This page exists so that the narrative pages don’t have to report repetitive (but still necessary) technical checks of model quality. Every model discussed in this report converged cleanly and was checked for the usual things a Bayesian model needs checking for: this page is where that checking actually happens, in full, for every single-level model at once. If you’ve arrived here from another page wanting to confirm a specific model’s diagnostics, use the section links below rather than reading top to bottom.
model_files <- c(
linear = "lm_linear_tot.rds",
categorical_4_groups = "lm_categorical_4g_tot.rds",
categorical_2_groups = "lm_categorical_2g_tot.rds",
gam = "gam_tot.rds",
segmented_estimated = "segmented_estimated_knot_tot.rds",
floor_group_additive = "floor_group_additive_tot.rds"
)
models <- lapply(model_files, function(f) {
readRDS(system.file("models", f, package = "aphantasiaEmotions"))
})
pp_checks <- readRDS(
system.file("results", "pp_checks_all_models.rds", package = "aphantasiaEmotions")
)Convergence
Rhat close to 1 and a healthy effective sample size (ESS) indicate that a model’s chains mixed well and its posterior can be trusted. The table below is computed directly from each model’s fitted object.
convergence_summary <- do.call(rbind, lapply(names(models), function(nm) {
m <- models[[nm]]
rhats <- brms::rhat(m)
ess_bulk <- brms::neff_ratio(m) * brms::ndraws(m)
data.frame(
model = nm,
max_rhat = round(max(rhats, na.rm = TRUE), 4),
min_ess = round(min(ess_bulk, na.rm = TRUE), 0)
)
}))
convergence_summary |> knitr::kable(row.names = FALSE)| model | max_rhat | min_ess |
|---|---|---|
| linear | 1.0007 | 5929 |
| categorical_4_groups | 1.0013 | 5464 |
| categorical_2_groups | 1.0004 | 5218 |
| gam | 1.0016 | 3438 |
| segmented_estimated | 1.0021 | 2088 |
| floor_group_additive | 1.0008 | 5639 |
Every model here has a maximum Rhat well under the conventional 1.01 threshold, and a minimum bulk ESS well above the conventional floor of 400: none of the models discussed in this report needed to be excluded or re-fit on convergence grounds alone.
Posterior predictive checks
A posterior predictive check compares data simulated from a fitted model against the real, observed data. If a model’s family and structure are reasonable, simulated and observed distributions should look similar.
Why a Gaussian family
Every model in this report uses gaussian(), brms’s
default family. That choice is worth checking, not just assuming: TAS-20
total is technically a bounded, discrete sum (20-100), and a Gaussian
approximation is only appropriate if the data don’t show serious skew,
heteroscedasticity, or a pile-up at the boundaries.
tas_vals <- all_data$tas
tas_skew <- mean((tas_vals - mean(tas_vals))^3) / sd(tas_vals)^3
tas_at_boundary <- any(tas_vals <= 20 | tas_vals >= 100)
resid_skew <- sapply(models, function(m) {
r <- residuals(m)[, "Estimate"]
mean((r - mean(r))^3) / sd(r)^3
})
heteroscedasticity <- sapply(models, function(m) {
f <- fitted(m)[, "Estimate"]
r <- residuals(m)[, "Estimate"]
cor(abs(r), f)
})
family_check_table <- data.frame(
model = names(models),
residual_skewness = round(resid_skew, 3),
heteroscedasticity_r = round(heteroscedasticity, 3)
)The raw TAS-20 total ranges from 20 to 94, with a skewness of 0.21 (near 0 is symmetric, this is mild). Some participants do sit exactly at the scale’s floor (20).
family_check_table |> knitr::kable(row.names = FALSE)| model | residual_skewness | heteroscedasticity_r |
|---|---|---|
| linear | 0.139 | 0.121 |
| categorical_4_groups | 0.170 | 0.054 |
| categorical_2_groups | 0.152 | 0.108 |
| gam | 0.174 | 0.065 |
| segmented_estimated | 0.173 | 0.060 |
| floor_group_additive | 0.171 | 0.063 |
Residual skewness stays small and heteroscedasticity (the correlation between absolute residuals and fitted values) stays close to zero across every model: nothing here would have motivated switching away from a Gaussian family.
Continuing through the Extended Online Report: this page is a technical reference, linked to from the narrative pages rather than meant to be read start to finish. Return to the model comparison or floor-group model pages, or continue to implementation notes.
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