For those who come after
Source:vignettes/articles/for-those-who-come-after.Rmd
for-those-who-come-after.RmdSome of the most interesting directions this project surfaced didn’t make it into the final analyses — not because they weren’t worth pursuing, but because a study has to stop somewhere, and this project’s own philosophy (see how this study found its shape) is that the reasoning behind a stopping point deserves to be written down, not quietly dropped. Each of the four ideas below has a real motivation, a rough sense of what the next step would look like, and an honest account of why it’s here rather than in the main report.
Mixture regression on the VVIQ floor spike
The pooled VVIQ distribution isn’t smoothly continuous: there’s a sharp, isolated spike at the scale’s floor (VVIQ = 16), visually distinct from a more continuous, if irregular, remainder from about 20 to 80. The floor-group additive model (see the floor-group page) treats that floor group as a single, discrete category with its own mean, which the evidence supports well, but which assumes the floor group is internally homogeneous.
A genuinely different, and more ambitious, way to ask the same question is finite mixture regression: rather than assuming a fixed number of researcher-defined groups, a mixture model asks whether the sample itself is a blend of several latent sub-populations, each with its own regression relationship, estimated directly from the data rather than assumed in advance. This is close to what one reviewer specifically suggested, pointing to the flexmix R package (Leisch, 2004) as a tool for exactly this: modelling the VVIQ-TAS relationship as potentially modified by empirical clusters in the data, particularly relevant if aphantasics themselves consist of distinguishable subgroups.
This is a meaningfully larger step than the floor-group model, not just a variant of it: it’s a different kind of claim (multiple populations, not one population with one distinct subgroup), and mixture models bring real complications of their own (label-switching during estimation, convergence sensitivity, the same challenge of choosing how many components to fit that a purely category-driven analysis avoids). It’s flagged here, not attempted, because taking it on properly would have meant introducing a third major statistical paradigm into an already substantial modelling arc. This is a deliberate scope decision, not a technical dead end.
Bayesian MARS (BASS)
The segmented model’s estimated knot (see the model
comparison page) was first located using earth::earth()
— a fast, frequentist implementation of Multivariate Adaptive Regression
Splines (MARS). That result was then re-estimated properly in a Bayesian
framework, but only for the single-knot structure earth had
already found.
A more thoroughly Bayesian version of the same idea exists: the BASS package (Francom & Sansó, 2020) (Bayesian Adaptive Spline Surfaces) fits genuinely Bayesian MARS models (Denison et al., 1998), using reversible-jump MCMC to put a full posterior not just over a spline’s parameters, but over its structure: how many knots there are and where they sit, estimated jointly rather than fixed in advance. That’s a more complete answer to “where does this relationship change shape” than even the estimated-knot segmented model gives, since it doesn’t assume in advance that there’s exactly one breakpoint.
The practical cost is real: BASS doesn’t give WAIC or LOO directly,
so comparing it formally to the brms-based models in this report would
need new work (likely a custom cross-validated predictive-density
calculation), and its prior structure (inverse-gamma and beta
hyperpriors on spline complexity) is unfamiliar territory relative to
the priors used throughout this project. None of that makes it a bad
idea — it’s a genuinely distinctive, rare thing to see worked through in
this literature, and fitting a first model is mechanically simple (a
single function call, not unlike earth::earth()). It’s
parked here specifically because understanding and defending
the result is the real cost, not the fitting itself, and that’s a task
for its own dedicated adventure.
A per-study estimate of the segmented model’s knot
The segmented model’s knot is estimated once, pooling all five
studies. A natural extension is to let the knot location vary by study:
k | study rather than a single pooled k. This
would directly answer a specific, sharp question: does Kvamme et al.’s
(2026) own data, on its own, actually support their chosen threshold of
VVIQ = 32 better than the pooled estimate of about 19.5 does? A
per-study knot posterior would show, directly, which studies (if any)
pull the pooled estimate toward or away from any given value.
This is a harder model to fit than it might sound. The knot parameter
k sits inside a non-linear term (multiplying
step(vviq - k)), so letting it vary by study means the
sampler has to jointly resolve, separately for each of the five studies,
both where the breakpoint is and how steep each
segment is using only that study’s own data. The smallest study in this
project’s pool (n = 105) is a fraction of what the pooled estimate
needed to be well-identified in the first place; asking a study that
size to support its own independent knot estimate is a real statistical
stretch, likely requiring careful priors, generous
adapt_delta/max_treedepth settings well beyond
what the pooled model needed (see implementation
notes for what the pooled estimated-knot model already
required), and probably more debugging than any other model in this
report. It’s a genuinely interesting question with a genuinely hard
model behind it, but a question worth flagging clearly for those who
come after, including its difficulty, rather than downplaying
it.
This is the last page of the Extended Online Report’s narrative arc. If you’ve read through from the start, thank you for following the whole story. Two technical pages remain, for anyone building on this project’s code directly: model diagnostics and implementation notes. The superseded models page contains the legacy of the 4-group and GAM models that were once central to this study’s first iteration. Otherwise, you can jump back to how this study found its shape, or return to the package homepage.