ERDC Davis Solute Stats

Kelly Loria 2026-04-06

• Data Summary
• Exploratory Analysis
  • Covariate Relationships
• Statistical Models
  • Frequentist Mixed Models (Precipitation)
  • Bayesian Models
• Combined Results
• Session Info

Data Summary

For all burned locations.

Summary of water quality sampling by site

Exploratory Analysis

Covariate Relationships

Statistical Models

Frequentist Mixed Models (Precipitation)

AIC comparison of precipitation models

Model selection based on AICc

Best model: ppt_mod.2 (TSS ~ PPT + TSF + Flow)

Rationale:

• ΔAICc difference trivial from ppt_mod.2 to the interaction models (ppt_mod and ppt_mod.3)

• Interaction unsupported and more complex in ppt_mod

• Strong collinearity (r = −0.871) in ppt_mod

Bayesian Models

Model Setup

TSS Model

##  Family: lognormal 
##   Links: mu = identity; sigma = identity 
## Formula: TSS ~ scale(lag_C_PPT) + scale(tsf) + scale(flow_filled) + catchment + (1 | catchment:site) 
##    Data: data (Number of observations: 66) 
##   Draws: 3 chains, each with iter = 3000; warmup = 1500; thin = 1;
##          total post-warmup draws = 4500
## 
## Multilevel Hyperparameters:
## ~catchment:site (Number of levels: 4) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.53      0.44     0.02     1.68 1.00     1166     1506
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept            0.90      0.51    -0.00     2.05 1.00     1313     1363
## scalelag_C_PPT       0.03      0.18    -0.32     0.39 1.00     2752     2544
## scaletsf             0.94      0.20     0.54     1.33 1.00     2175     2142
## scaleflow_filled    -0.11      0.27    -0.64     0.43 1.00     1773     1852
## catchmentwinters     1.06      0.68    -0.43     2.23 1.00     1663     1316
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     1.37      0.13     1.15     1.64 1.00     2559     2840
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## 
## Computed from 4500 by 66 log-likelihood matrix.
## 
##          Estimate   SE
## elpd_loo   -216.3 15.3
## p_loo         7.5  1.5
## looic       432.5 30.7
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.4, 1.1]).
## 
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.

TSS Model Effects (Log and Exponentiated Scale)

Look at solute with TSS, PPT, and flow

DOC Model

##  Family: lognormal 
##   Links: mu = identity; sigma = identity 
## Formula: DOC_QC ~ scale(lag_C_PPT) + scale(tsf) + scale(flow_filled) + catchment + (1 | catchment:site) 
##    Data: data (Number of observations: 69) 
##   Draws: 3 chains, each with iter = 3000; warmup = 1500; thin = 1;
##          total post-warmup draws = 4500
## 
## Multilevel Hyperparameters:
## ~catchment:site (Number of levels: 4) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.21      0.19     0.01     0.66 1.00      718      871
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept            0.91      0.19     0.50     1.29 1.00     1121      844
## scalelag_C_PPT       0.10      0.05    -0.01     0.21 1.00     3285     2752
## scaletsf             0.00      0.06    -0.12     0.12 1.00     3050     2933
## scaleflow_filled    -0.04      0.09    -0.21     0.12 1.00     2561     2576
## catchmentwinters     0.04      0.27    -0.54     0.58 1.00     1393     1119
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.41      0.04     0.35     0.49 1.00     3248     2922
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## 
## Computed from 4500 by 69 log-likelihood matrix.
## 
##          Estimate   SE
## elpd_loo   -105.6  7.5
## p_loo         7.5  1.2
## looic       211.2 15.0
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.5, 1.0]).
## 
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.

DOC Model Effects (Log and Exponentiated Scale)

Look at solute with TSF, PPT, and flow

TDN Model

##  Family: lognormal 
##   Links: mu = identity; sigma = identity 
## Formula: TDN_QC ~ scale(lag_C_PPT) + scale(tsf) + scale(flow_filled) + catchment + (1 | catchment:site) 
##    Data: data (Number of observations: 69) 
##   Draws: 3 chains, each with iter = 3000; warmup = 1500; thin = 1;
##          total post-warmup draws = 4500
## 
## Multilevel Hyperparameters:
## ~catchment:site (Number of levels: 4) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.42      0.31     0.04     1.30 1.00      697      756
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           -2.93      0.35    -3.70    -2.22 1.00     1428     1320
## scalelag_C_PPT       0.13      0.09    -0.05     0.31 1.00     3222     2367
## scaletsf            -0.00      0.10    -0.21     0.19 1.00     1936     1685
## scaleflow_filled     0.20      0.15    -0.08     0.48 1.00     2016     2727
## catchmentwinters     0.27      0.46    -0.61     1.27 1.00     1453     1420
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.66      0.06     0.56     0.80 1.00     2264     2750
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## 
## Computed from 4500 by 69 log-likelihood matrix.
## 
##          Estimate   SE
## elpd_loo    117.2  6.1
## p_loo         6.7  0.8
## looic      -234.5 12.2
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.4, 1.1]).
## 
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.

TDN Model Effects (Log and Exponentiated Scale)

Look at solute with TSF, PPT, and flow

PO4.P Model

##  Family: lognormal 
##   Links: mu = identity; sigma = identity 
## Formula: PO4.P_QC ~ scale(lag_C_PPT) + scale(tsf) + scale(flow_filled) + catchment + (1 | catchment:site) 
##    Data: data (Number of observations: 55) 
##   Draws: 3 chains, each with iter = 3000; warmup = 1500; thin = 1;
##          total post-warmup draws = 4500
## 
## Multilevel Hyperparameters:
## ~catchment:site (Number of levels: 4) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.27      0.27     0.01     1.05 1.00      461      220
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           -2.92      0.31    -3.52    -2.28 1.00      750      471
## scalelag_C_PPT       0.15      0.13    -0.10     0.41 1.00     1889     1863
## scaletsf            -0.25      0.14    -0.51     0.02 1.00     1331     1539
## scaleflow_filled    -0.20      0.18    -0.54     0.17 1.00     1558      954
## catchmentwinters    -0.33      0.45    -1.28     0.54 1.01      470      171
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.83      0.09     0.68     1.03 1.00     1042      511
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## 
## Computed from 4500 by 55 log-likelihood matrix.
## 
##          Estimate   SE
## elpd_loo     99.4  9.1
## p_loo         6.4  1.3
## looic      -198.9 18.1
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.2, 0.9]).
## 
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.

PO4.P Model Effects (Log and Exponentiated Scale)

Look at solute with TSF, PPT, and flow

Sr Model

##  Family: lognormal 
##   Links: mu = identity; sigma = identity 
## Formula: Sr_QC ~ scale(lag_C_PPT) + scale(tsf) + scale(flow_filled) + catchment + (1 | catchment:site) 
##    Data: data (Number of observations: 69) 
##   Draws: 3 chains, each with iter = 3000; warmup = 1500; thin = 1;
##          total post-warmup draws = 4500
## 
## Multilevel Hyperparameters:
## ~catchment:site (Number of levels: 4) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.15      0.11     0.01     0.43 1.00      796     1210
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept            4.83      0.13     4.53     5.10 1.00     1136      548
## scalelag_C_PPT       0.03      0.03    -0.03     0.08 1.00     2572     1871
## scaletsf             0.10      0.03     0.04     0.15 1.00     2339     2293
## scaleflow_filled     0.06      0.04    -0.02     0.14 1.00     2173     2217
## catchmentwinters    -0.31      0.18    -0.69     0.07 1.01     1038      684
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.20      0.02     0.16     0.24 1.00     2715     2317
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## 
## Computed from 4500 by 69 log-likelihood matrix.
## 
##          Estimate   SE
## elpd_loo   -310.6  7.2
## p_loo         7.5  1.4
## looic       621.2 14.3
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.4, 0.9]).
## 
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.

Sr Model Effects (Log and Exponentiated Scale)

Look at solute with TSF, PPT, and flow

Fe Model

##  Family: lognormal 
##   Links: mu = identity; sigma = identity 
## Formula: Fe_QC ~ scale(lag_C_PPT) + scale(tsf) + scale(flow_filled) + catchment + (1 | catchment:site) 
##    Data: data (Number of observations: 69) 
##   Draws: 3 chains, each with iter = 3000; warmup = 1500; thin = 1;
##          total post-warmup draws = 4500
## 
## Multilevel Hyperparameters:
## ~catchment:site (Number of levels: 4) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.38      0.39     0.01     1.71 1.05       43       21
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept            5.45      0.33     4.74     6.05 1.01      269      566
## scalelag_C_PPT      -0.09      0.10    -0.28     0.11 1.00     2544     3028
## scaletsf             0.56      0.11     0.35     0.78 1.01     2648     2956
## scaleflow_filled    -0.58      0.16    -0.89    -0.27 1.00     1301     1815
## catchmentwinters     0.22      0.42    -0.58     1.10 1.02      164      331
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.76      0.07     0.63     0.92 1.00      360      131
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## 
## Computed from 4500 by 69 log-likelihood matrix.
## 
##          Estimate   SE
## elpd_loo   -466.9  8.6
## p_loo         7.3  1.3
## looic       933.9 17.1
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.1, 0.8]).
## 
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.

Fe Model Effects (Log and Exponentiated Scale)

Look at solute with TSF, PPT, and flow

Mn Model

##  Family: lognormal 
##   Links: mu = identity; sigma = identity 
## Formula: Mn_QC ~ scale(lag_C_PPT) + scale(tsf) + scale(flow_filled) + catchment + (1 | catchment:site) 
##    Data: data (Number of observations: 69) 
##   Draws: 3 chains, each with iter = 3000; warmup = 1500; thin = 1;
##          total post-warmup draws = 4500
## 
## Multilevel Hyperparameters:
## ~catchment:site (Number of levels: 4) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.19      0.17     0.01     0.63 1.01      652      677
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept            2.60      0.19     2.15     2.98 1.00      754      478
## scalelag_C_PPT       0.23      0.05     0.13     0.33 1.00     2616     2668
## scaletsf             0.32      0.06     0.21     0.44 1.00     1619     2022
## scaleflow_filled    -0.37      0.09    -0.54    -0.19 1.00     1463     1650
## catchmentwinters     0.08      0.27    -0.43     0.74 1.00      839      370
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.40      0.04     0.34     0.48 1.00     2220     2085
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## 
## Computed from 4500 by 69 log-likelihood matrix.
## 
##          Estimate   SE
## elpd_loo   -221.2  9.1
## p_loo         8.3  2.5
## looic       442.5 18.1
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.4, 0.9]).
## 
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.

Mn Model Effects (Log and Exponentiated Scale)

Look at solute with TSF, PPT, and flow

Ba Model

##  Family: lognormal 
##   Links: mu = identity; sigma = identity 
## Formula: Ba_QC ~ scale(lag_C_PPT) + scale(tsf) + scale(flow_filled) + catchment + (1 | catchment:site) 
##    Data: data (Number of observations: 69) 
##   Draws: 3 chains, each with iter = 3000; warmup = 1500; thin = 1;
##          total post-warmup draws = 4500
## 
## Multilevel Hyperparameters:
## ~catchment:site (Number of levels: 4) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.20      0.15     0.01     0.60 1.01      490      933
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept            3.10      0.18     2.61     3.40 1.01      357      110
## scalelag_C_PPT       0.03      0.03    -0.04     0.09 1.00     2882     2787
## scaletsf             0.04      0.04    -0.04     0.11 1.00     2663     2927
## scaleflow_filled     0.11      0.05     0.00     0.22 1.00     2789     3066
## catchmentwinters    -0.57      0.25    -0.99     0.12 1.01      326      111
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.26      0.02     0.22     0.31 1.00     2531     2776
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## 
## Computed from 4500 by 69 log-likelihood matrix.
## 
##          Estimate   SE
## elpd_loo   -199.0  7.6
## p_loo         7.2  1.2
## looic       398.1 15.2
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.5, 1.0]).
## 
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.

##    Estimate Est.Error      Q2.5     Q97.5
## R2 0.614033 0.0577231 0.4935263 0.7126013

Ba Model Effects (Log and Exponentiated Scale)

Look at solute with TSF, PPT, and flow

Ca Model

##  Family: lognormal 
##   Links: mu = identity; sigma = identity 
## Formula: Ca_QC ~ scale(lag_C_PPT) + scale(tsf) + scale(flow_filled) + catchment + (1 | catchment:site) 
##    Data: data (Number of observations: 69) 
##   Draws: 3 chains, each with iter = 3000; warmup = 1500; thin = 1;
##          total post-warmup draws = 4500
## 
## Multilevel Hyperparameters:
## ~catchment:site (Number of levels: 4) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.21      0.17     0.03     0.75 1.00      295      123
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept            7.29      0.16     6.95     7.64 1.01     1523     1269
## scalelag_C_PPT      -0.01      0.03    -0.08     0.05 1.01      489      139
## scaletsf             0.12      0.03     0.05     0.18 1.00     2489     2825
## scaleflow_filled    -0.01      0.05    -0.11     0.10 1.00      760      303
## catchmentwinters    -0.18      0.23    -0.64     0.30 1.00      648      193
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.23      0.02     0.19     0.27 1.00     2694     2779
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## 
## Computed from 4500 by 69 log-likelihood matrix.
## 
##          Estimate   SE
## elpd_loo   -495.9  6.3
## p_loo         7.5  1.4
## looic       991.9 12.5
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.1, 1.0]).
## 
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.

Ca Model Effects (Log and Exponentiated Scale)

Look at solute with TSF, PPT, and flow

Al Model

##  Family: lognormal 
##   Links: mu = identity; sigma = identity 
## Formula: Al_QC ~ scale(lag_C_PPT) + scale(tsf) + scale(flow_filled) + catchment + (1 | catchment:site) 
##    Data: data (Number of observations: 69) 
##   Draws: 3 chains, each with iter = 3000; warmup = 1500; thin = 1;
##          total post-warmup draws = 4500
## 
## Multilevel Hyperparameters:
## ~catchment:site (Number of levels: 4) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.23      0.22     0.01     0.87 1.01      637      702
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept            1.17      0.27     0.66     1.73 1.00     1186      882
## scalelag_C_PPT       0.02      0.10    -0.18     0.22 1.00     2761     2644
## scaletsf             0.26      0.11     0.04     0.48 1.00     2376     2307
## scaleflow_filled     0.26      0.16    -0.05     0.56 1.00     1636     2189
## catchmentwinters     0.79      0.37    -0.00     1.49 1.00     1209      814
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.77      0.07     0.65     0.92 1.00     3358     2917
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## 
## Computed from 4500 by 69 log-likelihood matrix.
## 
##          Estimate   SE
## elpd_loo   -195.6  7.6
## p_loo         6.5  1.3
## looic       391.3 15.1
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.5, 1.1]).
## 
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.

Al Model Effects (Log and Exponentiated Scale)

Look at solute with TSF, PPT, and flow

As Model

##  Family: lognormal 
##   Links: mu = identity; sigma = identity 
## Formula: As_QC ~ scale(lag_C_PPT) + scale(tsf) + scale(flow_filled) + catchment + (1 | catchment:site) 
##    Data: data (Number of observations: 69) 
##   Draws: 3 chains, each with iter = 3000; warmup = 1500; thin = 1;
##          total post-warmup draws = 4500
## 
## Multilevel Hyperparameters:
## ~catchment:site (Number of levels: 4) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.18      0.17     0.01     0.63 1.00      909     1088
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           -1.77      0.20    -2.20    -1.36 1.00     1025      592
## scalelag_C_PPT      -0.06      0.07    -0.19     0.07 1.00     2568     3018
## scaletsf            -0.01      0.07    -0.16     0.13 1.00     2138     2305
## scaleflow_filled    -0.14      0.10    -0.35     0.07 1.00     1810     1610
## catchmentwinters    -0.16      0.28    -0.74     0.39 1.00     1239      882
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.52      0.05     0.44     0.62 1.00     3149     2924
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## 
## Computed from 4500 by 69 log-likelihood matrix.
## 
##          Estimate   SE
## elpd_loo     72.5  5.9
## p_loo         6.7  1.3
## looic      -144.9 11.8
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.5, 1.0]).
## 
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.

Al Model Effects (Log and Exponentiated Scale)

Combined Results

Session Info

## R version 4.4.2 (2024-10-31)
## Platform: aarch64-apple-darwin20
## Running under: macOS Sequoia 15.7.4
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: America/Los_Angeles
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] broom_1.0.7                slider_0.3.3              
##  [3] kableExtra_1.4.0           knitr_1.50                
##  [5] ggpmisc_0.6.3              ggpp_0.5.9                
##  [7] ggpubr_0.6.0               cowplot_1.1.3             
##  [9] viridis_0.6.5              viridisLite_0.4.2         
## [11] dataRetrieval_2.7.17       readxl_1.4.3              
## [13] loo_2.8.0                  PerformanceAnalytics_2.0.8
## [15] xts_0.14.1                 zoo_1.8-12                
## [17] MuMIn_1.48.4               brms_2.22.0               
## [19] Rcpp_1.1.0                 lmerTest_3.1-3            
## [21] lme4_1.1-35.5              Matrix_1.7-1              
## [23] here_1.0.1                 lubridate_1.9.4           
## [25] forcats_1.0.0              stringr_1.5.1             
## [27] dplyr_1.1.4                purrr_1.1.0               
## [29] readr_2.1.5                tidyr_1.3.1               
## [31] tibble_3.3.0               ggplot2_3.5.2             
## [33] tidyverse_2.0.0           
## 
## loaded via a namespace (and not attached):
##   [1] RColorBrewer_1.1-3   tensorA_0.36.2.1     rstudioapi_0.17.1   
##   [4] jsonlite_2.0.0       magrittr_2.0.3       TH.data_1.1-2       
##   [7] estimability_1.5.1   farver_2.1.2         nloptr_2.1.1        
##  [10] rmarkdown_2.29       ragg_1.3.3           vctrs_0.6.5         
##  [13] minqa_1.2.8          rstatix_0.7.2        htmltools_0.5.8.1   
##  [16] polynom_1.4-1        curl_7.0.0           distributional_0.5.0
##  [19] cellranger_1.1.0     Formula_1.2-5        StanHeaders_2.32.10 
##  [22] sass_0.4.10          KernSmooth_2.23-24   bslib_0.9.0         
##  [25] plyr_1.8.9           sandwich_3.1-1       emmeans_1.10.6      
##  [28] cachem_1.1.0         lifecycle_1.0.4      pkgconfig_2.0.3     
##  [31] R6_2.6.1             fastmap_1.2.0        digest_0.6.37       
##  [34] numDeriv_2016.8-1.1  colorspace_2.1-1     rprojroot_2.1.1     
##  [37] warp_0.2.2           textshaping_0.4.1    labeling_0.4.3      
##  [40] timechange_0.3.0     abind_1.4-8          compiler_4.4.2      
##  [43] proxy_0.4-27         bit64_4.5.2          withr_3.0.2         
##  [46] inline_0.3.20        backports_1.5.0      carData_3.0-5       
##  [49] DBI_1.2.3            QuickJSR_1.4.0       pkgbuild_1.4.8      
##  [52] ggsignif_0.6.4       MASS_7.3-61          quantreg_6.1        
##  [55] classInt_0.4-11      tools_4.4.2          units_0.8-7         
##  [58] glue_1.8.0           quadprog_1.5-8       nlme_3.1-166        
##  [61] grid_4.4.2           sf_1.0-21            checkmate_2.3.2     
##  [64] reshape2_1.4.4       generics_0.1.4       gtable_0.3.6        
##  [67] tzdb_0.4.0           class_7.3-22         hms_1.1.3           
##  [70] xml2_1.4.0           car_3.1-3            pillar_1.11.0       
##  [73] vroom_1.6.5          posterior_1.6.0      splines_4.4.2       
##  [76] lattice_0.22-6       survival_3.7-0       bit_4.5.0.1         
##  [79] SparseM_1.84-2       tidyselect_1.2.1     gridExtra_2.3       
##  [82] V8_6.0.0             svglite_2.1.3        stats4_4.4.2        
##  [85] xfun_0.53            bridgesampling_1.1-2 matrixStats_1.4.1   
##  [88] rstan_2.32.6         stringi_1.8.7        yaml_2.3.10         
##  [91] boot_1.3-31          evaluate_1.0.5       codetools_0.2-20    
##  [94] cli_3.6.5            RcppParallel_5.1.9   xtable_1.8-4        
##  [97] systemfonts_1.1.0    jquerylib_0.1.4      dichromat_2.0-0.1   
## [100] coda_0.19-4.1        parallel_4.4.2       rstantools_2.4.0    
## [103] MatrixModels_0.5-3   bayesplot_1.11.1     Brobdingnag_1.2-9   
## [106] mvtnorm_1.3-2        scales_1.4.0         e1071_1.7-16        
## [109] crayon_1.5.3         rlang_1.1.6          multcomp_1.4-26

# Clear all cached results
unlink("_cache", recursive = TRUE)
unlink("models", recursive = TRUE)

# Re-render (will take 2-3 hours for all models)
rmarkdown::render("ERDC_MS_solute_stats_REFACTORED.Rmd")