Transition-dynamics revision analyses (switch-repeat & intervals-since-switch; drift/threshold + Euclidean distance) — summary + final analyses

[igrahek]

Purpose

Briefing + task list for a follow-up agent that will run final transition-dynamics analyses. Nothing here is decided for the paper — the goal is to produce clean, reportable results and figures so @igrahek can decide what (if anything) goes into the revision.

These analyses probe the reviewer concern (R1/R3, JEP:G) that the varying-block undershoot might be a static "in-between" strategic setpoint rather than a genuine slow transition through drift–threshold space, and whether the paper's block-level age effect (slower transitions with age) holds at finer (trial/interval) timescales.

Convention: these are Bayesian models; "p" = posterior tail probability (proportion of the posterior on the far side of 0), matching the lab's DDM_analyses_and_plots.Rmd. * p<.05, ** p<.01. Coding: intervalType Accuracy=+.5/Speed=−.5; Switch Repeat=+.5/Switch=−.5; SinceSwitch 0=switch…4="4+"; Age linear, scaled ×100; congruency cong=+.5.

Models involved

Model	Spec (v & a)	Data	Output
Switch/repeat (binary)	intervalType * Switch * Age	varying blocks	analyses/hssm/output/Model3 (this repo)
Model 4 (intervals-since-switch)	intervalType * SinceSwitch * Age	varying blocks	Oscar ~/data/igrahek/aging_switch-repeat/analyses/hssm/output/Model4
Block-level (for reference)	intervalType * blockType * Age (Fixed vs Varying)	all blocks	Model1 (this repo) / Fig. 2F metric

Model 4 is a strict generalization of the switch/repeat model (SinceSwitch==0 ⟺ Switch=="Switch"). Analysis scripts + figures are in analyses/hssm/analysis/recovery_analysis/ (see its README).

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What we found

1. Switch/repeat (binary) — drift & threshold

• Switch cost is weak: v_Switch = +0.021, p=.083 (drift a touch lower on switch trials); a_Switch ≈ 0.
• The undershoot signature exists on threshold: a_intervalType:Switch = +0.021, p=.011 ✱; on drift v_intervalType:Switch = +0.024, p=.20 (n.s.).
• Age × switch is null: 3-way v_intervalType:Switch:Age = −0.16, p=.12; a_intervalType:Switch:Age = −0.04, p=.15. Switch-effect-at-young-vs-old is flat overall (drift young +0.023 → old +0.019).

2. Switch/repeat — Euclidean distance (in v,a space)

• Trial-level undershoot is present (Repeat–Switch Speed↔Accuracy distance ~0.67 vs 0.65) but tiny (~3% vs ~21% at block level).
• It decreases with age (opposite of block level): slope −0.0014/yr, P(slope<0)=0.90 — a trend, not credible.
• No coding error (settled R3's concern): reconstructing the block-level distance from Model1 confirms undershoot increases with age robustly — slope +0.0055/yr, P(>0)=1.00 (dist Fixed 1.48 > Varying 1.16). The block-level 3-way sign is correct.

3. Intervals-since-switch (Model 4) — drift & threshold

• The recovery mechanism is credible: v_SinceSwitch = +0.021, p=.002 ✱✱ (drift rebuilds across intervals since the switch); a_intervalType:SinceSwitch = +0.011, p=.011 ✱ (goal-specific boundary undershoot recovers).
• Age × recovery is null: 3-way v_intervalType:SinceSwitch:Age = −0.058, p=.199; a_intervalType:SinceSwitch:Age = −0.018, p=.205.
• Recovery slope (Speed↔Accuracy gap growth per interval) young vs old — correctly signed (slower in old) but not credible: drift young +0.029 (P>0=.86) → old −0.006, P(slower in old)=.80; boundary young +0.017 (P>0=.98) → old +0.006, P(slower)=.80.
• Replicates the core aging effect: a_Age = +0.199, p=.003 ✱✱ (older = more cautious).
• Convergence: population fixed effects max R̂=1.02, key SinceSwitch terms R̂=1.00, ESS 1300–2100. Whole model (incl. 245× random effects) max R̂=1.21, min ESS=17, 3.6% of params R̂>1.01 → a few subject-level effects mixed poorly (typical; does not affect population inference).

4. Intervals-since-switch — Euclidean distance (in v,a space)

Speed↔Accuracy distance vs SinceSwitch (SD-scaled, fully Bayesian):

SinceSwitch	0	1	2	3	4
Young (25)	5.80	6.16	6.52	6.89	7.25 (rising)
Old (75)	4.62	4.67	4.73	4.80	4.87 (flat)

• Genuine transition, not a setpoint: whole-sample recovery (dist SS=4 − SS=0) = +0.78, P(>0)=0.96; young recovery = +1.45, P(>0)=0.965. The distance rises across intervals → configs are moving toward targets, not parked at a compressed setpoint.
• Old is nearly flat (recovery +0.26, P=0.65). Old−young recovery = −1.19, P(slower with age)=0.835 — combining v+a nudged this above the separate-parameter ~.80, but still not credible.

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Interpretation so far (for discussion, not decided)

• Transition vs. setpoint → transition. The (v,a) distance credibly grows across intervals (P=.96 sample-wide, P=.965 in young), which a static in-between strategy can't produce. Older adults being ~flat is, on its own, ambiguous (setpoint vs. a transition too slow to resolve within the short observed run lengths), but the paper's preserved configural flexibility in fixed blocks (older reach full Speed↔Accuracy separation when the goal is stable) breaks the tie toward "adjusting, but slower," not "strategic compression."
• Age-related slowing is correctly signed everywhere but only credible at the block level. Every trial/interval-level measure (switch/repeat and intervals-since-switch; drift, threshold, and combined distance) points to slower recovery with age, at P ≈ .80–.84 — a coherent trend, not a confirmed effect. The credible evidence for age-related slowing remains the block-level Fixed vs Varying contrast (the paper's main result).

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Final analyses to run (agent tasks)

1. Recovery-curve figure (priority). Model-4 analog of Fig. 2F: Speed↔Accuracy distance in (v,a) space vs intervals-since-switch, young vs old, with 95% credible bands, and the fixed-block asymptote marked (pull it from the block-level model). This single panel carries the transition-vs-setpoint story. Base it on model4_distance_vs_sinceswitch.py.
2. Model comparison (LOO/WAIC). Does the graded SinceSwitch improve fit over (a) binary Switch and (b) a no-transition base? Justifies reporting the recovery model at all. (log-likelihood is stored in the InferenceData.)
3. Categorical SinceSwitch robustness. Refit with C(SinceSwitch) to cleanly separate the switch-cost (0 vs rest) from the graded recovery (1→2→3→4), and confirm the linear-slope reading. The 0-vs-rest contrast should reproduce the binary switch effect.
4. Quadratic age. The paper found quadratic age enhances the block-level effect — test intervalType * SinceSwitch * Age_2 to see whether the interval-level slowing concentrates in the oldest-old (may push P above the credibility line).
5. Reporting tables for SI. Full estimate / 95% CrI / tail-p / R̂ / ESS tables for the switch-repeat and intervals-since-switch models (drift, threshold) and the distance-recovery contrasts, formatted like Tables S1/S2.
6. Convergence follow-up. Identify which subject-level parameters had R̂>1.1 / low ESS; decide whether a longer warmup or non-centered reparam is warranted for a clean SI statement (population inference already fine).

Provenance / caveats

• SinceSwitch attached via analyses/hssm/data/add_sinceswitch.R (binary boundary exact; 0.14% of trials / 119 rows carry graded ambiguity from indistinguishable trials). A full modern-tidyverse re-run of Preprocessing.R drifts ~6% of Switch labels (not reproducible), so canonical data was preserved. For a fully exact regeneration, run Preprocessing.R under the original tidyverse.
• Model 4 fit: Oscar, account carney-frankmj-condo2, partition batch, env pyHSSM_New_Nov24, ~45 h, Model4.sh.
• Model 4 output (2.79 GB) lives only on Oscar (aging_switch-repeat/analyses/hssm/output/Model4); analyze there (scripts open only the posterior group with engine="h5netcdf").

cc @igrahek — final call on what enters the revision is yours.