Decide whether `WR_t → NW_{t+1}` belongs in the lagged DAG (and refresh the stale d-separation asset)

[frankbuckley]

Note

Drafted by a LLM-based AI tool (Claude Code/Opus 4.8).

The decision

Does WR_t → NW_{t+1} — prior word reading feeding subsequent nonword reading — belong in dag/dag-language-reading-lagged.dagitty? This is a team decision, not a build, and it is the item that gates whether the strongest descriptive signal in notes/202607241600-findings-word-reading-bands.md has any identified estimand behind it at all. Nothing downstream can be specified until it is settled, so it is recorded here as its own issue rather than inside a model-building one.

Why it is open

The lagged graph currently contains WR_t → { TE, TR, PA, RW, LS }_{t+1} and no NW. Any WR → NW coupling estimated on the graph as it stands is therefore the total lagged effect routed through letter sounds and blending — and conditioning on those, as several candidate adjustment sets do, simultaneously blocks the paths being sought and opens colliders. A machine-searched minimal sufficient set for the coupling on the current graph runs to 8 nodes on the randomised transition and 12 post-crossover, which is unfittable at n ≈ 54 regardless of what one thinks of the estimand.

Evidence for adding the edge. Among children scoring zero on nonword reading at t1, 2 of 20 (10%) in the bottom word-reading half had moved off the floor by t2 against 10 of 16 (62%) in the top half. It holds inside both arms (immediate 18% vs 80%; wait-list 0% vs 33%), and arm is balanced across the bands (14/11 vs 13/12) as randomisation implies — the t1 split is pre-randomisation, so arm cannot confound it. This is the Roch & Jarrold (2012) WR → NW pattern for children with Down syndrome (doi:10.1016/j.jcomdis.2011.11.001) visible descriptively in this cohort. The mechanism is not exotic: a growing sight-word lexicon supplies the orthographic-phonological mappings a child then generalises to unfamiliar strings.

Evidence against. The committed graph already routes reading's influence on nonword reading through letter sounds and blending, and if that were the whole story it should be visible on those legs — where it mostly is not. The descriptive WR → LS contrast is flat but censored (by t3 the top word-reading half sits at a median 28 of 32 letter sounds with 11% at ceiling, so it cannot gain), so that leg is uninformative rather than null; lcsm-082's prior-reading → blending-change coupling is +0.055 (89% CrI −0.036 to +0.147, P = 0.835), suggestive at best. So the "it must already be visible upstream" argument is weaker than it looks, but it has not been ruled out either.

There is also a measurement reading worth putting on the table before any edge is drawn: NW is a 6-item task floored at zero for 72 / 64 / 52 / 40% of children at t1–t4, so "moving off the floor" is a one-item event. The 62%-vs-10% contrast is a floor-exit contrast, and a graph edge is a strong response to it.

What to do once it is settled

If the edge is adopted: add WR_t → NW_{t+1} to dag/dag-language-reading-lagged.dagitty; extend the REVERSE edge list in tests/test_lagged_dag_adjustment_sets.py (which currently carries the corrected five-edge list including LS); re-derive the minimal sufficient sets for the affected couplings against the amended graph; and record whether the resulting set is fittable at this sample size before anything is specified as a model. Sweep the DAG-dependent families for adjustment sets that change, in the #247 idiom.

If it is rejected: record the rationale as a dated notes/ decision entry in the same form as notes/202607241240-decision-drop-vocabulary-letter-sound-analyses.md, so the descriptive result has a standing explanation rather than being re-raised each time someone reads the bands note. The framing to use is the one the note lands on: the floor-exit contrast is real, but under the committed graph it is a total lagged effect through letter sounds and blending plus shared latent general ability, not a direct edge.

Second, smaller item — a stale archived asset

notes/assets/202607141030-lagged-dsep-checks.py has a REVERSE list of ["TE", "TR", "PA", "RW"], missing the WR_t → LS_{t+1} edge added on 2026-07-17, so re-running it today builds a graph the DAG no longer matches. The CI guard is fine — tests/test_lagged_dag_adjustment_sets.py carries the corrected five-edge list and test_unroll_slices_mirror_the_dagitty_template asserts the unroll matches the parsed template — so nothing published is wrong; only the archived reproducible record attached to notes/202607141030-time-lagged-model-designs.md went stale. Either refresh its edge list or replace it with a pointer to the test that supersedes it. Worth doing in the same pass as this decision, since whoever re-derives the sets will be in exactly that code.

Acceptance criteria

• Decision recorded (adopt / reject) with its rationale, in a dated notes/ entry.
• If adopted: dag/dag-language-reading-lagged.dagitty amended, tests/test_lagged_dag_adjustment_sets.py REVERSE list extended, minimal sufficient sets re-derived and their fittability at n ≈ 54 stated explicitly.
• If adopted: DAG-dependent families swept for changed adjustment sets (Re-derive gain/level-factor upstream adjustments; sweep remaining DAG-dependent families #247 idiom); if rejected: no model changes, decision note only.
• notes/assets/202607141030-lagged-dsep-checks.py refreshed or replaced by a pointer to the superseding test.
• notes/202607241600-findings-word-reading-bands.md updated with the outcome.
• ruff check src/, npm run format:check, npm run spellcheck pass.

Related

Raised by notes/202607241600-findings-word-reading-bands.md (pass 3 and "What would be worth building", first item). Graph and design context: notes/202607131200-time-lagged-dag.md, notes/202607141030-time-lagged-model-designs.md, #250 (lagged DAG workstream, closed), #251 (2026-07-10 DAG revision, closed), #247 (adjustment-set re-derivation, closed). Companion follow-ups from the same pair of notes: #421 and #404.

[frankbuckley]

Note

Drafted by a LLM-based AI tool (Claude Code/Opus 4.8).

New evidence bearing directly on this decision, from notes/202607241900-findings-word-reading-threshold.md (pending commit). The question asked was whether children need a minimum word-reading level before they can progress in letter sounds, blending or nonword reading; the nonword half of the answer is the part that matters here.

Period-start word reading predicts end-of-period nonword reading strongly. Over 143 child-period transitions with headroom, dropping the word-reading term costs 18 ± 4.4 elpd in a PSIS-LOO comparison of four Beta-Binomial ANCOVA specifications sharing the same covariates (own baseline, age, arm, on-intervention status, hearing, speech, child random intercept). The association survives adjusting for period-start letter sounds (+0.71 [+0.50, +0.94] → +0.57 [+0.33, +0.81]), so it is not the letter-sound route in disguise — which speaks to the "it should already be visible upstream" argument on the reject side of this issue.

But the shape is diminishing returns, not a threshold, and that reframes the floor-exit contrast this issue was partly raised on. A free-breakpoint hinge — the prerequisite hypothesis — loses to a straight line in log1p(words) by 6 ± 2.9 elpd across the full range and by 10 ± 2.5 once the tail above the 25-word EWRSWR instrument switch is dropped. Fitted expected nonword score by period-start words read: 0.29 (0 words), 0.48 (1), 0.63 (2), 0.98 (5), 1.41 (10), 2.21 (25) — roughly half the climb across 0–40 words happens over the first five. The 62 %-vs-10 % floor-exit contrast quoted in the issue body is a real pattern, but it is the top of a concave curve rather than a step, and the children reading one to four words are already well up it.

Two consequences for the decision as framed:

1. The measurement caveat gets heavier, not lighter. A concave rise on a logit link with a 6-item outcome floored for 72 / 64 / 52 / 40 % of children is partly manufacturable by the instrument. The issue already flags that a floor-exit contrast is thin ground for a graph edge; the shape result does not rescue it.
2. Direction remains unaddressed by any of this. A child beginning to decode also reads more words, and neither the descriptive nor the model-based version of this analysis separates the two.

So the new evidence strengthens the case that something runs from reading to decoding in this cohort, and simultaneously weakens the case that it is a discrete developmental gate. Whichever way this issue goes, #433 specifies the model that should carry the finding — and it is explicitly blocked on this decision, since a rejected edge means it ships as descriptive rather than as an adjusted association.