\(Models\ comparison\ trough\ Widely\ applicable\ information\ criterion\ (WAIC),\ using\ the dataset\\ with\ the\ visit\ length\ at\ the\ feeder\ when\ the\ next\ visit\ was\ less\ than\ or\ equal\ to\ 60sc,\ and\ greater\ than\ or\ equal\ to\ 600sc, from\ 7\ trials,\\ in\ pig\ production\)

\(The\ matrix\ to\ each\ model\ contain:\\ elpd_{waic}:\ expected\ log\ predictive\ pointwise\ density\\p_{waic}:\ effective\ number\ of\ parameters\\ waic:\ information\ ciretion\ converted\ to\ deviance\ scale=\ -2*elpd_{waic}\)

1. Model comparison visit length as the next visit is less or equal than 60 seconds (58255 records)

1.1. WAIC criterion

print(m1.60s.waic)
## 
## Computed from 30000 by 58255 log-likelihood matrix
## 
##            Estimate    SE
## elpd_waic -192339.2 236.7
## p_waic        181.7   2.0
## waic       384678.4 473.4
## Warning: 2 (0.0%) p_waic estimates greater than 0.4. We recommend trying loo
## instead.
print(m2.60s.waic)
## 
## Computed from 30000 by 58255 log-likelihood matrix
## 
##            Estimate    SE
## elpd_waic -191608.1 240.3
## p_waic        301.0   3.2
## waic       383216.3 480.6
## Warning: 2 (0.0%) p_waic estimates greater than 0.4. We recommend trying loo
## instead.
print(m3.60s.waic)
## 
## Computed from 30000 by 58255 log-likelihood matrix
## 
##            Estimate    SE
## elpd_waic -191608.3 240.3
## p_waic        301.3   3.2
## waic       383216.6 480.6
## Warning: 2 (0.0%) p_waic estimates greater than 0.4. We recommend trying loo
## instead.

1.2. Model comparison

\(compare\ fitted\ models\ based\ on\ expected\ log\ pointwise\ predictive\ density\ (elpd_{waic}),\\ the\ matrix\ contain:\\ elpd_{diff}: is\ the\ diference\ in\ elpd\ for\ two\ models,\ if\ more\ than\ two\ models\ asre\ comared,\ the\ difference\ is\ computed\ relative\ to\ the model\ with\ highest\ elpd\\ se_{diff}:\ standard\ error\ of\ deifference\\ se-elpd_{waic}:\ standard \ error \ expected\ log\ predictive\ pointwise\ density\\ se-p_{waic}:\ standard \ error\ effective\ number\ of\ parameters\)

print(loo_compare(m1.60s.waic,m2.60s.waic, m3.60s.waic), simplify = F)
##        elpd_diff se_diff   elpd_waic se_elpd_waic p_waic    se_p_waic waic     
## model2       0.0       0.0 -191608.1     240.3        301.0       3.2  383216.3
## model3      -0.1       0.5 -191608.3     240.3        301.3       3.2  383216.6
## model1    -731.1      41.0 -192339.2     236.7        181.7       2.0  384678.4
##        se_waic  
## model2     480.6
## model3     480.6
## model1     473.4
print(compare(m1.60s.waic,m2.60s.waic, m3.60s.waic), simplify = F)
##             elpd_diff se_diff   elpd_waic se_elpd_waic p_waic    se_p_waic
## m2.60s.waic       0.0       0.0 -191608.1     240.3        301.0       3.2
## m3.60s.waic      -0.1       0.5 -191608.3     240.3        301.3       3.2
## m1.60s.waic    -731.1      41.0 -192339.2     236.7        181.7       2.0
##             waic      se_waic  
## m2.60s.waic  383216.3     480.6
## m3.60s.waic  383216.6     480.6
## m1.60s.waic  384678.4     473.4

2. Model comparison visit length as the next visit is greater or equal than 600 seconds (6258 records)

2.1. WAIC criterion

print(m1.600s.waic)
## 
## Computed from 30000 by 6258 log-likelihood matrix
## 
##           Estimate    SE
## elpd_waic -21071.1 211.5
## p_waic       179.3  20.2
## waic       42142.1 423.1
## Warning: 33 (0.5%) p_waic estimates greater than 0.4. We recommend trying loo
## instead.
print(m2.600s.waic)
## 
## Computed from 30000 by 6258 log-likelihood matrix
## 
##           Estimate    SE
## elpd_waic -21069.4 210.6
## p_waic       184.0  20.5
## waic       42138.9 421.2
## Warning: 37 (0.6%) p_waic estimates greater than 0.4. We recommend trying loo
## instead.
print(m3.600s.waic)
## 
## Computed from 30000 by 6258 log-likelihood matrix
## 
##           Estimate    SE
## elpd_waic -21072.1 211.1
## p_waic       186.1  20.8
## waic       42144.2 422.2
## Warning: 37 (0.6%) p_waic estimates greater than 0.4. We recommend trying loo
## instead.

2.2. Model comparison

print(loo_compare(m1.600s.waic,m2.600s.waic, m3.600s.waic),simplify=F)
##        elpd_diff se_diff  elpd_waic se_elpd_waic p_waic   se_p_waic waic    
## model2      0.0       0.0 -21069.4     210.6        184.0     20.5   42138.9
## model1     -1.6       1.4 -21071.1     211.5        179.3     20.2   42142.1
## model3     -2.7       1.4 -21072.1     211.1        186.1     20.8   42144.2
##        se_waic 
## model2    421.2
## model1    423.1
## model3    422.2
print(compare(m1.600s.waic,m2.600s.waic, m3.600s.waic),simplify=F)
##              elpd_diff se_diff  elpd_waic se_elpd_waic p_waic   se_p_waic
## m2.600s.waic      0.0       0.0 -21069.4     210.6        184.0     20.5 
## m1.600s.waic     -1.6       1.4 -21071.1     211.5        179.3     20.2 
## m3.600s.waic     -2.7       1.4 -21072.1     211.1        186.1     20.8 
##              waic     se_waic 
## m2.600s.waic  42138.9    421.2
## m1.600s.waic  42142.1    423.1
## m3.600s.waic  42144.2    422.2