef 
##      0.17577     -0.24695     -0.37251      0.02375      0.99474 
##   var_Eartag var_Follower        var_e 
##     -0.92731      1.13242      0.43647
traplot(m3.mcmc.chain, col = "slateblue4")

denplot(m3.mcmc.chain, col = "slateblue4")

bugs.log("Trial_1_covariate_OpenBugs/EFcovariance_wtmodel/log.txt")
## $stats
##                    mean     sd   val2.5pc     median  val97.5pc sample
## Locat_eff[1]  2.103e+01 1.8380  1.745e+01  2.103e+01    24.6700  80000
## Locat_eff[2]  1.939e+01 1.8300  1.584e+01  1.938e+01    22.9700  80000
## deviance      3.545e+04 9.6440  3.543e+04  3.545e+04 35470.0000  80000
## eff_wt       -8.148e-02 0.0148 -1.104e-01 -8.145e-02    -0.0522  80000
## rho_ef        4.234e-01 0.2023 -1.921e-02  4.428e-01     0.7565  80000
## var_Eartag    1.423e+01 5.0390  7.399e+00  1.328e+01    26.0400  80000
## var_Follower  1.431e+00 0.5798  6.502e-01  1.322e+00     2.8550  80000
## var_e         6.654e+01 1.3370  6.396e+01  6.652e+01    69.2100  80000
## 
## $DIC
##        Dbar  Dhat   DIC    pD
## y     35450 35410 35490 42.45
## total 35450 35410 35490 42.45

2.2. Summary posterior distribution

summary(m3.mcmc.chain)
## 
## Iterations = 2001:82000
## Thinning interval = 1 
## Number of chains = 1 
## Sample size per chain = 80000 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                    Mean      SD  Naive SE Time-series SE
## Locat_eff[1]  2.103e+01  1.8377 6.497e-03      0.0442009
## Locat_eff[2]  1.939e+01  1.8302 6.471e-03      0.0470212
## deviance      3.545e+04 10.0746 3.562e-02      0.0423890
## eff_wt       -8.148e-02  0.0148 5.233e-05      0.0003803
## rho_ef        4.234e-01  0.2023 7.152e-04      0.0026671
## var_Eartag    1.423e+01  5.0388 1.781e-02      0.0691230
## var_Follower  1.431e+00  0.5798 2.050e-03      0.0032346
## var_e         6.654e+01  1.3370 4.727e-03      0.0047157
## 
## 2. Quantiles for each variable:
## 
##                    2.5%        25%        50%        75%      97.5%
## Locat_eff[1]    17.4500  1.979e+01  2.103e+01  2.225e+01  2.467e+01
## Locat_eff[2]    15.8000  1.817e+01  1.938e+01  2.061e+01  2.297e+01
## deviance     35430.0000  3.544e+04  3.545e+04  3.546e+04  3.547e+04
## eff_wt          -0.1103 -9.164e-02 -8.152e-02 -7.144e-02 -5.251e-02
## rho_ef          -0.0220  2.973e-01  4.424e-01  5.718e-01  7.583e-01
## var_Eartag       7.4030  1.074e+01  1.328e+01  1.661e+01  2.650e+01
## var_Follower     0.6497  1.028e+00  1.321e+00  1.709e+00  2.856e+00
## var_e           63.9600  6.563e+01  6.652e+01  6.743e+01  6.921e+01

Plot of posterior correlations between model parameters from MCMC simulation

parcorplot(m3.mcmc.chain,col = terrain.colors(15,0.5,T), cex.axis=0.5)