Following protocol §3.7, we retained only contrasts with total sample size \(n_1 + n_2 \geq 40\).
Changed: the analysis includes 5,253 of 7,237 contrasts after applying the sample-size threshold.
Unchanged: the moderator definitions, phylogenetic effect, ref_id effect, priors, and MCMC settings match the primary models.
Models were fit on a remote server, not while rendering this book. Each model uses 4 chains × 4,000 iterations (2,000 warmup), adapt_delta = 0.97, max_treedepth = 15, and the cmdstanr backend. This chapter reads cached summary tables only.
dat_n40 <- dat_es |> dplyr::filter(n_total >= 40)
phylo <- prepare_phylo_and_data(dat_mod, A_full)
formula <- build_ls_formula(moderator, has_phylogeny = phylo$has_phylo)
fit <- fit_ls_model(
phylo$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 |
|---|---|---|---|---|---|
| Trait type (m05) | 1.0127 | 454 | 627 | 133 | 0 |
| Comparison design (m02) | 1.0074 | 550 | 656 | 0 | 0 |
| Disturbance context (m01) | 1.0055 | 599 | 1134 | 0 | 0 |
| Phenotypic vs genetic study (m07) | 1.0154 | 630 | 1423 | 0 | 0 |
| Elapsed time — log₁₀ generations (m04) | 1.0072 | 645 | 1217 | 0 | 0 |
| Elapsed time — log₁₀ years (m03) | 1.0053 | 748 | 1820 | 0 | 0 |
Models requiring convergence caution: Phenotypic vs genetic study (m07): max Rhat = 1.0154, min bulk/tail ESS = 630/1423, divergences = 0; Trait type (m05): max Rhat = 1.0127, min bulk/tail ESS = 454/627, divergences = 133. 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: 3 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('sens1_n40', 'disturbance')| Sub-model | Term | Sensitivity β [95% CrI] | Primary β [95% CrI] | Stability |
|---|---|---|---|---|
| Location (mean lnM) | Intercept (ref.) | -1.039 [-1.792, -0.301] | -0.530 [-1.338, 0.319] | DIFFERS |
| Location (mean lnM) | Hunt_harv | -0.044 [-0.679, 0.591] | -0.276 [-0.630, 0.079] | consistent |
| Location (mean lnM) | Introduction | 0.261 [-0.364, 0.879] | 0.006 [-0.384, 0.399] | consistent |
| Location (mean lnM) | Landscapechange | 0.456 [-0.230, 1.182] | 0.207 [-0.251, 0.672] | consistent |
| Location (mean lnM) | Other | -0.067 [-0.692, 0.562] | -0.281 [-0.623, 0.063] | consistent |
| Location (mean lnM) | Pollution | 0.539 [-0.254, 1.329] | 0.173 [-0.381, 0.729] | consistent |
| Location (mean lnM) | Responsetointroductions | 0.596 [-0.225, 1.423] | 0.100 [-0.503, 0.692] | consistent |
| Scale (log-SD) | Intercept (ref.) | -0.550 [-0.745, -0.358] | -0.692 [-0.871, -0.527] | consistent |
| Scale (log-SD) | Hunt_harv | 0.228 [0.027, 0.431] | 0.365 [0.189, 0.554] | consistent |
| Scale (log-SD) | Introduction | -0.087 [-0.282, 0.109] | 0.015 [-0.155, 0.199] | DIFFERS |
| Scale (log-SD) | Landscapechange | -0.438 [-0.753, -0.136] | -0.431 [-0.737, -0.142] | consistent |
| Scale (log-SD) | Other | 0.109 [-0.093, 0.311] | 0.138 [-0.038, 0.329] | consistent |
| Scale (log-SD) | Pollution | -0.320 [-0.763, 0.089] | -0.184 [-0.489, 0.119] | consistent |
| Scale (log-SD) | Responsetointroductions | 0.137 [-0.116, 0.395] | 0.256 [0.028, 0.486] | DIFFERS |
sens_moderator_table('sens1_n40', 'design')| Sub-model | Term | Sensitivity β [95% CrI] | Primary β [95% CrI] | Stability |
|---|---|---|---|---|
| Location (mean lnM) | Intercept (ref.) | -0.978 [-1.506, -0.444] | -0.724 [-1.471, 0.025] | DIFFERS |
| Location (mean lnM) | Synchronic | 0.242 [0.043, 0.438] | 0.250 [0.077, 0.418] | consistent |
| Scale (log-SD) | Intercept (ref.) | -0.399 [-0.441, -0.356] | -0.468 [-0.507, -0.428] | consistent |
| Scale (log-SD) | Synchronic | -0.231 [-0.288, -0.174] | -0.208 [-0.260, -0.157] | consistent |
sens_moderator_table('sens1_n40', 'log10_years')| Sub-model | Term | Sensitivity β [95% CrI] | Primary β [95% CrI] | Stability |
|---|---|---|---|---|
| Location (mean lnM) | Intercept (ref.) | -1.276 [-2.001, -0.587] | -1.021 [-1.855, -0.173] | consistent |
| Location (mean lnM) | slope | 0.305 [0.229, 0.382] | 0.307 [0.235, 0.381] | consistent |
| Scale (log-SD) | Intercept (ref.) | -0.358 [-0.437, -0.278] | -0.354 [-0.427, -0.279] | consistent |
| Scale (log-SD) | slope | -0.128 [-0.181, -0.074] | -0.167 [-0.215, -0.119] | consistent |
sens_moderator_table('sens1_n40', 'log10_generations')| Sub-model | Term | Sensitivity β [95% CrI] | Primary β [95% CrI] | Stability |
|---|---|---|---|---|
| Location (mean lnM) | Intercept (ref.) | -1.194 [-1.857, -0.530] | -0.918 [-1.839, 0.017] | DIFFERS |
| Location (mean lnM) | slope | 0.294 [0.216, 0.373] | 0.286 [0.215, 0.359] | consistent |
| Scale (log-SD) | Intercept (ref.) | -0.334 [-0.386, -0.281] | -0.401 [-0.450, -0.350] | consistent |
| Scale (log-SD) | slope | -0.159 [-0.195, -0.124] | -0.149 [-0.182, -0.117] | consistent |
sens_moderator_table('sens1_n40', 'trait_type')| Sub-model | Term | Sensitivity β [95% CrI] | Primary β [95% CrI] | Stability |
|---|---|---|---|---|
| Location (mean lnM) | Intercept (ref.) | -1.947 [-3.123, -0.709] | -1.332 [-2.519, -0.105] | consistent |
| Location (mean lnM) | growth | 1.275 [0.184, 2.309] | 0.829 [0.042, 1.616] | consistent |
| Location (mean lnM) | otherLH | 1.257 [0.179, 2.291] | 0.907 [0.131, 1.681] | consistent |
| Location (mean lnM) | othermorphology | 1.095 [0.020, 2.128] | 0.782 [0.003, 1.555] | consistent |
| Location (mean lnM) | phenology | 1.288 [0.154, 2.372] | 0.806 [-0.022, 1.626] | DIFFERS |
| Location (mean lnM) | physio | 1.045 [-0.028, 2.090] | 0.698 [-0.077, 1.477] | consistent |
| Location (mean lnM) | response | 1.820 [0.534, 3.154] | 1.167 [0.313, 2.024] | consistent |
| Location (mean lnM) | size | 1.213 [0.142, 2.249] | 0.835 [0.058, 1.611] | consistent |
| Scale (log-SD) | Intercept (ref.) | -0.247 [-0.774, 0.333] | -0.373 [-0.863, 0.129] | consistent |
| Scale (log-SD) | growth | -1.173 [-1.889, -0.514] | -0.977 [-1.615, -0.387] | consistent |
| Scale (log-SD) | otherLH | -0.283 [-0.864, 0.250] | -0.181 [-0.688, 0.314] | consistent |
| Scale (log-SD) | othermorphology | -0.595 [-1.172, -0.064] | -0.519 [-1.027, -0.025] | consistent |
| Scale (log-SD) | phenology | -0.469 [-1.102, 0.127] | -0.383 [-0.937, 0.171] | consistent |
| Scale (log-SD) | physio | -0.600 [-1.234, -0.013] | -0.698 [-1.225, -0.179] | consistent |
| Scale (log-SD) | response | -1.007 [-3.881, 0.695] | -0.550 [-1.354, 0.158] | consistent |
| Scale (log-SD) | size | -0.121 [-0.705, 0.408] | -0.037 [-0.538, 0.454] | consistent |
sens_moderator_table('sens1_n40', 'genphen')| Sub-model | Term | Sensitivity β [95% CrI] | Primary β [95% CrI] | Stability |
|---|---|---|---|---|
| Location (mean lnM) | Intercept (ref.) | -0.696 [-1.233, -0.120] | -0.427 [-1.208, 0.371] | DIFFERS |
| Location (mean lnM) | Phenotypic | -0.201 [-0.385, -0.017] | -0.210 [-0.355, -0.063] | consistent |
| Scale (log-SD) | Intercept (ref.) | -0.795 [-0.853, -0.735] | -0.836 [-0.889, -0.784] | consistent |
| Scale (log-SD) | Phenotypic | 0.357 [0.289, 0.425] | 0.338 [0.278, 0.398] | consistent |