Bayesian estimating variance components visit length
Results bayesian estimating of variance components (proportion of variance) with Stan program, on 6340 records of visit length time at the feeder when the next visit was greater than or equal to 600 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 1.0000000000 1.0000000000 1.000000000
## Lag 1 -0.123219351 0.030606405 -0.0027361820 0.0277572751 -0.042774155
## Lag 5 -0.003719797 0.005388703 0.0004586849 0.0031132885 0.001276780
## Lag 10 -0.003289315 -0.002384619 -0.0123514165 0.0037294188 0.011243352
## Lag 50 -0.002556636 0.009619004 0.0048439521 -0.0003218926 0.000844602
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## Lag 0 1.000000000 1.000000000 1.0000000000 1.000000000 1.000000000
## Lag 1 0.088885363 -0.152710721 0.0969594107 -0.040774306 0.012355589
## Lag 5 -0.004751602 0.010558704 0.0008419433 0.001473400 -0.002832736
## Lag 10 -0.004902686 -0.013772505 0.0071626593 0.006899904 0.008814537
## Lag 50 -0.013929373 -0.007107068 -0.0061876952 -0.004377233 -0.008986992
## Loc2_t_5 Loc2_t_6 Median Weight var_eartag var_error
## Lag 0 1.000000000 1.0000000000 1.000000000 1.000000000 1.0000000000
## Lag 1 -0.064942550 0.0902470819 -0.242858516 -0.052990045 -0.0506629856
## Lag 5 0.006004856 -0.0046901289 -0.002714338 -0.001559744 -0.0004506333
## Lag 10 -0.009275450 0.0012285914 -0.004339515 -0.009737167 -0.0185931108
## Lag 50 -0.001465892 0.0006513584 -0.003297619 0.002778049 0.0099192557
## prp_var_eartag prp_var_error lp__
## Lag 0 1.0000000000 1.0000000000 1.000000000
## Lag 1 -0.0592111009 -0.0592111009 0.466606858
## Lag 5 -0.0009034701 -0.0009034701 0.025307346
## Lag 10 -0.0111778705 -0.0111778705 0.007658301
## Lag 50 0.0014477176 0.0014477176 0.003917856effectiveSize(outp1)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4 Loc1_t_5
## 37985.03 27656.69 30128.92 28455.50 32688.36
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## 24062.25 38725.60 24301.97 32295.20 28016.88
## Loc2_t_5 Loc2_t_6 Median Weight var_eartag var_error
## 31873.65 26053.69 48842.10 30358.05 32486.45
## prp_var_eartag prp_var_error lp__
## 30878.61 30878.61 10913.35geweke.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
## -0.36396 -1.85268 0.07577 -0.09846 1.08525
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## -0.52947 0.87057 1.93327 1.17557 -0.39824
## Loc2_t_5 Loc2_t_6 Median Weight var_eartag var_error
## -0.39121 -0.46271 -1.47142 0.81954 0.22433
## prp_var_eartag prp_var_error lp__
## 0.86875 -0.86875 -0.62494
##
##
## [[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
## 0.595030 0.632443 1.394575 1.131809 -0.263163
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## -0.074885 0.619106 -0.204757 0.113504 -0.007772
## Loc2_t_5 Loc2_t_6 Median Weight var_eartag var_error
## 1.442023 -1.476442 -0.342529 -0.520152 -1.434722
## prp_var_eartag prp_var_error lp__
## -0.364132 0.364132 0.808282
##
##
## [[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
## -1.11566 -0.65446 -0.84040 -0.55622 0.51736
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## -0.79585 1.35607 0.53859 -0.39525 1.22817
## Loc2_t_5 Loc2_t_6 Median Weight var_eartag var_error
## 0.06132 0.22072 0.45356 0.65454 0.26027
## prp_var_eartag prp_var_error lp__
## 0.72174 -0.72174 -0.05650#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 1.597e+01 1.162377 6.711e-03 5.966e-03
## Loc1_t_2 1.110e+01 1.078043 6.224e-03 6.485e-03
## Loc1_t_3 1.200e+01 1.098629 6.343e-03 6.336e-03
## Loc1_t_4 1.093e+01 1.241993 7.171e-03 7.387e-03
## Loc1_t_5 1.234e+01 1.260559 7.278e-03 6.975e-03
## Loc1_t_6 8.193e+00 1.158840 6.691e-03 7.476e-03
## Loc2_t_1 1.534e+01 1.165684 6.730e-03 5.927e-03
## Loc2_t_2 1.107e+01 1.077227 6.219e-03 6.911e-03
## Loc2_t_3 1.853e+01 1.117674 6.453e-03 6.228e-03
## Loc2_t_4 1.169e+01 1.253040 7.234e-03 7.490e-03
## Loc2_t_5 1.222e+01 1.267159 7.316e-03 7.099e-03
## Loc2_t_6 1.009e+01 1.184568 6.839e-03 7.401e-03
## Median Weight -2.543e-02 0.005109 2.949e-05 2.321e-05
## var_eartag 1.077e+01 1.780594 1.028e-02 1.023e-02
## var_error 4.499e+01 0.804623 4.645e-03 4.470e-03
## prp_var_eartag 1.923e-01 0.025555 1.475e-04 1.455e-04
## prp_var_error 8.077e-01 0.025555 1.475e-04 1.455e-04
## lp__ -1.543e+04 8.437806 4.872e-02 8.083e-02
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.371e+01 1.518e+01 1.597e+01 1.675e+01 1.825e+01
## Loc1_t_2 8.964e+00 1.037e+01 1.110e+01 1.183e+01 1.321e+01
## Loc1_t_3 9.829e+00 1.126e+01 1.200e+01 1.273e+01 1.416e+01
## Loc1_t_4 8.493e+00 1.009e+01 1.092e+01 1.176e+01 1.336e+01
## Loc1_t_5 9.841e+00 1.150e+01 1.235e+01 1.319e+01 1.479e+01
## Loc1_t_6 5.930e+00 7.422e+00 8.193e+00 8.956e+00 1.049e+01
## Loc2_t_1 1.305e+01 1.456e+01 1.534e+01 1.612e+01 1.762e+01
## Loc2_t_2 8.954e+00 1.035e+01 1.107e+01 1.180e+01 1.318e+01
## Loc2_t_3 1.635e+01 1.779e+01 1.852e+01 1.928e+01 2.073e+01
## Loc2_t_4 9.230e+00 1.085e+01 1.169e+01 1.252e+01 1.416e+01
## Loc2_t_5 9.716e+00 1.137e+01 1.223e+01 1.307e+01 1.470e+01
## Loc2_t_6 7.756e+00 9.281e+00 1.010e+01 1.089e+01 1.241e+01
## Median Weight -3.541e-02 -2.889e-02 -2.542e-02 -2.194e-02 -1.552e-02
## var_eartag 7.783e+00 9.515e+00 1.060e+01 1.183e+01 1.475e+01
## var_error 4.344e+01 4.444e+01 4.499e+01 4.553e+01 4.659e+01
## prp_var_eartag 1.472e-01 1.745e-01 1.907e-01 2.085e-01 2.475e-01
## prp_var_error 7.525e-01 7.915e-01 8.093e-01 8.255e-01 8.528e-01
## lp__ -1.545e+04 -1.544e+04 -1.543e+04 -1.543e+04 -1.542e+04print(Et600.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] 15.97 0.01 1.16 13.71 15.18 15.97
## beta[2] 11.10 0.01 1.08 8.96 10.37 11.10
## beta[3] 12.00 0.01 1.10 9.83 11.26 12.00
## beta[4] 10.93 0.01 1.24 8.49 10.09 10.92
## beta[5] 12.34 0.01 1.26 9.84 11.50 12.35
## beta[6] 8.19 0.01 1.16 5.93 7.42 8.19
## beta[7] 15.34 0.01 1.17 13.05 14.56 15.34
## beta[8] 11.07 0.01 1.08 8.95 10.35 11.07
## beta[9] 18.53 0.01 1.12 16.35 17.79 18.52
## beta[10] 11.69 0.01 1.25 9.23 10.85 11.69
## beta[11] 12.22 0.01 1.27 9.72 11.37 12.23
## beta[12] 10.09 0.01 1.18 7.76 9.28 10.10
## beta[13] -0.03 0.00 0.01 -0.04 -0.03 -0.03
## var_eartag 10.77 0.01 1.78 7.78 9.51 10.60
## var_error 44.99 0.00 0.80 43.44 44.44 44.99
## prp_var_eartag 0.19 0.00 0.03 0.15 0.17 0.19
## prp_var_error 0.81 0.00 0.03 0.75 0.79 0.81
## lp__ -15430.80 0.08 8.44 -15448.30 -15436.31 -15430.43
## 75% 97.5% n_eff Rhat
## beta[1] 16.75 18.25 37311 1
## beta[2] 11.83 13.21 27315 1
## beta[3] 12.73 14.16 29892 1
## beta[4] 11.76 13.36 27934 1
## beta[5] 13.19 14.79 32093 1
## beta[6] 8.96 10.49 24289 1
## beta[7] 16.12 17.62 38792 1
## beta[8] 11.80 13.18 23752 1
## beta[9] 19.28 20.73 32118 1
## beta[10] 12.52 14.16 27929 1
## beta[11] 13.07 14.70 32621 1
## beta[12] 10.89 12.41 24645 1
## beta[13] -0.02 -0.02 49445 1
## var_eartag 11.83 14.75 30522 1
## var_error 45.53 46.59 32199 1
## prp_var_eartag 0.21 0.25 30968 1
## prp_var_error 0.83 0.85 30968 1
## lp__ -15425.01 -15415.17 10419 1
##
## Samples were drawn using NUTS(diag_e) at Sat Sep 28 15:35:50 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
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 1.0000000000 1.0000000000 1.000000000 1.000000000
## Lag 1 0.277345544 0.4196344490 0.3973699491 0.409145035 0.350193933
## Lag 5 0.053244766 0.0966399305 0.0944191369 0.102381788 0.065670571
## Lag 10 0.001044912 0.0197189427 0.0127843476 0.031434276 0.012203519
## Lag 50 0.005506888 -0.0005492996 0.0008222674 -0.006504922 0.001073529
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## Lag 0 1.000000000 1.000000000 1.00000000 1.0000000000 1.0000000000
## Lag 1 0.469502395 0.238090616 0.44391085 0.3445634150 0.4060235543
## Lag 5 0.121053517 0.045584304 0.10689896 0.0612964999 0.0844277861
## Lag 10 0.014685136 0.001459716 0.01739168 0.0120646482 0.0308657487
## Lag 50 -0.008235679 -0.001566534 0.01384540 -0.0003546347 -0.0009485515
## Loc2_t_5 Loc2_t_6 Median Weight var_eartag var_follower
## Lag 0 1.0000000000 1.00000000 1.000000000 1.000000000 1.0000000
## Lag 1 0.3429667309 0.43166446 0.049522596 0.018164104 0.9273889
## Lag 5 0.0583932280 0.10904637 0.010668537 0.009894689 0.8106728
## Lag 10 0.0020727306 0.02226329 0.002916006 -0.004022975 0.7013771
## Lag 50 -0.0004777744 -0.00918393 -0.001098588 0.004222454 0.3599078
## var_error prp_var_eartag prp_var_follower prp_var_error
## Lag 0 1.0000000000 1.000000000 1.0000000 1.000000000
## Lag 1 -0.1212494014 0.011235743 0.9264340 0.013518961
## Lag 5 0.0147830142 0.010596576 0.8105582 0.012513035
## Lag 10 0.0017169946 -0.004806980 0.7007018 -0.002894323
## Lag 50 0.0006702087 0.003552112 0.3608713 0.004078517
## lp__
## Lag 0 1.0000000
## Lag 1 0.9871143
## Lag 5 0.9513092
## Lag 10 0.9149820
## Lag 50 0.7138857effectiveSize(outp2)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## 11743.4250 8096.9579 8523.7487 7894.6461
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## 10193.9699 7340.7163 13190.4084 8078.8760
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## 9950.1580 8265.6068 10192.7366 7975.5620
## Median Weight var_eartag var_follower var_error
## 20948.2100 21308.3968 314.6344 34543.7098
## prp_var_eartag prp_var_follower prp_var_error lp__
## 21626.7402 313.5091 21341.4385 119.0512geweke.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
## 0.92024 0.85663 -1.80129 -0.26708
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## -0.13450 1.37329 0.15194 -1.09330
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## -0.43670 0.56791 1.56347 0.07124
## Median Weight var_eartag var_follower var_error
## -0.32501 -1.44362 -11.03370 0.26964
## prp_var_eartag prp_var_follower prp_var_error lp__
## -1.23112 -11.01760 2.50750 8.11959
##
##
## [[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
## -1.13201 -0.76172 1.03205 0.25712
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## 0.16436 0.50142 1.67090 1.27928
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## 0.20274 -0.05022 -0.03729 -0.65809
## Median Weight var_eartag var_follower var_error
## -1.68008 -0.39777 0.62514 -0.07591
## prp_var_eartag prp_var_follower prp_var_error lp__
## -0.43531 0.63709 0.23502 -0.17239
##
##
## [[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
## -0.662166 0.326359 0.107180 0.070864
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## -0.669161 -0.008255 -0.897337 0.731771
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## 0.227043 -0.867101 0.307943 -0.177592
## Median Weight var_eartag var_follower var_error
## 0.933469 0.504168 -6.772088 1.566189
## prp_var_eartag prp_var_follower prp_var_error lp__
## 0.647419 -6.835494 0.581293 4.246211gelman.diag(outp2)## 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
## 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
## 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 1.13
## prp_var_error 1.00 1.00
## lp__ 1.08 1.23
##
## Multivariate psrf
##
## 1.05traplot(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 1.598e+01 1.161324 6.705e-03 1.088e-02
## Loc1_t_2 1.110e+01 1.084175 6.259e-03 1.220e-02
## Loc1_t_3 1.198e+01 1.124449 6.492e-03 1.236e-02
## Loc1_t_4 1.094e+01 1.255333 7.248e-03 1.424e-02
## Loc1_t_5 1.236e+01 1.281745 7.400e-03 1.284e-02
## Loc1_t_6 8.182e+00 1.174839 6.783e-03 1.379e-02
## Loc2_t_1 1.535e+01 1.170864 6.760e-03 1.030e-02
## Loc2_t_2 1.104e+01 1.084434 6.261e-03 1.221e-02
## Loc2_t_3 1.855e+01 1.114696 6.436e-03 1.124e-02
## Loc2_t_4 1.166e+01 1.262317 7.288e-03 1.391e-02
## Loc2_t_5 1.225e+01 1.267830 7.320e-03 1.258e-02
## Loc2_t_6 1.011e+01 1.192722 6.886e-03 1.348e-02
## Median Weight -2.551e-02 0.005174 2.987e-05 3.584e-05
## var_eartag 1.079e+01 1.777894 1.026e-02 1.219e-02
## var_follower 6.588e-02 0.076956 4.443e-04 4.362e-03
## var_error 4.496e+01 0.816196 4.712e-03 4.427e-03
## prp_var_eartag 1.926e-01 0.025549 1.475e-04 1.738e-04
## prp_var_follower 1.180e-03 0.001378 7.953e-06 7.820e-05
## prp_var_error 8.062e-01 0.025548 1.475e-04 1.750e-04
## lp__ -1.528e+04 92.418753 5.336e-01 8.954e+00
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.374e+01 1.520e+01 1.597e+01 1.675e+01 1.829e+01
## Loc1_t_2 8.979e+00 1.037e+01 1.109e+01 1.182e+01 1.322e+01
## Loc1_t_3 9.781e+00 1.122e+01 1.197e+01 1.273e+01 1.420e+01
## Loc1_t_4 8.466e+00 1.010e+01 1.094e+01 1.178e+01 1.338e+01
## Loc1_t_5 9.850e+00 1.152e+01 1.237e+01 1.321e+01 1.489e+01
## Loc1_t_6 5.887e+00 7.388e+00 8.182e+00 8.980e+00 1.048e+01
## Loc2_t_1 1.305e+01 1.455e+01 1.535e+01 1.613e+01 1.764e+01
## Loc2_t_2 8.929e+00 1.031e+01 1.103e+01 1.175e+01 1.320e+01
## Loc2_t_3 1.637e+01 1.779e+01 1.855e+01 1.930e+01 2.073e+01
## Loc2_t_4 9.197e+00 1.080e+01 1.165e+01 1.251e+01 1.415e+01
## Loc2_t_5 9.755e+00 1.140e+01 1.224e+01 1.309e+01 1.475e+01
## Loc2_t_6 7.742e+00 9.308e+00 1.011e+01 1.091e+01 1.244e+01
## Median Weight -3.561e-02 -2.900e-02 -2.552e-02 -2.203e-02 -1.535e-02
## var_eartag 7.773e+00 9.539e+00 1.063e+01 1.187e+01 1.475e+01
## var_follower 5.118e-04 1.097e-02 3.763e-02 9.407e-02 2.778e-01
## var_error 4.338e+01 4.441e+01 4.495e+01 4.551e+01 4.659e+01
## prp_var_eartag 1.469e-01 1.746e-01 1.910e-01 2.089e-01 2.471e-01
## prp_var_follower 9.171e-06 1.967e-04 6.729e-04 1.685e-03 4.979e-03
## prp_var_error 7.516e-01 7.899e-01 8.079e-01 8.242e-01 8.518e-01
## lp__ -1.541e+04 -1.535e+04 -1.530e+04 -1.522e+04 -1.505e+04print(Fol600.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] 15.98 0.01 1.16 13.74 15.20 15.97
## beta[2] 11.10 0.01 1.08 8.98 10.37 11.09
## beta[3] 11.98 0.01 1.12 9.78 11.22 11.97
## beta[4] 10.94 0.01 1.26 8.47 10.10 10.94
## beta[5] 12.36 0.01 1.28 9.85 11.52 12.37
## beta[6] 8.18 0.01 1.17 5.89 7.39 8.18
## beta[7] 15.35 0.01 1.17 13.05 14.55 15.35
## beta[8] 11.04 0.01 1.08 8.93 10.31 11.03
## beta[9] 18.55 0.01 1.11 16.37 17.79 18.55
## beta[10] 11.66 0.01 1.26 9.20 10.80 11.65
## beta[11] 12.25 0.01 1.27 9.76 11.40 12.24
## beta[12] 10.11 0.01 1.19 7.74 9.31 10.11
## beta[13] -0.03 0.00 0.01 -0.04 -0.03 -0.03
## var_eartag 10.79 0.01 1.78 7.77 9.54 10.63
## var_follower 0.07 0.01 0.08 0.00 0.01 0.04
## var_error 44.96 0.00 0.82 43.38 44.41 44.95
## prp_var_eartag 0.19 0.00 0.03 0.15 0.17 0.19
## prp_var_follower 0.00 0.00 0.00 0.00 0.00 0.00
## prp_var_error 0.81 0.00 0.03 0.75 0.79 0.81
## lp__ -15277.16 15.14 92.42 -15407.26 -15347.24 -15295.64
## 75% 97.5% n_eff Rhat
## beta[1] 16.75 18.29 11740 1.00
## beta[2] 11.82 13.22 7942 1.00
## beta[3] 12.73 14.20 8313 1.00
## beta[4] 11.78 13.38 7668 1.00
## beta[5] 13.21 14.89 9829 1.00
## beta[6] 8.98 10.48 7242 1.00
## beta[7] 16.13 17.64 12509 1.00
## beta[8] 11.75 13.20 7695 1.00
## beta[9] 19.30 20.73 9986 1.00
## beta[10] 12.51 14.15 7936 1.00
## beta[11] 13.09 14.75 10285 1.00
## beta[12] 10.91 12.44 7292 1.00
## beta[13] -0.02 -0.02 20521 1.00
## var_eartag 11.87 14.75 21251 1.00
## var_follower 0.09 0.28 91 1.05
## var_error 45.51 46.59 31992 1.00
## prp_var_eartag 0.21 0.25 21487 1.00
## prp_var_follower 0.00 0.00 92 1.05
## prp_var_error 0.82 0.85 21010 1.00
## lp__ -15224.75 -15046.17 37 1.12
##
## Samples were drawn using NUTS(diag_e) at Sat Sep 28 16:00:36 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 1.000000000 1.00000000 1.00000000 1.00000000
## Lag 1 0.388345783 0.561278010 0.51619089 0.53824081 0.49825772
## Lag 5 0.074619105 0.183451619 0.14950699 0.14613662 0.11616679
## Lag 10 0.021652150 0.058778096 0.05452070 0.03799377 0.02004265
## Lag 50 0.002627114 0.003250855 0.00579956 0.01314557 0.00634679
## Loc1_t_6 Loc2_t_1 Loc2_t_2 Loc2_t_3 Loc2_t_4
## Lag 0 1.00000000 1.000000000 1.000000000 1.000000000 1.0000000000
## Lag 1 0.58742137 0.377316482 0.553900659 0.466116672 0.5267186525
## Lag 5 0.18107311 0.081115100 0.168560182 0.113149751 0.1473224912
## Lag 10 0.06577199 0.022176431 0.035531630 0.025288026 0.0294788540
## Lag 50 -0.00473355 -0.005777988 -0.007080582 -0.003507294 -0.0006505342
## Loc2_t_5 Loc2_t_6 Median Weight rho var_eartag
## Lag 0 1.000000000 1.000000000 1.0000000000 1.0000000 1.0000000000
## Lag 1 0.488803596 0.539506172 0.1763347200 0.8425725 0.0695928519
## Lag 5 0.130016402 0.150394201 0.0180483298 0.5608405 0.0180952709
## Lag 10 0.029333830 0.032027190 0.0007420065 0.3775070 0.0094963702
## Lag 50 -0.007257083 -0.001264897 0.0006501307 0.1007295 -0.0002404154
## var_follower var_error prp_var_eartag prp_var_follower
## Lag 0 1.0000000 1.000000000 1.0000000000 1.0000000
## Lag 1 0.8956518 -0.060174177 0.0637359686 0.8967390
## Lag 5 0.7311775 0.001253008 0.0188491955 0.7326070
## Lag 10 0.6126288 0.008911430 0.0104061956 0.6138267
## Lag 50 0.2362441 -0.003697967 0.0001498439 0.2360492
## prp_var_error lp__
## Lag 0 1.000000000 1.0000000
## Lag 1 0.066564607 0.9714803
## Lag 5 0.021511206 0.8919174
## Lag 10 0.012872261 0.8100203
## Lag 50 0.002574868 0.3747367effectiveSize(outp3)## Loc1_t_1 Loc1_t_2 Loc1_t_3 Loc1_t_4
## 8896.0346 5430.8242 6228.6199 6277.7030
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## 7232.8533 5433.8754 8908.7473 5835.7185
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## 7483.8863 6302.1433 6963.3690 6246.2011
## Median Weight rho var_eartag var_follower
## 15785.0523 1456.4451 18105.5747 525.2394
## var_error prp_var_eartag prp_var_follower prp_var_error
## 31297.5247 18170.5661 525.2657 17650.9187
## lp__
## 297.2521traplot(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
## -1.27431 0.07056 -0.11132 2.10192
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## -0.37715 0.24376 -1.04813 -1.24940
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## -0.51429 2.18446 1.64316 -2.41339
## Median Weight rho var_eartag var_follower
## -0.40416 0.14330 0.71262 -0.41287
## var_error prp_var_eartag prp_var_follower prp_var_error
## 1.62776 0.63326 -0.43210 -0.44679
## lp__
## 1.15415
##
##
## [[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
## -0.16258 -0.79322 0.35383 -1.46624
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## 0.73680 -0.07457 -0.68298 0.58418
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## -0.15568 -0.54302 0.25337 0.46109
## Median Weight rho var_eartag var_follower
## 1.07663 0.18811 -0.97623 -0.28084
## var_error prp_var_eartag prp_var_follower prp_var_error
## 0.60169 -0.96307 -0.26369 1.03082
## lp__
## 0.27574
##
##
## [[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
## -0.5168 0.2442 -0.8276 -0.4234
## Loc1_t_5 Loc1_t_6 Loc2_t_1 Loc2_t_2
## -0.7211 0.6097 -0.9469 1.3834
## Loc2_t_3 Loc2_t_4 Loc2_t_5 Loc2_t_6
## -1.4617 -0.2312 -0.6740 0.8537
## Median Weight rho var_eartag var_follower
## 1.8139 0.6791 -1.1441 -0.3619
## var_error prp_var_eartag prp_var_follower prp_var_error
## -2.3285 -0.9241 -0.3272 1.0329
## lp__
## 0.6467#gelman.diag(outp3)
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 1.599e+01 1.149357 6.636e-03 1.243e-02
## Loc1_t_2 1.109e+01 1.074233 6.202e-03 1.475e-02
## Loc1_t_3 1.202e+01 1.095814 6.327e-03 1.402e-02
## Loc1_t_4 1.092e+01 1.221481 7.052e-03 1.545e-02
## Loc1_t_5 1.238e+01 1.267039 7.315e-03 1.507e-02
## Loc1_t_6 8.233e+00 1.143845 6.604e-03 1.551e-02
## Loc2_t_1 1.536e+01 1.156957 6.680e-03 1.232e-02
## Loc2_t_2 1.103e+01 1.072370 6.191e-03 1.421e-02
## Loc2_t_3 1.854e+01 1.103172 6.369e-03 1.297e-02
## Loc2_t_4 1.169e+01 1.218158 7.033e-03 1.543e-02
## Loc2_t_5 1.225e+01 1.242491 7.174e-03 1.500e-02
## Loc2_t_6 1.009e+01 1.156800 6.679e-03 1.470e-02
## Median Weight -2.566e-02 0.005171 2.986e-05 4.150e-05
## rho -3.602e-01 0.392439 2.266e-03 1.048e-02
## var_eartag 1.087e+01 1.783456 1.030e-02 1.332e-02
## var_follower 7.555e-02 0.069811 4.031e-04 3.078e-03
## var_error 4.496e+01 0.814365 4.702e-03 4.737e-03
## prp_var_eartag 1.938e-01 0.025545 1.475e-04 1.904e-04
## prp_var_follower 1.350e-03 0.001244 7.184e-06 5.486e-05
## prp_var_error 8.049e-01 0.025581 1.477e-04 1.932e-04
## lp__ -1.529e+04 62.217342 3.592e-01 3.600e+00
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## Loc1_t_1 1.374e+01 1.522e+01 1.600e+01 1.677e+01 1.827e+01
## Loc1_t_2 9.010e+00 1.036e+01 1.109e+01 1.182e+01 1.318e+01
## Loc1_t_3 9.855e+00 1.128e+01 1.202e+01 1.276e+01 1.417e+01
## Loc1_t_4 8.532e+00 1.010e+01 1.092e+01 1.174e+01 1.332e+01
## Loc1_t_5 9.880e+00 1.153e+01 1.238e+01 1.323e+01 1.483e+01
## Loc1_t_6 6.000e+00 7.461e+00 8.223e+00 8.999e+00 1.048e+01
## Loc2_t_1 1.308e+01 1.460e+01 1.537e+01 1.614e+01 1.762e+01
## Loc2_t_2 8.906e+00 1.031e+01 1.103e+01 1.174e+01 1.312e+01
## Loc2_t_3 1.637e+01 1.781e+01 1.854e+01 1.927e+01 2.070e+01
## Loc2_t_4 9.324e+00 1.086e+01 1.169e+01 1.250e+01 1.410e+01
## Loc2_t_5 9.821e+00 1.142e+01 1.225e+01 1.308e+01 1.470e+01
## Loc2_t_6 7.818e+00 9.318e+00 1.010e+01 1.087e+01 1.236e+01
## Median Weight -3.576e-02 -2.915e-02 -2.564e-02 -2.216e-02 -1.562e-02
## rho -9.373e-01 -6.679e-01 -4.124e-01 -1.106e-01 5.394e-01
## var_eartag 7.846e+00 9.624e+00 1.070e+01 1.195e+01 1.484e+01
## var_follower 1.118e-02 2.624e-02 5.326e-02 1.006e-01 2.678e-01
## var_error 4.340e+01 4.440e+01 4.494e+01 4.550e+01 4.659e+01
## prp_var_eartag 1.482e-01 1.760e-01 1.921e-01 2.099e-01 2.486e-01
## prp_var_follower 2.009e-04 4.702e-04 9.529e-04 1.801e-03 4.761e-03
## prp_var_error 7.500e-01 7.888e-01 8.066e-01 8.228e-01 8.505e-01
## lp__ -1.540e+04 -1.534e+04 -1.529e+04 -1.525e+04 -1.516e+04print(efcov600.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] 15.99 0.01 1.15 13.74 15.22 16.00
## beta[2] 11.09 0.02 1.07 9.01 10.36 11.09
## beta[3] 12.02 0.01 1.10 9.86 11.28 12.02
## beta[4] 10.92 0.02 1.22 8.53 10.10 10.92
## beta[5] 12.38 0.02 1.27 9.88 11.53 12.38
## beta[6] 8.23 0.02 1.14 6.00 7.46 8.22
## beta[7] 15.36 0.01 1.16 13.08 14.60 15.37
## beta[8] 11.03 0.01 1.07 8.91 10.31 11.03
## beta[9] 18.54 0.01 1.10 16.37 17.81 18.54
## beta[10] 11.69 0.02 1.22 9.32 10.86 11.69
## beta[11] 12.25 0.02 1.24 9.82 11.42 12.25
## beta[12] 10.09 0.01 1.16 7.82 9.32 10.10
## beta[13] -0.03 0.00 0.01 -0.04 -0.03 -0.03
## rho -0.36 0.01 0.39 -0.94 -0.67 -0.41
## var_eartag 10.87 0.01 1.78 7.85 9.62 10.70
## var_follower 0.08 0.00 0.07 0.01 0.03 0.05
## var_error 44.96 0.00 0.81 43.40 44.40 44.94
## prp_var_eartag 0.19 0.00 0.03 0.15 0.18 0.19
## prp_var_follower 0.00 0.00 0.00 0.00 0.00 0.00
## prp_var_error 0.80 0.00 0.03 0.75 0.79 0.81
## lp__ -15289.86 3.86 62.22 -15397.39 -15336.14 -15293.52
## 75% 97.5% n_eff Rhat
## beta[1] 16.77 18.27 8506 1.00
## beta[2] 11.82 13.18 5051 1.00
## beta[3] 12.76 14.17 5619 1.00
## beta[4] 11.74 13.32 5828 1.00
## beta[5] 13.23 14.83 6646 1.00
## beta[6] 9.00 10.48 4950 1.00
## beta[7] 16.14 17.62 8650 1.00
## beta[8] 11.74 13.12 5338 1.00
## beta[9] 19.27 20.70 7259 1.00
## beta[10] 12.50 14.10 6064 1.00
## beta[11] 13.08 14.70 6570 1.00
## beta[12] 10.87 12.36 6092 1.00
## beta[13] -0.02 -0.02 15110 1.00
## rho -0.11 0.54 954 1.00
## var_eartag 11.95 14.84 17799 1.00
## var_follower 0.10 0.27 413 1.00
## var_error 45.50 46.59 29891 1.00
## prp_var_eartag 0.21 0.25 17992 1.00
## prp_var_follower 0.00 0.00 413 1.00
## prp_var_error 0.82 0.85 17302 1.00
## lp__ -15248.28 -15156.53 259 1.01
##
## Samples were drawn using NUTS(diag_e) at Sat Sep 28 15:58:22 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)