The study-system term (sys_id) is fitted only in this sensitivity analysis. The primary model captures study-level dependence through ref_id and shared ancestry through the phylogeny, but does not include a separate study-system term. In PROCEED, sys_id, ref_id, and species identity are strongly associated. Most systems map to one species and often one source.
Changed: a study-system random intercept, (1 | sys_id), was added.
Unchanged: the full dataset, moderator definitions, phylogenetic effect, ref_id effect, priors, and MCMC settings match the primary models.
The comparison uses the fixed-effect tables. The three variance components are not reported separately.
Models were fit on a remote server, not while rendering this book: 4 chains × 4,000 iterations (2,000 warmup), adapt_delta = 0.97, max_treedepth = 15, and the cmdstanr backend.
phylo <- prepare_phylo_and_data(dat_mod, A_full)
formula <- build_ls_formula(moderator, has_phylogeny = phylo$has_phylo,
has_sys_id = TRUE)
fit <- fit_ls_model(
phylo$dat_model, formula,
build_ls_priors(formula, phylo$dat_model, phylo$V, A = phylo$A_mod),
V = phylo$V, A = phylo$A_mod, mcmc_args = default_mcmc_args)Six moderator models are reported (m01–m05, m07). The environmental-change model (m08) is excluded because its primary fit did not converge. Convergence criteria: max \(\hat{R} \leq 1.01\), bulk and tail ESS \(\geq 400\), and no divergent transitions.
sens_diagnostics_table(variant)| Moderator | Max R̂ | Min bulk ESS | Min tail ESS | Divergences | Max-treedepth hits |
|---|---|---|---|---|---|
| Elapsed time — log₁₀ generations (m04) | 1.0222 | 248 | 60 | 191 | 0 |
| Disturbance context (m01) | 1.0054 | 646 | 1311 | 21 | 0 |
| Phenotypic vs genetic study (m07) | 1.0063 | 742 | 1867 | 21 | 0 |
| Trait type (m05) | 1.0116 | 580 | 678 | 16 | 0 |
| Comparison design (m02) | 1.0194 | 571 | 1321 | 6 | 0 |
| Elapsed time — log₁₀ years (m03) | 1.0058 | 946 | 1518 | 0 | 0 |
Models requiring convergence caution: Comparison design (m02): max Rhat = 1.0194, min bulk/tail ESS = 571/1321, divergences = 6; Disturbance context (m01): max Rhat = 1.0054, min bulk/tail ESS = 646/1311, divergences = 21; Phenotypic vs genetic study (m07): max Rhat = 1.0063, min bulk/tail ESS = 742/1867, divergences = 21; Elapsed time in log10 generations (m04): max Rhat = 1.0222, min bulk/tail ESS = 248/60, divergences = 191; Trait type (m05): max Rhat = 1.0116, min bulk/tail ESS = 580/678, divergences = 16. See the table above for ESS and treedepth diagnostics.
The comparison label uses a fixed rule: DIFFERS means that the posterior median changed sign or that the 95% credible interval changed between including and excluding zero. Consistent means neither occurred; it does not mean the two estimates are identical. Intercepts are omitted from the overall count.
cat("**Overall:** ", sens_stability_summary(variant), "\n")Overall: 5 of 34 moderator coefficients change their credible-interval conclusion relative to the primary fit.
Each table reports raw treatment-coded coefficients for the location (mean ln M) and scale (log-SD) submodels. See the sensitivity overview for column definitions.
sens_all_moderator_tables(variant)sens_moderator_table('sens3_sysid', 'disturbance')| Sub-model | Term | Sensitivity β [95% CrI] | Primary β [95% CrI] | Stability |
|---|---|---|---|---|
| Location (mean lnM) | Intercept (ref.) | -0.714 [-1.224, -0.153] | -0.530 [-1.338, 0.319] | DIFFERS |
| Location (mean lnM) | Hunt_harv | -0.037 [-0.510, 0.429] | -0.276 [-0.630, 0.079] | consistent |
| Location (mean lnM) | Introduction | 0.177 [-0.300, 0.652] | 0.006 [-0.384, 0.399] | consistent |
| Location (mean lnM) | Landscapechange | 0.152 [-0.433, 0.728] | 0.207 [-0.251, 0.672] | consistent |
| Location (mean lnM) | Other | -0.043 [-0.510, 0.420] | -0.281 [-0.623, 0.063] | consistent |
| Location (mean lnM) | Pollution | 0.409 [-0.194, 1.012] | 0.173 [-0.381, 0.729] | consistent |
| Location (mean lnM) | Responsetointroductions | 0.259 [-0.406, 0.892] | 0.100 [-0.503, 0.692] | consistent |
| Scale (log-SD) | Intercept (ref.) | -0.804 [-1.036, -0.593] | -0.692 [-0.871, -0.527] | consistent |
| Scale (log-SD) | Hunt_harv | 0.332 [0.110, 0.570] | 0.365 [0.189, 0.554] | consistent |
| Scale (log-SD) | Introduction | 0.127 [-0.086, 0.361] | 0.015 [-0.155, 0.199] | consistent |
| Scale (log-SD) | Landscapechange | -0.331 [-0.655, -0.017] | -0.431 [-0.737, -0.142] | consistent |
| Scale (log-SD) | Other | 0.067 [-0.157, 0.309] | 0.138 [-0.038, 0.329] | consistent |
| Scale (log-SD) | Pollution | -0.069 [-0.410, 0.274] | -0.184 [-0.489, 0.119] | consistent |
| Scale (log-SD) | Responsetointroductions | 0.369 [0.110, 0.643] | 0.256 [0.028, 0.486] | consistent |
sens_moderator_table('sens3_sysid', 'design')| Sub-model | Term | Sensitivity β [95% CrI] | Primary β [95% CrI] | Stability |
|---|---|---|---|---|
| Location (mean lnM) | Intercept (ref.) | -0.723 [-1.157, -0.293] | -0.724 [-1.471, 0.025] | DIFFERS |
| Location (mean lnM) | Synchronic | 0.220 [0.057, 0.386] | 0.250 [0.077, 0.418] | consistent |
| Scale (log-SD) | Intercept (ref.) | -0.688 [-0.762, -0.616] | -0.468 [-0.507, -0.428] | consistent |
| Scale (log-SD) | Synchronic | 0.015 [-0.066, 0.095] | -0.208 [-0.260, -0.157] | DIFFERS |
sens_moderator_table('sens3_sysid', 'log10_years')| Sub-model | Term | Sensitivity β [95% CrI] | Primary β [95% CrI] | Stability |
|---|---|---|---|---|
| Location (mean lnM) | Intercept (ref.) | -0.968 [-1.499, -0.422] | -1.021 [-1.855, -0.173] | consistent |
| Location (mean lnM) | slope | 0.264 [0.193, 0.337] | 0.307 [0.235, 0.381] | consistent |
| Scale (log-SD) | Intercept (ref.) | -0.583 [-0.694, -0.478] | -0.354 [-0.427, -0.279] | consistent |
| Scale (log-SD) | slope | -0.058 [-0.120, 0.008] | -0.167 [-0.215, -0.119] | DIFFERS |
sens_moderator_table('sens3_sysid', 'log10_generations')| Sub-model | Term | Sensitivity β [95% CrI] | Primary β [95% CrI] | Stability |
|---|---|---|---|---|
| Location (mean lnM) | Intercept (ref.) | -0.937 [-2.206, -0.340] | -0.918 [-1.839, 0.017] | DIFFERS |
| Location (mean lnM) | slope | 0.261 [0.187, 0.332] | 0.286 [0.215, 0.359] | consistent |
| Scale (log-SD) | Intercept (ref.) | -0.558 [-0.645, -0.478] | -0.401 [-0.450, -0.350] | consistent |
| Scale (log-SD) | slope | -0.073 [-0.118, -0.024] | -0.149 [-0.182, -0.117] | consistent |
sens_moderator_table('sens3_sysid', 'trait_type')| Sub-model | Term | Sensitivity β [95% CrI] | Primary β [95% CrI] | Stability |
|---|---|---|---|---|
| Location (mean lnM) | Intercept (ref.) | -1.323 [-2.220, -0.374] | -1.332 [-2.519, -0.105] | consistent |
| Location (mean lnM) | growth | 0.784 [-0.038, 1.564] | 0.829 [0.042, 1.616] | DIFFERS |
| Location (mean lnM) | otherLH | 0.863 [0.041, 1.636] | 0.907 [0.131, 1.681] | consistent |
| Location (mean lnM) | othermorphology | 0.739 [-0.078, 1.500] | 0.782 [0.003, 1.555] | DIFFERS |
| Location (mean lnM) | phenology | 0.777 [-0.096, 1.596] | 0.806 [-0.022, 1.626] | consistent |
| Location (mean lnM) | physio | 0.654 [-0.167, 1.420] | 0.698 [-0.077, 1.477] | consistent |
| Location (mean lnM) | response | 1.147 [0.258, 1.969] | 1.167 [0.313, 2.024] | consistent |
| Location (mean lnM) | size | 0.802 [-0.018, 1.576] | 0.835 [0.058, 1.611] | DIFFERS |
| Scale (log-SD) | Intercept (ref.) | -0.328 [-0.824, 0.179] | -0.373 [-0.863, 0.129] | consistent |
| Scale (log-SD) | growth | -1.018 [-1.661, -0.420] | -0.977 [-1.615, -0.387] | consistent |
| Scale (log-SD) | otherLH | -0.229 [-0.732, 0.268] | -0.181 [-0.688, 0.314] | consistent |
| Scale (log-SD) | othermorphology | -0.581 [-1.081, -0.087] | -0.519 [-1.027, -0.025] | consistent |
| Scale (log-SD) | phenology | -0.469 [-1.075, 0.095] | -0.383 [-0.937, 0.171] | consistent |
| Scale (log-SD) | physio | -0.727 [-1.244, -0.211] | -0.698 [-1.225, -0.179] | consistent |
| Scale (log-SD) | response | -0.632 [-1.571, 0.089] | -0.550 [-1.354, 0.158] | consistent |
| Scale (log-SD) | size | -0.157 [-0.663, 0.338] | -0.037 [-0.538, 0.454] | consistent |
sens_moderator_table('sens3_sysid', 'genphen')| Sub-model | Term | Sensitivity β [95% CrI] | Primary β [95% CrI] | Stability |
|---|---|---|---|---|
| Location (mean lnM) | Intercept (ref.) | -0.467 [-0.896, -0.031] | -0.427 [-1.208, 0.371] | DIFFERS |
| Location (mean lnM) | Phenotypic | -0.182 [-0.324, -0.043] | -0.210 [-0.355, -0.063] | consistent |
| Scale (log-SD) | Intercept (ref.) | -0.837 [-0.890, -0.787] | -0.836 [-0.889, -0.784] | consistent |
| Scale (log-SD) | Phenotypic | 0.256 [0.193, 0.322] | 0.338 [0.278, 0.398] | consistent |