Bayesian estimating variance components visit length
\(Results\ bayesian\ estimating\ of\ variance\ components\ (proportion\ of\ variance)\ with\ Stan\ program,\\ on\ 6258\ records\ of\ visit\ length\ time\ at\ the\ feeder\ when\ the\ next\ visit\ was\ greater\ than\ or\ equal\ to\ 600\ sc,\\ from\ 7\ trials,\ including\ locations\ (2\ per\ trial),\ median\ weight\ and\ hour\ entry\ at\ the\ feeder\ as\ fixed\ effects\ and\ Eartag (135\ individuals)\\ and\ followers\ (135)\ as\ random\ effects\ in\ the\ mixed\ models.\)
\(iter = 12000,\ chain= 3,\ burn-in = 2000,\ Thin=1.\)
\(For\ the\ fixed\ parameters\ in\ {\beta},\ flat\ priors\ were\ assumed,\ thus\ {\beta}\ {\sim} U(-\infty,+\infty),\\the\ priors\ distributions\ for\ covariance\ components\ {\sigma}_d^2,\ {\sigma}_f^2\ {\sim }\ U(0,100),\\ {\rho} {\sim}\ U(-1,1)\ and\ the\ prior\ distribution\ for\ the\ error\ variance\ was\ {\sigma}_e^2\ {\sim}\ U(0,\infty).\)
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 1.0000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 -0.0806765135 0.078348294 0.042152044 0.050582159 -0.007527785
## Lag 5 0.0040981455 -0.004334612 -0.011696204 0.001598290 -0.003642978
## Lag 10 -0.0010802935 -0.009251905 0.005329925 -0.002660295 -0.002894577
## Lag 50 -0.0005191697 0.010638242 0.004452321 0.003370326 -0.002474767
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000e+00 1.0000000000
## Lag 1 0.095722791 -0.057859814 -0.109054095 8.371408e-02 -0.0130269561
## Lag 5 -0.010278623 0.001043675 -0.008338515 1.718260e-03 -0.0042566663
## Lag 10 -0.014536064 0.001293064 -0.006472716 2.542436e-06 0.0017099812
## Lag 50 -0.003652679 0.002452046 -0.003163743 -1.008490e-02 0.0002246578
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## Lag 0 1.0000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.0244181949 -0.034779280 0.112927880 -0.007397232 0.063437149
## Lag 5 -0.0052511618 0.009871005 -0.002853504 -0.001580639 -0.003744466
## Lag 10 0.0076000113 0.003383672 0.000905834 0.005924726 -0.011321778
## Lag 50 0.0002176478 -0.003353398 0.010113865 0.001573876 0.005160267
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## Lag 0 1.000000000 1.000000000 1.0000000000 1.000000000 1.0000000000
## Lag 1 0.066535111 0.070244593 0.0665812518 0.044779851 0.0246942090
## Lag 5 -0.008527170 -0.002411589 -0.0069813602 0.001607147 -0.0011808816
## Lag 10 0.001816267 -0.011194250 0.0009857068 -0.001613891 -0.0076916600
## Lag 50 -0.002091288 0.005307324 -0.0055213201 -0.002367464 -0.0009487992
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## Lag 0 1.000000000 1.000000000 1.000000e+00 1.000000000 1.000000000
## Lag 1 -0.007668466 -0.005122568 -1.759793e-02 -0.006385269 -0.036925004
## Lag 5 -0.004592072 -0.008128433 2.687776e-05 -0.006969032 -0.005042282
## Lag 10 0.006374891 -0.003965750 -7.686399e-04 -0.008295338 -0.001454742
## Lag 50 -0.001282225 -0.004836014 1.213604e-03 -0.008188033 0.009420749
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## Lag 0 1.000000000 1.0000000000 1.000000000 1.0000000000 1.000000e+00
## Lag 1 -0.033137389 -0.0662346791 -0.041456446 -0.0251601236 5.316397e-03
## Lag 5 0.004756246 0.0044317102 -0.001668097 -0.0008752910 -1.070280e-03
## Lag 10 -0.005371129 -0.0002255266 -0.001648272 0.0052231602 -2.917933e-06
## Lag 50 -0.002215620 0.0016739433 -0.002554802 -0.0007472463 -9.170425e-03
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## Lag 0 1.000000000 1.0000000000 1.0000000000 1.000000000 1.000000e+00
## Lag 1 0.035722995 0.0279882751 0.0358391715 0.035723553 6.070593e-02
## Lag 5 -0.010082977 0.0002044898 0.0029560448 0.007151787 -4.158019e-03
## Lag 10 0.000521334 -0.0031984623 -0.0007229254 -0.005557993 1.590099e-05
## Lag 50 0.007147066 0.0035918923 -0.0061945622 -0.004884287 2.655412e-03
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## Lag 0 1.000000000 1.000000000 1.000000000 1.0000000000 1.000000000
## Lag 1 0.061877752 0.047770821 -0.165016697 -0.0207821834 -0.054618833
## Lag 5 0.003346751 -0.010033002 0.003108077 -0.0011979405 -0.005285141
## Lag 10 0.002917041 -0.007839018 -0.006197676 -0.0039672420 -0.005723229
## Lag 50 -0.006221501 -0.006447905 -0.007516538 0.0001474205 0.007005817
## prp_var_eartag prp_var_error lp__
## Lag 0 1.0000000000 1.0000000000 1.000000000
## Lag 1 -0.0271228526 -0.0271228526 0.468498851
## Lag 5 -0.0025122619 -0.0025122619 0.015233802
## Lag 10 -0.0037570833 -0.0037570833 -0.021305364
## Lag 50 -0.0005361679 -0.0005361679 -0.003040697effectiveSize(outp1)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4 Loc1_t_5
## 34778.96 25618.35 27693.92 26925.65 30293.29
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## 25334.18 33507.47 35744.71 25592.16 30215.31
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## 28264.82 32199.50 22925.75 30700.12 24136.79
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 23464.10 24386.04 24711.80 25626.80 26355.33
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## 28219.20 28697.94 30563.96 29307.12 29853.53
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## 31128.01 33700.65 31904.75 30382.31 27414.40
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## 26912.94 26566.75 25347.93 26294.39 25398.51
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## 24945.06 25739.18 41990.79 28433.05 34625.21
## prp_var_eartag prp_var_error lp__
## 28881.60 28881.60 10979.76geweke.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
## 0.003529 -2.612762 -0.817744 1.369892 2.115478
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## -0.391547 -1.422575 -1.650831 -1.044948 0.519910
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## 0.116349 1.126305 0.008929 -0.387358 1.375316
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 1.673418 2.092870 1.141099 0.616561 1.062574
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## 1.594087 0.904526 1.089101 2.568498 0.271522
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## 0.916690 1.976910 0.484038 0.728033 1.497959
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## 1.306614 1.619677 2.035635 1.900576 2.239521
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## 0.343686 1.829840 -1.297720 -0.135402 -1.053953
## prp_var_eartag prp_var_error lp__
## 0.043331 -0.043331 0.679905
##
##
## [[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
## 1.2229 0.8824 0.2784 -1.5415 0.1560
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## 1.5259 -0.8987 -0.3528 1.0111 -0.2718
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## -0.2831 0.3371 0.8776 -2.2134 -1.0251
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## 0.1271 -0.9564 -0.9594 0.3462 0.2203
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## -0.4621 -0.9327 0.8954 -0.4234 -0.2630
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## -1.0004 -0.9423 -0.5618 0.6243 -0.4159
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## -0.3137 0.1408 -1.0270 -0.8621 -1.6123
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## -0.0967 -0.8391 0.4239 -0.0389 1.0734
## prp_var_eartag prp_var_error lp__
## -0.1581 0.1581 -1.5447
##
##
## [[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
## 0.26652 -0.36798 0.26560 -0.34874 1.05720
## Loc1_t_6 Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3
## 0.79832 0.01751 1.80523 1.13484 -0.02947
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 h_ent_1
## 0.40549 1.48545 3.31964 -0.11039 -1.91382
## h_ent_2 h_ent_3 h_ent_4 h_ent_5 h_ent_6
## -1.72381 -2.60233 -1.45159 -1.50384 -2.20918
## h_ent_7 h_ent_8 h_ent_9 h_ent_10 h_ent_11
## -2.23738 -1.87938 -0.18026 -1.58359 -1.69469
## h_ent_12 h_ent_13 h_ent_14 h_ent_15 h_ent_16
## 0.22213 -0.58635 0.27379 -1.52316 0.13548
## h_ent_17 h_ent_18 h_ent_19 h_ent_20 h_ent_21
## -1.20320 -1.62935 -1.52729 -2.02067 -2.32837
## h_ent_22 h_ent_23 Median Weight var_eartag var_error
## -1.69286 -1.67457 -1.00067 -1.35059 -0.66647
## prp_var_eartag prp_var_error lp__
## -1.30662 1.30662 -0.11966gelman.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 1.625e+01 1.233280 7.120e-03 6.763e-03
## Loc1_t_2 1.143e+01 1.140711 6.586e-03 7.323e-03
## Loc1_t_3 1.233e+01 1.163985 6.720e-03 7.165e-03
## Loc1_t_4 1.103e+01 1.298799 7.499e-03 8.153e-03
## Loc1_t_5 1.245e+01 1.326909 7.661e-03 7.865e-03
## Loc1_t_6 8.357e+00 1.231078 7.108e-03 8.004e-03
## Loc1_t_7 1.297e+01 1.324038 7.644e-03 7.391e-03
## Loc2_t_1 1.591e+01 1.244530 7.185e-03 6.707e-03
## Loc2_t_2 1.146e+01 1.141210 6.589e-03 7.371e-03
## Loc2_t_3 1.907e+01 1.187386 6.855e-03 7.044e-03
## Loc2_t_4 1.205e+01 1.303935 7.528e-03 7.915e-03
## Loc2_t_5 1.250e+01 1.332989 7.696e-03 7.656e-03
## Loc2_t_6 1.042e+01 1.239801 7.158e-03 8.295e-03
## Loc2_t_7 1.279e+01 1.339263 7.732e-03 7.929e-03
## h_ent_1 -1.185e-01 0.466678 2.694e-03 3.026e-03
## h_ent_2 -8.526e-01 0.469054 2.708e-03 3.096e-03
## h_ent_3 -8.231e-01 0.467866 2.701e-03 3.033e-03
## h_ent_4 -7.093e-01 0.478932 2.765e-03 3.076e-03
## h_ent_5 -1.093e+00 0.501357 2.895e-03 3.156e-03
## h_ent_6 -1.132e+00 0.549781 3.174e-03 3.402e-03
## h_ent_7 -7.088e-01 0.672535 3.883e-03 4.006e-03
## h_ent_8 5.105e-01 0.795673 4.594e-03 4.699e-03
## h_ent_9 -1.630e-01 0.744882 4.301e-03 4.262e-03
## h_ent_10 9.569e-01 0.701217 4.048e-03 4.096e-03
## h_ent_11 3.248e-01 0.817672 4.721e-03 4.732e-03
## h_ent_12 1.916e+00 1.073864 6.200e-03 6.113e-03
## h_ent_13 1.830e-01 1.617140 9.337e-03 8.892e-03
## h_ent_14 -1.482e+00 1.282936 7.407e-03 7.229e-03
## h_ent_15 2.886e+00 0.808261 4.666e-03 4.640e-03
## h_ent_16 2.725e+00 0.620806 3.584e-03 3.753e-03
## h_ent_17 1.680e+00 0.537559 3.104e-03 3.290e-03
## h_ent_18 4.561e-01 0.515324 2.975e-03 3.180e-03
## h_ent_19 4.776e-01 0.500962 2.892e-03 3.160e-03
## h_ent_20 3.531e-03 0.510864 2.949e-03 3.184e-03
## h_ent_21 2.793e-01 0.487518 2.815e-03 3.087e-03
## h_ent_22 5.813e-01 0.481914 2.782e-03 3.071e-03
## h_ent_23 -3.649e-01 0.482611 2.786e-03 3.023e-03
## Median Weight -2.886e-02 0.005356 3.092e-05 2.644e-05
## var_eartag 1.094e+01 1.691085 9.763e-03 1.005e-02
## var_error 4.779e+01 0.863240 4.984e-03 4.690e-03
## prp_var_eartag 1.857e-01 0.023363 1.349e-04 1.378e-04
## prp_var_error 8.143e-01 0.023363 1.349e-04 1.378e-04
## lp__ -1.545e+04 9.569542 5.525e-02 9.134e-02
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.384e+01 1.541e+01 1.625e+01 1.707e+01 1.867e+01
## Loc1_t_2 9.179e+00 1.067e+01 1.143e+01 1.219e+01 1.367e+01
## Loc1_t_3 1.007e+01 1.155e+01 1.233e+01 1.312e+01 1.462e+01
## Loc1_t_4 8.479e+00 1.016e+01 1.103e+01 1.190e+01 1.362e+01
## Loc1_t_5 9.838e+00 1.156e+01 1.245e+01 1.334e+01 1.503e+01
## Loc1_t_6 5.916e+00 7.533e+00 8.362e+00 9.184e+00 1.077e+01
## Loc1_t_7 1.039e+01 1.208e+01 1.297e+01 1.386e+01 1.555e+01
## Loc2_t_1 1.348e+01 1.507e+01 1.591e+01 1.675e+01 1.836e+01
## Loc2_t_2 9.248e+00 1.068e+01 1.146e+01 1.223e+01 1.369e+01
## Loc2_t_3 1.673e+01 1.828e+01 1.907e+01 1.987e+01 2.138e+01
## Loc2_t_4 9.522e+00 1.116e+01 1.205e+01 1.291e+01 1.461e+01
## Loc2_t_5 9.900e+00 1.160e+01 1.249e+01 1.340e+01 1.513e+01
## Loc2_t_6 7.984e+00 9.592e+00 1.042e+01 1.125e+01 1.282e+01
## Loc2_t_7 1.017e+01 1.190e+01 1.278e+01 1.368e+01 1.539e+01
## h_ent_1 -1.030e+00 -4.359e-01 -1.170e-01 1.960e-01 7.974e-01
## h_ent_2 -1.771e+00 -1.170e+00 -8.519e-01 -5.350e-01 6.828e-02
## h_ent_3 -1.739e+00 -1.139e+00 -8.262e-01 -5.076e-01 8.928e-02
## h_ent_4 -1.652e+00 -1.032e+00 -7.125e-01 -3.832e-01 2.298e-01
## h_ent_5 -2.083e+00 -1.431e+00 -1.094e+00 -7.531e-01 -1.133e-01
## h_ent_6 -2.219e+00 -1.500e+00 -1.131e+00 -7.644e-01 -5.707e-02
## h_ent_7 -2.016e+00 -1.166e+00 -7.034e-01 -2.502e-01 5.959e-01
## h_ent_8 -1.030e+00 -2.957e-02 5.039e-01 1.052e+00 2.067e+00
## h_ent_9 -1.612e+00 -6.661e-01 -1.692e-01 3.442e-01 1.287e+00
## h_ent_10 -4.205e-01 4.829e-01 9.573e-01 1.430e+00 2.344e+00
## h_ent_11 -1.281e+00 -2.259e-01 3.254e-01 8.714e-01 1.925e+00
## h_ent_12 -1.888e-01 1.188e+00 1.917e+00 2.637e+00 4.022e+00
## h_ent_13 -2.952e+00 -9.046e-01 1.803e-01 1.283e+00 3.337e+00
## h_ent_14 -3.994e+00 -2.337e+00 -1.477e+00 -6.345e-01 1.042e+00
## h_ent_15 1.300e+00 2.349e+00 2.884e+00 3.430e+00 4.457e+00
## h_ent_16 1.515e+00 2.302e+00 2.726e+00 3.143e+00 3.943e+00
## h_ent_17 6.308e-01 1.314e+00 1.680e+00 2.047e+00 2.716e+00
## h_ent_18 -5.557e-01 1.069e-01 4.540e-01 8.051e-01 1.466e+00
## h_ent_19 -5.127e-01 1.396e-01 4.773e-01 8.129e-01 1.465e+00
## h_ent_20 -1.001e+00 -3.375e-01 2.022e-03 3.486e-01 9.995e-01
## h_ent_21 -6.749e-01 -5.041e-02 2.785e-01 6.087e-01 1.232e+00
## h_ent_22 -3.664e-01 2.567e-01 5.809e-01 9.123e-01 1.518e+00
## h_ent_23 -1.301e+00 -6.917e-01 -3.685e-01 -3.559e-02 5.819e-01
## Median Weight -3.941e-02 -3.247e-02 -2.894e-02 -2.523e-02 -1.837e-02
## var_eartag 8.033e+00 9.757e+00 1.081e+01 1.197e+01 1.463e+01
## var_error 4.612e+01 4.721e+01 4.778e+01 4.837e+01 4.950e+01
## prp_var_eartag 1.437e-01 1.694e-01 1.844e-01 2.007e-01 2.354e-01
## prp_var_error 7.646e-01 7.993e-01 8.156e-01 8.306e-01 8.563e-01
## lp__ -1.547e+04 -1.546e+04 -1.545e+04 -1.545e+04 -1.543e+04print(M1600s.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] 16.25 0.01 1.23 13.84 15.41 16.25 17.07
## beta[2] 11.43 0.01 1.14 9.18 10.67 11.43 12.19
## beta[3] 12.33 0.01 1.16 10.07 11.55 12.33 13.12
## beta[4] 11.03 0.01 1.30 8.48 10.16 11.03 11.90
## beta[5] 12.45 0.01 1.33 9.84 11.56 12.45 13.34
## beta[6] 8.36 0.01 1.23 5.92 7.53 8.36 9.18
## beta[7] 12.97 0.01 1.32 10.39 12.08 12.97 13.86
## beta[8] 15.91 0.01 1.24 13.48 15.07 15.91 16.75
## beta[9] 11.46 0.01 1.14 9.25 10.68 11.46 12.23
## beta[10] 19.07 0.01 1.19 16.73 18.28 19.07 19.87
## beta[11] 12.05 0.01 1.30 9.52 11.16 12.05 12.91
## beta[12] 12.50 0.01 1.33 9.90 11.60 12.49 13.40
## beta[13] 10.42 0.01 1.24 7.98 9.59 10.42 11.25
## beta[14] 12.79 0.01 1.34 10.17 11.90 12.78 13.68
## beta[15] -0.12 0.00 0.47 -1.03 -0.44 -0.12 0.20
## beta[16] -0.85 0.00 0.47 -1.77 -1.17 -0.85 -0.53
## beta[17] -0.82 0.00 0.47 -1.74 -1.14 -0.83 -0.51
## beta[18] -0.71 0.00 0.48 -1.65 -1.03 -0.71 -0.38
## beta[19] -1.09 0.00 0.50 -2.08 -1.43 -1.09 -0.75
## beta[20] -1.13 0.00 0.55 -2.22 -1.50 -1.13 -0.76
## beta[21] -0.71 0.00 0.67 -2.02 -1.17 -0.70 -0.25
## beta[22] 0.51 0.00 0.80 -1.03 -0.03 0.50 1.05
## beta[23] -0.16 0.00 0.74 -1.61 -0.67 -0.17 0.34
## beta[24] 0.96 0.00 0.70 -0.42 0.48 0.96 1.43
## beta[25] 0.32 0.00 0.82 -1.28 -0.23 0.33 0.87
## beta[26] 1.92 0.01 1.07 -0.19 1.19 1.92 2.64
## beta[27] 0.18 0.01 1.62 -2.95 -0.90 0.18 1.28
## beta[28] -1.48 0.01 1.28 -3.99 -2.34 -1.48 -0.63
## beta[29] 2.89 0.00 0.81 1.30 2.35 2.88 3.43
## beta[30] 2.72 0.00 0.62 1.51 2.30 2.73 3.14
## beta[31] 1.68 0.00 0.54 0.63 1.31 1.68 2.05
## beta[32] 0.46 0.00 0.52 -0.56 0.11 0.45 0.81
## beta[33] 0.48 0.00 0.50 -0.51 0.14 0.48 0.81
## beta[34] 0.00 0.00 0.51 -1.00 -0.34 0.00 0.35
## beta[35] 0.28 0.00 0.49 -0.67 -0.05 0.28 0.61
## beta[36] 0.58 0.00 0.48 -0.37 0.26 0.58 0.91
## beta[37] -0.36 0.00 0.48 -1.30 -0.69 -0.37 -0.04
## beta[38] -0.03 0.00 0.01 -0.04 -0.03 -0.03 -0.03
## var_eartag 10.94 0.01 1.69 8.03 9.76 10.81 11.97
## var_error 47.79 0.00 0.86 46.12 47.21 47.78 48.37
## prp_var_eartag 0.19 0.00 0.02 0.14 0.17 0.18 0.20
## prp_var_error 0.81 0.00 0.02 0.76 0.80 0.82 0.83
## lp__ -15452.00 0.09 9.57 -15471.90 -15458.21 -15451.63 -15445.36
## 97.5% n_eff Rhat
## beta[1] 18.67 32612 1
## beta[2] 13.67 24052 1
## beta[3] 14.62 26005 1
## beta[4] 13.62 24697 1
## beta[5] 15.03 28228 1
## beta[6] 10.77 22939 1
## beta[7] 15.55 31971 1
## beta[8] 18.36 34447 1
## beta[9] 13.69 23684 1
## beta[10] 21.38 27982 1
## beta[11] 14.61 26762 1
## beta[12] 15.13 28366 1
## beta[13] 12.82 22689 1
## beta[14] 15.39 28073 1
## beta[15] 0.80 23835 1
## beta[16] 0.07 23656 1
## beta[17] 0.09 23829 1
## beta[18] 0.23 23906 1
## beta[19] -0.11 24499 1
## beta[20] -0.06 25559 1
## beta[21] 0.60 28101 1
## beta[22] 2.07 29400 1
## beta[23] 1.29 29777 1
## beta[24] 2.34 29348 1
## beta[25] 1.92 29473 1
## beta[26] 4.02 30116 1
## beta[27] 3.34 32379 1
## beta[28] 1.04 31760 1
## beta[29] 4.46 30299 1
## beta[30] 3.94 26377 1
## beta[31] 2.72 26334 1
## beta[32] 1.47 25906 1
## beta[33] 1.47 25189 1
## beta[34] 1.00 24983 1
## beta[35] 1.23 24296 1
## beta[36] 1.52 23076 1
## beta[37] 0.58 25240 1
## beta[38] -0.02 40783 1
## var_eartag 14.63 26898 1
## var_error 49.50 32810 1
## prp_var_eartag 0.24 27440 1
## prp_var_error 0.86 27440 1
## lp__ -15434.28 10879 1
##
## Samples were drawn using NUTS(diag_e) at Wed Jan 22 12:10:33 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 1.000000000 1.00000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.365430111 0.49877133 0.474686702 0.486933976 0.457939972
## Lag 5 0.083889777 0.15257757 0.134260531 0.150178684 0.144391755
## Lag 10 0.016100268 0.04443468 0.030558521 0.042921593 0.043164497
## Lag 50 0.006546267 -0.00996789 -0.002706876 -0.007047579 -0.009404252
## 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 0.533873284 0.398627343 0.336376683 0.515457398 0.444691511
## Lag 5 0.166057837 0.109939893 0.077479108 0.165207740 0.142759364
## Lag 10 0.051500765 0.040046817 0.019949873 0.035523183 0.036947472
## Lag 50 -0.001878565 -0.001530104 -0.004108533 0.007822075 -0.001294146
## Loc2_t_4 Loc2_t_5 Loc2_t_6 Loc2_t_7 Hour_entry_1
## Lag 0 1.00000000 1.000000000 1.000000000 1.000000000 1.0000000000
## Lag 1 0.48577844 0.451473193 0.514069048 0.444910779 0.2217184668
## Lag 5 0.14625026 0.139901962 0.159303551 0.132410455 0.1044794651
## Lag 10 0.05058024 0.037488186 0.048654673 0.026834787 0.0368238491
## Lag 50 -0.00828065 0.007871835 -0.006711266 0.003192691 0.0006110651
## Hour_entry_2 Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## Lag 0 1.0000000000 1.00000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.2420894179 0.24588792 0.220996754 0.204923418 0.163166145
## Lag 5 0.1224509057 0.11825359 0.126467702 0.104429061 0.091455170
## Lag 10 0.0509112427 0.04444724 0.049588242 0.046923402 0.036040434
## Lag 50 -0.0006571431 0.00441772 0.006431162 0.005901224 0.001531167
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10 Hour_entry_11
## Lag 0 1.00000000 1.000000000 1.000000000 1.000000000 1.00000000
## Lag 1 0.07956726 0.035659433 0.050849956 0.065120305 0.04423231
## Lag 5 0.06860256 0.032306171 0.051645861 0.061997523 0.03970492
## Lag 10 0.03543192 0.023834547 0.017430600 0.025237139 0.01765515
## Lag 50 0.00118147 -0.004310668 0.005605319 0.007481644 0.01268018
## Hour_entry_12 Hour_entry_13 Hour_entry_14 Hour_entry_15 Hour_entry_16
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.001948751 -0.049573809 -0.022493816 0.033273387 0.100990348
## Lag 5 0.025255568 0.014660255 0.019651480 0.049289579 0.071258462
## Lag 10 0.018883339 0.011105323 0.016812569 0.014170854 0.036340805
## Lag 50 -0.001338919 -0.004232824 0.006203011 0.003366035 0.004962292
## Hour_entry_17 Hour_entry_18 Hour_entry_19 Hour_entry_20 Hour_entry_21
## Lag 0 1.00000000 1.000000000 1.0000000000 1.000000000 1.000000e+00
## Lag 1 0.15589394 0.180380776 0.1879839520 0.184100221 2.141039e-01
## Lag 5 0.09120608 0.102328760 0.1047695244 0.103853497 1.138075e-01
## Lag 10 0.02902115 0.037270521 0.0399253052 0.031347231 4.713363e-02
## Lag 50 0.00780725 0.008141829 -0.0008713695 0.005786387 -7.767529e-05
## Hour_entry_22 Hour_entry_23 Median Weight var_eartag var_follower
## Lag 0 1.000000000 1.000000000 1.000000000 1.0000000000 1.0000000
## Lag 1 0.224137150 0.214543828 0.160154356 0.0838933759 0.9387785
## Lag 5 0.115610716 0.120282118 0.030794237 0.0268753009 0.8373863
## Lag 10 0.047456936 0.035322133 0.001545536 -0.0005779126 0.7440077
## Lag 50 0.003974022 0.006431523 0.001609892 0.0072661414 0.4275423
## var_error prp_var_eartag prp_var_follower prp_var_error lp__
## Lag 0 1.000000000 1.000000000 1.0000000 1.0000000000 1.0000000
## Lag 1 -0.076765751 0.078772561 0.9379929 0.0805461659 0.9863423
## Lag 5 0.003566509 0.026058411 0.8367768 0.0276687037 0.9492876
## Lag 10 0.012382689 -0.001133064 0.7440610 -0.0003119371 0.9105897
## Lag 50 0.003620247 0.007450340 0.4278819 0.0079491825 0.6751050effectiveSize(outp2)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## 9150.4992 6135.0049 6964.5044 6384.5229
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 6509.7424 5552.2615 7655.7303 8947.2990
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 5901.3310 6630.4267 6059.5578 6719.0575
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## 5930.7290 6914.7592 7877.4538 7435.3168
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## 7918.4236 7410.6393 8489.4962 9487.5934
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## 11703.8238 14456.0264 13425.1094 11557.7417
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## 13775.8799 17020.5408 24759.3993 22138.2891
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## 15800.6814 10474.2755 9157.7004 8648.4182
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## 8431.7294 8888.0045 8011.5964 7939.9513
## Hour_entry_23 Median Weight var_eartag var_follower
## 8051.5888 15465.5130 17209.2564 252.8898
## var_error prp_var_eartag prp_var_follower prp_var_error
## 31782.9648 17466.1750 263.7279 17311.8902
## lp__
## 122.6549geweke.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
## -0.02377 -0.46574 -0.11086 -0.38246
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 1.27792 1.54126 -0.85298 0.09449
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## -0.24224 0.91579 -0.71007 0.21900
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## 0.73613 0.43663 -1.12954 -0.02496
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## 0.25157 0.39260 -0.55528 0.81844
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## 0.84038 1.65142 -0.51422 0.04664
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## 0.47887 0.07004 0.80239 0.26836
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## 0.37226 -0.18673 0.16015 1.18478
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## 0.25439 -0.60634 0.54535 0.76083
## Hour_entry_23 Median Weight var_eartag var_follower
## 0.54547 -0.89537 -0.15852 1.12274
## var_error prp_var_eartag prp_var_follower prp_var_error
## -0.14490 -0.22112 1.11645 -0.35013
## lp__
## -2.32095
##
##
## [[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
## 1.2767 1.6545 1.1753 -0.4917
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 0.5688 -0.3194 0.4090 2.5867
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 2.0611 2.3246 0.4045 1.0905
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## 3.0198 0.4590 -1.8639 -2.3406
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## -1.8842 -2.2951 -1.9862 -2.3738
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## -1.8891 -1.6750 -3.0928 -2.2913
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## -1.4324 -2.4266 -1.3546 -0.3658
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## -1.9634 -2.1584 -2.1966 -2.0259
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## -2.1247 -2.0141 -2.0998 -2.5858
## Hour_entry_23 Median Weight var_eartag var_follower
## -2.4264 -0.7325 2.1439 0.2199
## var_error prp_var_eartag prp_var_follower prp_var_error
## 2.0771 1.9236 0.2069 -2.0334
## lp__
## -0.3732
##
##
## [[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
## -1.47591 0.46908 -0.45203 -0.48389
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 0.37650 -0.36703 -0.51223 -0.35498
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## -0.13744 0.88151 -1.18395 0.75872
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## 1.69603 1.54953 0.18071 0.20664
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## -0.63750 -0.27833 -0.27674 -0.67851
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## -0.52385 -0.62072 0.14912 0.32138
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## -0.08377 -0.43127 -1.76133 0.17019
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## -0.50955 -0.59516 -0.27756 -0.02111
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## 0.45880 -0.61369 -0.19191 0.10567
## Hour_entry_23 Median Weight var_eartag var_follower
## -0.55132 -0.76664 0.31907 -1.53488
## var_error prp_var_eartag prp_var_follower prp_var_error
## -0.34364 0.54137 -1.52854 -0.02961
## lp__
## -0.21418gelman.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 1.04 1.14
## var_error 1.00 1.00
## prp_var_eartag 1.00 1.00
## prp_var_follower 1.04 1.14
## prp_var_error 1.00 1.00
## lp__ 1.04 1.13traplot(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 1.625e+01 1.225616 7.076e-03 1.284e-02
## Loc1_t_2 1.142e+01 1.146193 6.618e-03 1.484e-02
## Loc1_t_3 1.231e+01 1.171862 6.766e-03 1.417e-02
## Loc1_t_4 1.106e+01 1.299525 7.503e-03 1.642e-02
## Loc1_t_5 1.244e+01 1.340503 7.739e-03 1.661e-02
## Loc1_t_6 8.368e+00 1.216330 7.022e-03 1.659e-02
## Loc1_t_7 1.300e+01 1.318029 7.610e-03 1.513e-02
## Loc2_t_1 1.591e+01 1.246256 7.195e-03 1.327e-02
## Loc2_t_2 1.146e+01 1.146612 6.620e-03 1.496e-02
## Loc2_t_3 1.911e+01 1.205643 6.961e-03 1.483e-02
## Loc2_t_4 1.202e+01 1.323160 7.639e-03 1.701e-02
## Loc2_t_5 1.250e+01 1.341756 7.747e-03 1.638e-02
## Loc2_t_6 1.044e+01 1.254565 7.243e-03 1.631e-02
## Loc2_t_7 1.281e+01 1.326376 7.658e-03 1.599e-02
## Hour_entry_1 -1.224e-01 0.473415 2.733e-03 5.341e-03
## Hour_entry_2 -8.590e-01 0.471744 2.724e-03 5.474e-03
## Hour_entry_3 -8.257e-01 0.465487 2.687e-03 5.245e-03
## Hour_entry_4 -7.137e-01 0.476082 2.749e-03 5.543e-03
## Hour_entry_5 -1.090e+00 0.502247 2.900e-03 5.488e-03
## Hour_entry_6 -1.133e+00 0.553981 3.198e-03 5.706e-03
## Hour_entry_7 -7.046e-01 0.675561 3.900e-03 6.277e-03
## Hour_entry_8 5.270e-01 0.791506 4.570e-03 6.583e-03
## Hour_entry_9 -1.626e-01 0.738866 4.266e-03 6.395e-03
## Hour_entry_10 9.611e-01 0.696755 4.023e-03 6.486e-03
## Hour_entry_11 3.261e-01 0.819375 4.731e-03 7.008e-03
## Hour_entry_12 1.901e+00 1.083998 6.258e-03 8.378e-03
## Hour_entry_13 1.760e-01 1.610991 9.301e-03 1.028e-02
## Hour_entry_14 -1.493e+00 1.290909 7.453e-03 8.755e-03
## Hour_entry_15 2.899e+00 0.806819 4.658e-03 6.425e-03
## Hour_entry_16 2.732e+00 0.622990 3.597e-03 6.115e-03
## Hour_entry_17 1.684e+00 0.542152 3.130e-03 5.707e-03
## Hour_entry_18 4.587e-01 0.516991 2.985e-03 5.578e-03
## Hour_entry_19 4.774e-01 0.509106 2.939e-03 5.564e-03
## Hour_entry_20 1.289e-04 0.510658 2.948e-03 5.443e-03
## Hour_entry_21 2.874e-01 0.489681 2.827e-03 5.488e-03
## Hour_entry_22 5.769e-01 0.478422 2.762e-03 5.375e-03
## Hour_entry_23 -3.688e-01 0.485061 2.801e-03 5.406e-03
## Median Weight -2.893e-02 0.005356 3.093e-05 4.332e-05
## var_eartag 1.095e+01 1.692625 9.772e-03 1.295e-02
## var_follower 6.422e-02 0.080596 4.653e-04 4.941e-03
## var_error 4.775e+01 0.862197 4.978e-03 4.845e-03
## prp_var_eartag 1.857e-01 0.023365 1.349e-04 1.774e-04
## prp_var_follower 1.093e-03 0.001371 7.913e-06 8.265e-05
## prp_var_error 8.132e-01 0.023363 1.349e-04 1.782e-04
## lp__ -1.528e+04 99.248827 5.730e-01 8.797e+00
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.387e+01 1.543e+01 1.626e+01 1.708e+01 1.866e+01
## Loc1_t_2 9.192e+00 1.064e+01 1.140e+01 1.219e+01 1.368e+01
## Loc1_t_3 1.003e+01 1.152e+01 1.231e+01 1.310e+01 1.460e+01
## Loc1_t_4 8.493e+00 1.018e+01 1.107e+01 1.194e+01 1.359e+01
## Loc1_t_5 9.781e+00 1.155e+01 1.246e+01 1.334e+01 1.505e+01
## Loc1_t_6 5.983e+00 7.550e+00 8.365e+00 9.183e+00 1.076e+01
## Loc1_t_7 1.043e+01 1.211e+01 1.298e+01 1.387e+01 1.559e+01
## Loc2_t_1 1.348e+01 1.506e+01 1.591e+01 1.675e+01 1.838e+01
## Loc2_t_2 9.206e+00 1.068e+01 1.146e+01 1.223e+01 1.370e+01
## Loc2_t_3 1.672e+01 1.830e+01 1.911e+01 1.992e+01 2.143e+01
## Loc2_t_4 9.435e+00 1.113e+01 1.202e+01 1.292e+01 1.460e+01
## Loc2_t_5 9.858e+00 1.159e+01 1.249e+01 1.340e+01 1.515e+01
## Loc2_t_6 7.985e+00 9.596e+00 1.045e+01 1.128e+01 1.289e+01
## Loc2_t_7 1.021e+01 1.192e+01 1.281e+01 1.371e+01 1.543e+01
## Hour_entry_1 -1.052e+00 -4.449e-01 -1.243e-01 1.983e-01 8.029e-01
## Hour_entry_2 -1.787e+00 -1.179e+00 -8.621e-01 -5.386e-01 6.417e-02
## Hour_entry_3 -1.731e+00 -1.142e+00 -8.269e-01 -5.117e-01 8.704e-02
## Hour_entry_4 -1.635e+00 -1.035e+00 -7.191e-01 -3.956e-01 2.331e-01
## Hour_entry_5 -2.070e+00 -1.432e+00 -1.092e+00 -7.500e-01 -1.012e-01
## Hour_entry_6 -2.226e+00 -1.502e+00 -1.134e+00 -7.596e-01 -5.474e-02
## Hour_entry_7 -2.021e+00 -1.160e+00 -7.018e-01 -2.443e-01 6.111e-01
## Hour_entry_8 -1.015e+00 -1.156e-02 5.256e-01 1.063e+00 2.067e+00
## Hour_entry_9 -1.610e+00 -6.599e-01 -1.563e-01 3.382e-01 1.281e+00
## Hour_entry_10 -4.042e-01 4.834e-01 9.651e-01 1.431e+00 2.320e+00
## Hour_entry_11 -1.273e+00 -2.236e-01 3.286e-01 8.786e-01 1.951e+00
## Hour_entry_12 -2.412e-01 1.168e+00 1.912e+00 2.631e+00 4.011e+00
## Hour_entry_13 -2.989e+00 -9.150e-01 1.786e-01 1.256e+00 3.335e+00
## Hour_entry_14 -4.047e+00 -2.348e+00 -1.488e+00 -6.310e-01 1.001e+00
## Hour_entry_15 1.315e+00 2.355e+00 2.895e+00 3.437e+00 4.492e+00
## Hour_entry_16 1.506e+00 2.314e+00 2.728e+00 3.154e+00 3.956e+00
## Hour_entry_17 6.306e-01 1.317e+00 1.686e+00 2.048e+00 2.755e+00
## Hour_entry_18 -5.589e-01 1.094e-01 4.593e-01 8.080e-01 1.472e+00
## Hour_entry_19 -5.205e-01 1.331e-01 4.775e-01 8.232e-01 1.481e+00
## Hour_entry_20 -9.993e-01 -3.407e-01 -4.242e-03 3.403e-01 1.017e+00
## Hour_entry_21 -6.727e-01 -4.070e-02 2.906e-01 6.178e-01 1.250e+00
## Hour_entry_22 -3.547e-01 2.551e-01 5.737e-01 9.002e-01 1.515e+00
## Hour_entry_23 -1.314e+00 -6.991e-01 -3.708e-01 -4.045e-02 5.856e-01
## Median Weight -3.952e-02 -3.251e-02 -2.889e-02 -2.530e-02 -1.852e-02
## var_eartag 8.052e+00 9.761e+00 1.081e+01 1.198e+01 1.467e+01
## var_follower 1.075e-03 9.863e-03 3.223e-02 8.948e-02 2.950e-01
## var_error 4.608e+01 4.716e+01 4.774e+01 4.833e+01 4.945e+01
## prp_var_eartag 1.440e-01 1.694e-01 1.843e-01 2.005e-01 2.350e-01
## prp_var_follower 1.828e-05 1.679e-04 5.484e-04 1.527e-03 5.003e-03
## prp_var_error 7.637e-01 7.985e-01 8.146e-01 8.296e-01 8.551e-01
## lp__ -1.543e+04 -1.535e+04 -1.529e+04 -1.521e+04 -1.506e+04print(M2600s.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] 16.25 0.01 1.23 13.87 15.43 16.26
## beta[2] 11.42 0.01 1.15 9.19 10.64 11.40
## beta[3] 12.31 0.01 1.17 10.03 11.52 12.31
## beta[4] 11.06 0.02 1.30 8.49 10.18 11.07
## beta[5] 12.44 0.02 1.34 9.78 11.55 12.46
## beta[6] 8.37 0.02 1.22 5.98 7.55 8.36
## beta[7] 13.00 0.02 1.32 10.43 12.11 12.98
## beta[8] 15.91 0.01 1.25 13.48 15.06 15.91
## beta[9] 11.46 0.01 1.15 9.21 10.68 11.46
## beta[10] 19.11 0.01 1.21 16.72 18.30 19.11
## beta[11] 12.02 0.02 1.32 9.43 11.13 12.02
## beta[12] 12.50 0.02 1.34 9.86 11.59 12.49
## beta[13] 10.44 0.02 1.25 7.98 9.60 10.45
## beta[14] 12.81 0.02 1.33 10.21 11.92 12.81
## beta[15] -0.12 0.01 0.47 -1.05 -0.44 -0.12
## beta[16] -0.86 0.01 0.47 -1.79 -1.18 -0.86
## beta[17] -0.83 0.01 0.47 -1.73 -1.14 -0.83
## beta[18] -0.71 0.01 0.48 -1.63 -1.03 -0.72
## beta[19] -1.09 0.01 0.50 -2.07 -1.43 -1.09
## beta[20] -1.13 0.01 0.55 -2.23 -1.50 -1.13
## beta[21] -0.70 0.01 0.68 -2.02 -1.16 -0.70
## beta[22] 0.53 0.01 0.79 -1.01 -0.01 0.53
## beta[23] -0.16 0.01 0.74 -1.61 -0.66 -0.16
## beta[24] 0.96 0.01 0.70 -0.40 0.48 0.97
## beta[25] 0.33 0.01 0.82 -1.27 -0.22 0.33
## beta[26] 1.90 0.01 1.08 -0.24 1.17 1.91
## beta[27] 0.18 0.01 1.61 -2.99 -0.91 0.18
## beta[28] -1.49 0.01 1.29 -4.05 -2.35 -1.49
## beta[29] 2.90 0.01 0.81 1.32 2.36 2.90
## beta[30] 2.73 0.01 0.62 1.51 2.31 2.73
## beta[31] 1.68 0.01 0.54 0.63 1.32 1.69
## beta[32] 0.46 0.01 0.52 -0.56 0.11 0.46
## beta[33] 0.48 0.01 0.51 -0.52 0.13 0.48
## beta[34] 0.00 0.01 0.51 -1.00 -0.34 0.00
## beta[35] 0.29 0.01 0.49 -0.67 -0.04 0.29
## beta[36] 0.58 0.01 0.48 -0.35 0.26 0.57
## beta[37] -0.37 0.01 0.49 -1.31 -0.70 -0.37
## beta[38] -0.03 0.00 0.01 -0.04 -0.03 -0.03
## var_eartag 10.95 0.01 1.69 8.05 9.76 10.81
## var_follower 0.06 0.01 0.08 0.00 0.01 0.03
## var_error 47.75 0.00 0.86 46.08 47.16 47.74
## prp_var_eartag 0.19 0.00 0.02 0.14 0.17 0.18
## prp_var_follower 0.00 0.00 0.00 0.00 0.00 0.00
## prp_var_error 0.81 0.00 0.02 0.76 0.80 0.81
## lp__ -15275.05 12.29 99.25 -15428.76 -15353.69 -15287.34
## 75% 97.5% n_eff Rhat
## beta[1] 17.08 18.66 8448 1.00
## beta[2] 12.19 13.68 5957 1.00
## beta[3] 13.10 14.60 6586 1.00
## beta[4] 11.94 13.59 6063 1.00
## beta[5] 13.34 15.05 6217 1.00
## beta[6] 9.18 10.76 5393 1.00
## beta[7] 13.87 15.59 7117 1.00
## beta[8] 16.75 18.38 8666 1.00
## beta[9] 12.23 13.70 5874 1.00
## beta[10] 19.92 21.43 6680 1.00
## beta[11] 12.92 14.60 5952 1.00
## beta[12] 13.40 15.15 6158 1.00
## beta[13] 11.28 12.89 5499 1.00
## beta[14] 13.71 15.43 6577 1.00
## beta[15] 0.20 0.80 7588 1.00
## beta[16] -0.54 0.06 6557 1.00
## beta[17] -0.51 0.09 7215 1.00
## beta[18] -0.40 0.23 6930 1.00
## beta[19] -0.75 -0.10 7490 1.00
## beta[20] -0.76 -0.05 8813 1.00
## beta[21] -0.24 0.61 10383 1.00
## beta[22] 1.06 2.07 13813 1.00
## beta[23] 0.34 1.28 12837 1.00
## beta[24] 1.43 2.32 11175 1.00
## beta[25] 0.88 1.95 13169 1.00
## beta[26] 2.63 4.01 16573 1.00
## beta[27] 1.26 3.33 23582 1.00
## beta[28] -0.63 1.00 20444 1.00
## beta[29] 3.44 4.49 14792 1.00
## beta[30] 3.15 3.96 9717 1.00
## beta[31] 2.05 2.76 7785 1.00
## beta[32] 0.81 1.47 7987 1.00
## beta[33] 0.82 1.48 7578 1.00
## beta[34] 0.34 1.02 8164 1.00
## beta[35] 0.62 1.25 7202 1.00
## beta[36] 0.90 1.52 7069 1.00
## beta[37] -0.04 0.59 7270 1.00
## beta[38] -0.03 -0.02 14943 1.00
## var_eartag 11.98 14.67 17071 1.00
## var_follower 0.09 0.29 214 1.02
## var_error 48.33 49.45 31175 1.00
## prp_var_eartag 0.20 0.24 17277 1.00
## prp_var_follower 0.00 0.01 214 1.02
## prp_var_error 0.83 0.86 16955 1.00
## lp__ -15209.40 -15059.82 65 1.03
##
## Samples were drawn using NUTS(diag_e) at Fri Jan 24 13:11:27 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 1.000000000 1.00000000 1.0000000000 1.00000000 1.00000000
## Lag 1 0.416848666 0.561333302 0.54391887 0.5644129035 0.51230341 0.60327115
## Lag 5 0.104334414 0.165475093 0.15867972 0.1726446776 0.14536674 0.20038654
## Lag 10 0.034427970 0.049541827 0.04370248 0.0502566528 0.03738161 0.07475276
## Lag 50 0.005883668 -0.005623553 0.01630415 -0.0007346966 0.02332621 -0.01410284
## Loc1_t_7 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## Lag 0 1.000000000 1.0000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.455254829 0.4026232137 0.580516880 0.497384651 0.545149799
## Lag 5 0.123235939 0.0902359338 0.200444396 0.136949681 0.173816992
## Lag 10 0.022822395 0.0235600762 0.068137592 0.039800684 0.058660639
## Lag 50 0.002036312 -0.0004787841 0.001600629 -0.009047264 -0.001415135
## Loc2_t_5 Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## Lag 0 1.000000000 1.0000000000 1.000000000 1.000000000 1.000000000
## Lag 1 0.532735227 0.5573992165 0.504232324 0.274835419 0.267565825
## Lag 5 0.134876699 0.1760229503 0.134452975 0.143352261 0.141942498
## Lag 10 0.047549639 0.0601712272 0.040351578 0.062639008 0.052991905
## Lag 50 0.003767869 -0.0002592011 0.004654229 -0.001196254 0.006719161
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6 Hour_entry_7
## Lag 0 1.000000000 1.000000000 1.000000000 1.00000000 1.000000000
## Lag 1 0.266953028 0.272055285 0.228556802 0.16505760 0.099241682
## Lag 5 0.141367872 0.141669496 0.128937244 0.10946141 0.089354874
## Lag 10 0.051849526 0.066234943 0.061265462 0.04975663 0.036776703
## Lag 50 -0.003899269 -0.004495141 0.003930058 0.01324920 -0.002429438
## Hour_entry_8 Hour_entry_9 Hour_entry_10 Hour_entry_11 Hour_entry_12
## Lag 0 1.00000000 1.00000000 1.000000000 1.000000000 1.00000000
## Lag 1 0.06227710 0.05438290 0.065825634 0.039659671 -0.01875251
## Lag 5 0.06771778 0.06060169 0.072549431 0.050008971 0.01779703
## Lag 10 0.02200225 0.01958520 0.032534469 0.030078828 0.01609498
## Lag 50 0.00579953 0.00871555 0.009608437 0.003396896 0.01661139
## Hour_entry_13 Hour_entry_14 Hour_entry_15 Hour_entry_16 Hour_entry_17
## Lag 0 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
## Lag 1 -0.029303402 -0.019321596 0.048919220 0.132933737 0.179946611
## Lag 5 0.026297240 0.022542117 0.045910835 0.085150558 0.101648531
## Lag 10 0.004735660 0.014423984 0.017548555 0.030890854 0.044561295
## Lag 50 0.007606123 -0.006829067 -0.001729145 0.001531294 -0.003499541
## Hour_entry_18 Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## Lag 0 1.000000000 1.000000000 1.00000000 1.000000000 1.00000000
## Lag 1 0.204700507 0.214254546 0.21392584 0.248929999 0.24285270
## Lag 5 0.131998552 0.124348094 0.12036900 0.136125481 0.12913949
## Lag 10 0.048242208 0.044971798 0.04852117 0.053339080 0.05400589
## Lag 50 0.004014479 0.001645161 -0.01109872 0.004530829 0.01550195
## Hour_entry_23 Median Weight rho var_eartag var_follower
## Lag 0 1.00000000 1.000000000 1.00000000 1.000000000 1.0000000
## Lag 1 0.23480220 0.213783694 0.85679157 0.082982870 0.9276690
## Lag 5 0.13420795 0.032038287 0.58245118 0.031657088 0.8022633
## Lag 10 0.04389527 0.002850187 0.38793744 0.001213619 0.6930955
## Lag 50 -0.00441950 -0.002742106 0.05963788 -0.004382398 0.2648275
## var_error prp_var_eartag prp_var_follower prp_var_error lp__
## Lag 0 1.000000000 1.0000000000 1.0000000 1.000000000 1.0000000
## Lag 1 -0.060387418 0.0791118177 0.9269114 0.080939842 0.9740855
## Lag 5 0.006695304 0.0291789870 0.8011212 0.031229216 0.9046406
## Lag 10 -0.001296822 0.0007614215 0.6925437 0.002561068 0.8321043
## Lag 50 0.010233999 -0.0043289267 0.2651240 -0.003889684 0.4227874effectiveSize(outp3)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## 8339.8199 5577.0191 6045.5202 5803.7871
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 6259.8220 4904.7541 7420.7391 8721.3791
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 5277.4944 6681.2632 5543.2464 6480.3002
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## 5753.4017 6769.3160 6517.4232 6644.4896
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## 6929.7355 6429.5334 7138.4163 8653.5913
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## 10344.6463 13515.2452 12806.4663 11670.3658
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## 13781.1623 21970.0578 23212.4426 19894.2598
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## 15077.8297 10556.6432 8702.8918 7735.8555
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## 7718.4443 7532.3791 7209.8594 7232.2168
## Hour_entry_23 Median Weight rho var_eartag
## 7179.7278 15136.2984 1392.1006 16604.0193
## var_follower var_error prp_var_eartag prp_var_follower
## 439.2836 29401.8973 16786.9890 439.8346
## prp_var_error lp__
## 16176.2321 260.6580geweke.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
## -0.65885 0.28495 -0.70839 -0.50906
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 0.79588 -1.07038 2.50044 -1.63292
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## -0.41263 -1.09324 0.01499 0.60595
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## 1.66908 1.39903 -0.03386 0.44773
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## 0.39317 0.44353 0.16354 0.81761
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## 0.05811 0.14094 -0.22492 1.33869
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## -0.16581 -0.87614 -0.77730 -0.14297
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## 0.83624 0.89084 0.12795 0.08083
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## 0.79157 0.17788 0.59951 0.21994
## Hour_entry_23 Median Weight rho var_eartag
## 0.16646 0.09124 0.88743 0.82467
## var_follower var_error prp_var_eartag prp_var_follower
## 1.89765 -1.15027 0.76293 1.89371
## prp_var_error lp__
## -1.33352 -2.80184
##
##
## [[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
## 1.246311 1.220635 0.436887 1.867466
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 0.886620 1.431852 0.208662 0.592315
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## 1.272434 1.942405 0.235658 1.970415
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## 0.099881 0.652516 -2.503073 -2.350463
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## -2.632821 -2.014635 -2.258785 -2.781121
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## -2.080679 -2.139163 -1.139307 -0.948252
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## -1.622832 -2.755855 -2.337036 -1.734746
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## -2.522728 -2.701031 -2.038883 -2.412736
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## -3.221937 -1.766078 -2.552916 -2.049132
## Hour_entry_23 Median Weight rho var_eartag
## -2.146112 0.577313 -0.238615 -0.011534
## var_follower var_error prp_var_eartag prp_var_follower
## 0.110735 0.035315 -0.009083 0.111749
## prp_var_error lp__
## -0.047363 0.173658
##
##
## [[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
## 0.6510510 -0.8912933 -0.6725914 -0.0473414
## Loc1_t_5 Loc1_t_6 Loc1_t_7 Loc2_t_1
## 1.3155321 -0.5870277 0.1920562 1.2394874
## Loc2_t_2 Loc2_t_3 Loc2_t_4 Loc2_t_5
## -1.1683879 1.1975997 -0.1635976 0.2581464
## Loc2_t_6 Loc2_t_7 Hour_entry_1 Hour_entry_2
## -0.7715845 -0.4720908 -0.3988552 -0.6017766
## Hour_entry_3 Hour_entry_4 Hour_entry_5 Hour_entry_6
## 0.3313849 -0.4253149 0.4482269 -0.2318017
## Hour_entry_7 Hour_entry_8 Hour_entry_9 Hour_entry_10
## 0.5725001 -0.6342512 -0.5127320 -0.1118506
## Hour_entry_11 Hour_entry_12 Hour_entry_13 Hour_entry_14
## 0.0355949 -0.3532118 -0.6228066 -0.9621150
## Hour_entry_15 Hour_entry_16 Hour_entry_17 Hour_entry_18
## -0.3133297 -0.4937577 0.1115803 -0.0345834
## Hour_entry_19 Hour_entry_20 Hour_entry_21 Hour_entry_22
## 0.0453483 -0.0601229 0.5981076 0.0004912
## Hour_entry_23 Median Weight rho var_eartag
## -0.0741630 -0.2633315 -0.8309819 -0.9672478
## var_follower var_error prp_var_eartag prp_var_follower
## 1.2662583 -2.2324787 -0.8736135 1.2083735
## prp_var_error lp__
## 0.3481376 -0.8074075gelman.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 1.00
## Loc1_t_3 1.00 1.00
## Loc1_t_4 1.00 1.01
## Loc1_t_5 1.00 1.00
## Loc1_t_6 1.00 1.01
## Loc1_t_7 1.00 1.01
## Loc2_t_1 1.00 1.00
## Loc2_t_2 1.00 1.01
## Loc2_t_3 1.00 1.01
## 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 1.01
## Hour_entry_1 1.00 1.01
## Hour_entry_2 1.00 1.01
## Hour_entry_3 1.00 1.01
## 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 1.01
## 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 1.01
## Hour_entry_21 1.00 1.01
## Hour_entry_22 1.00 1.00
## Hour_entry_23 1.00 1.01
## Median Weight 1.00 1.00
## rho 1.00 1.01
## var_eartag 1.00 1.00
## var_follower 1.01 1.03
## var_error 1.00 1.00
## prp_var_eartag 1.00 1.00
## prp_var_follower 1.01 1.03
## prp_var_error 1.00 1.00
## lp__ 1.01 1.03traplot(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 1.625e+01 1.218468 7.035e-03 1.355e-02
## Loc1_t_2 1.143e+01 1.134487 6.550e-03 1.525e-02
## Loc1_t_3 1.231e+01 1.159587 6.695e-03 1.502e-02
## Loc1_t_4 1.100e+01 1.303749 7.527e-03 1.733e-02
## Loc1_t_5 1.245e+01 1.333720 7.700e-03 1.707e-02
## Loc1_t_6 8.357e+00 1.224306 7.069e-03 1.758e-02
## Loc1_t_7 1.294e+01 1.299231 7.501e-03 1.538e-02
## Loc2_t_1 1.591e+01 1.248100 7.206e-03 1.360e-02
## Loc2_t_2 1.143e+01 1.134165 6.548e-03 1.578e-02
## Loc2_t_3 1.907e+01 1.178560 6.804e-03 1.447e-02
## Loc2_t_4 1.205e+01 1.305329 7.536e-03 1.772e-02
## Loc2_t_5 1.248e+01 1.320794 7.626e-03 1.663e-02
## Loc2_t_6 1.043e+01 1.223298 7.063e-03 1.636e-02
## Loc2_t_7 1.280e+01 1.333821 7.701e-03 1.643e-02
## Hour_entry_1 -1.072e-01 0.470021 2.714e-03 5.865e-03
## Hour_entry_2 -8.440e-01 0.465972 2.690e-03 5.735e-03
## Hour_entry_3 -8.129e-01 0.465645 2.688e-03 5.611e-03
## Hour_entry_4 -6.954e-01 0.472609 2.729e-03 5.952e-03
## Hour_entry_5 -1.075e+00 0.505378 2.918e-03 6.074e-03
## Hour_entry_6 -1.126e+00 0.549128 3.170e-03 5.954e-03
## Hour_entry_7 -6.925e-01 0.675799 3.902e-03 6.763e-03
## Hour_entry_8 5.363e-01 0.799370 4.615e-03 6.984e-03
## Hour_entry_9 -1.448e-01 0.747351 4.315e-03 6.702e-03
## Hour_entry_10 9.705e-01 0.687225 3.968e-03 6.436e-03
## Hour_entry_11 3.356e-01 0.817611 4.720e-03 7.039e-03
## Hour_entry_12 1.926e+00 1.071452 6.186e-03 7.424e-03
## Hour_entry_13 1.728e-01 1.590315 9.182e-03 1.056e-02
## Hour_entry_14 -1.475e+00 1.269997 7.332e-03 9.025e-03
## Hour_entry_15 2.901e+00 0.803430 4.639e-03 6.623e-03
## Hour_entry_16 2.744e+00 0.616847 3.561e-03 6.021e-03
## Hour_entry_17 1.697e+00 0.538408 3.109e-03 5.786e-03
## Hour_entry_18 4.735e-01 0.512411 2.958e-03 5.850e-03
## Hour_entry_19 4.881e-01 0.502272 2.900e-03 5.722e-03
## Hour_entry_20 1.421e-02 0.513727 2.966e-03 5.934e-03
## Hour_entry_21 3.011e-01 0.483065 2.789e-03 5.705e-03
## Hour_entry_22 5.913e-01 0.482632 2.786e-03 5.701e-03
## Hour_entry_23 -3.580e-01 0.480405 2.774e-03 5.697e-03
## Median Weight -2.897e-02 0.005312 3.067e-05 4.420e-05
## rho -9.809e-02 0.432273 2.496e-03 1.198e-02
## var_eartag 1.098e+01 1.697367 9.800e-03 1.350e-02
## var_follower 7.457e-02 0.072930 4.211e-04 3.570e-03
## var_error 4.776e+01 0.867974 5.011e-03 5.111e-03
## prp_var_eartag 1.861e-01 0.023427 1.353e-04 1.850e-04
## prp_var_follower 1.268e-03 0.001239 7.152e-06 6.063e-05
## prp_var_error 8.126e-01 0.023433 1.353e-04 1.876e-04
## lp__ -1.530e+04 71.391477 4.122e-01 4.436e+00
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.385e+01 1.544e+01 1.626e+01 1.708e+01 1.861e+01
## Loc1_t_2 9.203e+00 1.066e+01 1.143e+01 1.218e+01 1.367e+01
## Loc1_t_3 9.986e+00 1.154e+01 1.233e+01 1.310e+01 1.455e+01
## Loc1_t_4 8.466e+00 1.012e+01 1.099e+01 1.188e+01 1.355e+01
## Loc1_t_5 9.862e+00 1.154e+01 1.244e+01 1.334e+01 1.505e+01
## Loc1_t_6 5.942e+00 7.535e+00 8.368e+00 9.171e+00 1.075e+01
## Loc1_t_7 1.040e+01 1.207e+01 1.294e+01 1.382e+01 1.553e+01
## Loc2_t_1 1.344e+01 1.507e+01 1.591e+01 1.675e+01 1.835e+01
## Loc2_t_2 9.222e+00 1.066e+01 1.143e+01 1.219e+01 1.367e+01
## Loc2_t_3 1.674e+01 1.828e+01 1.907e+01 1.987e+01 2.136e+01
## Loc2_t_4 9.499e+00 1.118e+01 1.205e+01 1.291e+01 1.464e+01
## Loc2_t_5 9.869e+00 1.161e+01 1.248e+01 1.335e+01 1.512e+01
## Loc2_t_6 8.047e+00 9.604e+00 1.042e+01 1.125e+01 1.283e+01
## Loc2_t_7 1.020e+01 1.191e+01 1.280e+01 1.369e+01 1.545e+01
## Hour_entry_1 -1.025e+00 -4.261e-01 -1.100e-01 2.111e-01 8.160e-01
## Hour_entry_2 -1.751e+00 -1.158e+00 -8.447e-01 -5.357e-01 7.339e-02
## Hour_entry_3 -1.721e+00 -1.127e+00 -8.078e-01 -4.968e-01 9.236e-02
## Hour_entry_4 -1.626e+00 -1.014e+00 -6.933e-01 -3.785e-01 2.289e-01
## Hour_entry_5 -2.055e+00 -1.416e+00 -1.077e+00 -7.365e-01 -7.226e-02
## Hour_entry_6 -2.211e+00 -1.495e+00 -1.123e+00 -7.563e-01 -5.233e-02
## Hour_entry_7 -2.001e+00 -1.148e+00 -6.977e-01 -2.371e-01 6.423e-01
## Hour_entry_8 -1.030e+00 -5.199e-03 5.419e-01 1.079e+00 2.083e+00
## Hour_entry_9 -1.602e+00 -6.486e-01 -1.474e-01 3.502e-01 1.326e+00
## Hour_entry_10 -3.839e-01 5.139e-01 9.715e-01 1.435e+00 2.334e+00
## Hour_entry_11 -1.263e+00 -2.144e-01 3.349e-01 8.856e-01 1.931e+00
## Hour_entry_12 -1.812e-01 1.202e+00 1.935e+00 2.646e+00 4.011e+00
## Hour_entry_13 -2.942e+00 -9.084e-01 1.757e-01 1.251e+00 3.306e+00
## Hour_entry_14 -3.963e+00 -2.332e+00 -1.472e+00 -6.194e-01 1.003e+00
## Hour_entry_15 1.323e+00 2.367e+00 2.899e+00 3.441e+00 4.473e+00
## Hour_entry_16 1.542e+00 2.327e+00 2.742e+00 3.162e+00 3.945e+00
## Hour_entry_17 6.275e-01 1.333e+00 1.700e+00 2.056e+00 2.758e+00
## Hour_entry_18 -5.211e-01 1.252e-01 4.727e-01 8.210e-01 1.476e+00
## Hour_entry_19 -5.031e-01 1.506e-01 4.882e-01 8.313e-01 1.472e+00
## Hour_entry_20 -9.879e-01 -3.364e-01 1.359e-02 3.611e-01 1.018e+00
## Hour_entry_21 -6.480e-01 -2.301e-02 3.029e-01 6.304e-01 1.243e+00
## Hour_entry_22 -3.357e-01 2.648e-01 5.870e-01 9.190e-01 1.542e+00
## Hour_entry_23 -1.287e+00 -6.821e-01 -3.588e-01 -3.553e-02 5.931e-01
## Median Weight -3.940e-02 -3.252e-02 -2.893e-02 -2.539e-02 -1.857e-02
## rho -8.677e-01 -4.176e-01 -1.176e-01 1.945e-01 8.028e-01
## var_eartag 8.086e+00 9.772e+00 1.085e+01 1.204e+01 1.470e+01
## var_follower 1.108e-02 2.410e-02 4.931e-02 1.004e-01 2.713e-01
## var_error 4.609e+01 4.717e+01 4.775e+01 4.834e+01 4.948e+01
## prp_var_eartag 1.441e-01 1.695e-01 1.848e-01 2.012e-01 2.354e-01
## prp_var_follower 1.888e-04 4.106e-04 8.398e-04 1.708e-03 4.612e-03
## prp_var_error 7.634e-01 7.975e-01 8.139e-01 8.291e-01 8.547e-01
## lp__ -1.542e+04 -1.535e+04 -1.530e+04 -1.525e+04 -1.515e+04print(M3600s.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] 16.25 0.01 1.22 13.85 15.44 16.26
## beta[2] 11.43 0.02 1.13 9.20 10.66 11.43
## beta[3] 12.31 0.02 1.16 9.99 11.54 12.33
## beta[4] 11.00 0.02 1.30 8.47 10.12 10.99
## beta[5] 12.45 0.02 1.33 9.86 11.54 12.44
## beta[6] 8.36 0.02 1.22 5.94 7.53 8.37
## beta[7] 12.94 0.02 1.30 10.40 12.07 12.94
## beta[8] 15.91 0.01 1.25 13.44 15.07 15.91
## beta[9] 11.43 0.02 1.13 9.22 10.66 11.43
## beta[10] 19.07 0.01 1.18 16.74 18.28 19.07
## beta[11] 12.05 0.02 1.31 9.50 11.18 12.05
## beta[12] 12.48 0.02 1.32 9.87 11.61 12.48
## beta[13] 10.43 0.02 1.22 8.05 9.60 10.42
## beta[14] 12.80 0.02 1.33 10.20 11.91 12.80
## beta[15] -0.11 0.01 0.47 -1.02 -0.43 -0.11
## beta[16] -0.84 0.01 0.47 -1.75 -1.16 -0.84
## beta[17] -0.81 0.01 0.47 -1.72 -1.13 -0.81
## beta[18] -0.70 0.01 0.47 -1.63 -1.01 -0.69
## beta[19] -1.07 0.01 0.51 -2.06 -1.42 -1.08
## beta[20] -1.13 0.01 0.55 -2.21 -1.50 -1.12
## beta[21] -0.69 0.01 0.68 -2.00 -1.15 -0.70
## beta[22] 0.54 0.01 0.80 -1.03 -0.01 0.54
## beta[23] -0.14 0.01 0.75 -1.60 -0.65 -0.15
## beta[24] 0.97 0.01 0.69 -0.38 0.51 0.97
## beta[25] 0.34 0.01 0.82 -1.26 -0.21 0.33
## beta[26] 1.93 0.01 1.07 -0.18 1.20 1.93
## beta[27] 0.17 0.01 1.59 -2.94 -0.91 0.18
## beta[28] -1.48 0.01 1.27 -3.96 -2.33 -1.47
## beta[29] 2.90 0.01 0.80 1.32 2.37 2.90
## beta[30] 2.74 0.01 0.62 1.54 2.33 2.74
## beta[31] 1.70 0.01 0.54 0.63 1.33 1.70
## beta[32] 0.47 0.01 0.51 -0.52 0.13 0.47
## beta[33] 0.49 0.01 0.50 -0.50 0.15 0.49
## beta[34] 0.01 0.01 0.51 -0.99 -0.34 0.01
## beta[35] 0.30 0.01 0.48 -0.65 -0.02 0.30
## beta[36] 0.59 0.01 0.48 -0.34 0.26 0.59
## beta[37] -0.36 0.01 0.48 -1.29 -0.68 -0.36
## beta[38] -0.03 0.00 0.01 -0.04 -0.03 -0.03
## rho -0.10 0.01 0.43 -0.87 -0.42 -0.12
## var_eartag 10.98 0.01 1.70 8.09 9.77 10.85
## var_follower 0.07 0.00 0.07 0.01 0.02 0.05
## var_error 47.76 0.01 0.87 46.09 47.17 47.75
## prp_var_eartag 0.19 0.00 0.02 0.14 0.17 0.18
## prp_var_follower 0.00 0.00 0.00 0.00 0.00 0.00
## prp_var_error 0.81 0.00 0.02 0.76 0.80 0.81
## lp__ -15299.02 4.48 71.39 -15420.71 -15353.87 -15302.31
## 75% 97.5% n_eff Rhat
## beta[1] 17.08 18.61 7431 1.00
## beta[2] 12.18 13.67 5553 1.00
## beta[3] 13.10 14.55 5802 1.00
## beta[4] 11.88 13.55 5245 1.00
## beta[5] 13.34 15.05 6145 1.00
## beta[6] 9.17 10.75 4345 1.00
## beta[7] 13.82 15.53 7206 1.00
## beta[8] 16.75 18.35 7565 1.00
## beta[9] 12.19 13.67 4823 1.00
## beta[10] 19.87 21.36 6567 1.00
## beta[11] 12.91 14.64 5253 1.00
## beta[12] 13.35 15.12 5714 1.00
## beta[13] 11.25 12.83 5249 1.00
## beta[14] 13.69 15.45 6101 1.00
## beta[15] 0.21 0.82 6215 1.00
## beta[16] -0.54 0.07 6720 1.00
## beta[17] -0.50 0.09 6757 1.00
## beta[18] -0.38 0.23 6114 1.00
## beta[19] -0.74 -0.07 6544 1.00
## beta[20] -0.76 -0.05 8264 1.00
## beta[21] -0.24 0.64 9850 1.00
## beta[22] 1.08 2.08 12207 1.00
## beta[23] 0.35 1.33 11223 1.00
## beta[24] 1.44 2.33 10421 1.00
## beta[25] 0.89 1.93 13357 1.00
## beta[26] 2.65 4.01 17209 1.00
## beta[27] 1.25 3.31 21777 1.00
## beta[28] -0.62 1.00 19085 1.00
## beta[29] 3.44 4.47 13844 1.00
## beta[30] 3.16 3.95 9949 1.00
## beta[31] 2.06 2.76 8134 1.00
## beta[32] 0.82 1.48 7376 1.00
## beta[33] 0.83 1.47 7478 1.00
## beta[34] 0.36 1.02 7418 1.00
## beta[35] 0.63 1.24 7039 1.00
## beta[36] 0.92 1.54 7049 1.00
## beta[37] -0.04 0.59 7053 1.00
## beta[38] -0.03 -0.02 13316 1.00
## rho 0.19 0.80 1042 1.00
## var_eartag 12.04 14.70 14472 1.00
## var_follower 0.10 0.27 324 1.01
## var_error 48.34 49.48 28619 1.00
## prp_var_eartag 0.20 0.24 14483 1.00
## prp_var_follower 0.00 0.00 325 1.01
## prp_var_error 0.83 0.85 13811 1.00
## lp__ -15247.58 -15150.11 254 1.01
##
## Samples were drawn using NUTS(diag_e) at Fri Jan 24 13:15:07 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)