Single Compartment and Single Exposure : Male Gammarus Single
data("dataMaleGammarusSingle")
# work only when replicate have the same length !!!
data_MGS <- dataMaleGammarusSingle[dataMaleGammarusSingle$replicate == 1,]
modelData_MGS <- dataPBK(
object = data_MGS,
col_time = "time",
col_replicate = "replicate",
col_exposure = "expw",
col_compartment = "conc",
time_accumulation = 4,
nested_model = NA)
fitPBK_MGS <- fitPBK(modelData_MGS)
#>
#> SAMPLING FOR MODEL 'PBK_AD' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.000122 seconds
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#> SAMPLING FOR MODEL 'PBK_AD' NOW (CHAIN 3).
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#> Chain 4:
#> Warning: There were 2403 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
library(loo)
#> This is loo version 2.6.0
#> - Online documentation and vignettes at mc-stan.org/loo
#> - As of v2.0.0 loo defaults to 1 core but we recommend using as many as possible. Use the 'cores' argument or set options(mc.cores = NUM_CORES) for an entire session.
log_lik_MGS <- loo::extract_log_lik(fitPBK_MGS$stanfit, merge_chains = FALSE)
WAIC_MGS <- waic(log_lik_MGS)
#> Warning:
#> 1 (12.5%) p_waic estimates greater than 0.4. We recommend trying loo instead.
Multiple Compartiment, Single Exposure - Default interaction
data("dataCompartment4")
data_C4 <- dataCompartment4
modelData_C4 <- dataPBK(
object = data_C4,
col_time = "temps",
col_replicate = "replicat",
col_exposure = "condition",
col_compartment = c("intestin", "reste", "caecum", "cephalon"),
time_accumulation = 7)
You can have a look at the assumption on the interaction
nested_model(modelData_C4)
#> $ku_nest
#> uptake intestin uptake reste uptake caecum uptake cephalon
#> 1 1 1 1
#>
#> $ke_nest
#> excretion intestin excretion reste excretion caecum excretion cephalon
#> 1 1 1 1
#>
#> $k_nest
#> intestin reste caecum cephalon
#> intestin 0 1 1 1
#> reste 1 0 1 1
#> caecum 1 1 0 1
#> cephalon 1 1 1 0
fitPBK_C4 <- fitPBK(modelData_C4, chains = 1, iter = 1000)
#>
#> SAMPLING FOR MODEL 'PBK_AD' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.00137 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 13.7 seconds.
#> Chain 1: Adjust your expectations accordingly!
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#> Chain 1:
#> Chain 1: Elapsed Time: 117.057 seconds (Warm-up)
#> Chain 1: 47.546 seconds (Sampling)
#> Chain 1: 164.603 seconds (Total)
#> Chain 1:
#> Warning: There were 480 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: The largest R-hat is NA, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
Compute WAIC with loo library:
library(loo)
log_lik_C4 <- loo::extract_log_lik(fitPBK_C4$stanfit, merge_chains = FALSE)
WAIC_C4 <- waic(log_lik_C4)
#> Warning:
#> 17 (20.2%) p_waic estimates greater than 0.4. We recommend trying loo instead.
print(WAIC_C4)
#>
#> Computed from 500 by 84 log-likelihood matrix
#>
#> Estimate SE
#> elpd_waic -231.4 17.1
#> p_waic 18.4 2.4
#> waic 462.8 34.1
#>
#> 17 (20.2%) p_waic estimates greater than 0.4. We recommend trying loo instead.
Compute LOO:
r_eff_C4 <- relative_eff(exp(log_lik_C4))
LOO_C4 <- loo(log_lik_C4, r_eff = r_eff_C4, cores = 2)
#> Warning: Some Pareto k diagnostic values are slightly high. See help('pareto-k-diagnostic') for details.
print(LOO_C4)
#>
#> Computed from 500 by 84 log-likelihood matrix
#>
#> Estimate SE
#> elpd_loo -231.0 17.0
#> p_loo 18.0 2.3
#> looic 462.0 34.0
#> ------
#> Monte Carlo SE of elpd_loo is 1.7.
#>
#> Pareto k diagnostic values:
#> Count Pct. Min. n_eff
#> (-Inf, 0.5] (good) 83 98.8% 2
#> (0.5, 0.7] (ok) 1 1.2% 3
#> (0.7, 1] (bad) 0 0.0% <NA>
#> (1, Inf) (very bad) 0 0.0% <NA>
#>
#> All Pareto k estimates are ok (k < 0.7).
#> See help('pareto-k-diagnostic') for details.
Multiple Compartiment, Single Exposure : Change nesting
You can have a look at the assumption on the interaction
nm_C4 = nested_model(modelData_C4)
We want to change the interaction between organs. For now, all organs
interact with each other but not with themselve, the the interaction
matrix look like:
nm_C4$k_nest
#> intestin reste caecum cephalon
#> intestin 0 1 1 1
#> reste 1 0 1 1
#> caecum 1 1 0 1
#> cephalon 1 1 1 0
which can be written like:
matrix(c(
c(0,1,1,1),
c(1,0,1,1),
c(1,1,0,0),
c(1,1,1,0)),
ncol=4,nrow=4,byrow=TRUE)
#> [,1] [,2] [,3] [,4]
#> [1,] 0 1 1 1
#> [2,] 1 0 1 1
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
Let assume interaction are only one way, so a triangular matrix:
matrix(c(
c(0,1,1,1),
c(0,0,1,1),
c(0,0,0,0),
c(0,0,0,0)),
ncol=4,nrow=4,byrow=TRUE)
#> [,1] [,2] [,3] [,4]
#> [1,] 0 1 1 1
#> [2,] 0 0 1 1
#> [3,] 0 0 0 0
#> [4,] 0 0 0 0
modelData_C42 <- dataPBK(
object = data_C4,
col_time = "temps",
col_replicate = "replicat",
col_exposure = "condition",
col_compartment = c("intestin", "reste", "caecum", "cephalon"),
time_accumulation = 7,
ku_nest = c(1,1,1,1), # No Change here
ke_nest = c(1,1,1,1), # No Change here
k_nest = matrix(c(
c(0,1,1,1),
c(0,0,1,1),
c(0,0,0,0),
c(0,0,0,0)),
ncol=4,nrow=4,byrow=TRUE) # Remove
)
nested_model(modelData_C42)
#> $ku_nest
#> uptake intestin uptake reste uptake caecum uptake cephalon
#> 1 1 1 1
#>
#> $ke_nest
#> excretion intestin excretion reste excretion caecum excretion cephalon
#> 1 1 1 1
#>
#> $k_nest
#> intestin reste caecum cephalon
#> intestin 0 1 1 1
#> reste 0 0 1 1
#> caecum 0 0 0 0
#> cephalon 0 0 0 0
fitPBK_C42 <- fitPBK(modelData_C42, chains = 1, iter = 1000)
#>
#> SAMPLING FOR MODEL 'PBK_AD' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.001871 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 18.71 seconds.
#> Chain 1: Adjust your expectations accordingly!
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#> Chain 1:
#> Chain 1: Elapsed Time: 9.832 seconds (Warm-up)
#> Chain 1: 23.241 seconds (Sampling)
#> Chain 1: 33.073 seconds (Total)
#> Chain 1:
#> Warning: There were 500 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: There were 1 chains where the estimated Bayesian Fraction of Missing Information was low. See
#> https://mc-stan.org/misc/warnings.html#bfmi-low
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: The largest R-hat is NA, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
log_lik_C42 <- loo::extract_log_lik(fitPBK_C42$stanfit, merge_chains = FALSE)
WAIC_C42 <- waic(log_lik_C42)
#> Warning:
#> 10 (11.9%) p_waic estimates greater than 0.4. We recommend trying loo instead.
print(WAIC_C42)
#>
#> Computed from 500 by 84 log-likelihood matrix
#>
#> Estimate SE
#> elpd_waic -315.7 11.3
#> p_waic 14.0 2.0
#> waic 631.5 22.6
#>
#> 10 (11.9%) p_waic estimates greater than 0.4. We recommend trying loo instead.
Compare WAIC with previous model
comp_C4_C42 <- loo_compare(WAIC_C4, WAIC_C42)
print(comp_C4_C42)
#> elpd_diff se_diff
#> model1 0.0 0.0
#> model2 -84.3 7.7
The first column shows the difference in ELPD relative to the model
with the largest ELPD. In this case, the difference in elpd and its
scale relative to the approximate standard error of the difference)
indicates a preference for the second model (model2).