feat(psychometric): recover Driver p.16 TDPREDMEANSstd on main

[seonghobae]

Summary

psychometric_core recovers the Driver, Oud, and Voelkle (2017, p. 16) scalar TDPREDMEANSstd as μ_x / √v after strictly positive TDPREDVAR v.

This is an independent successor of queued TDPREDVARstd (#335) and discreteTDPREDEFFECTstd (#337). It does not depend on those unpublished crates. Table 2 names TDPREDMEANS the n.TDpred × Tpoints × 1 matrix of free means of time-dependent predictors and names TDPREDVAR the Cholesky of time-dependent predictor variance. Page 16 prints standardised matrices with the suffix std when appropriate. The printed example on p. 16 is discreteDRIFTstd, not TDPREDMEANSstd. Footnote 4 standardises using only the relevant variance, not the total. The relevant variance for that named predictor mean is TDPREDVAR v, not process-dynamics asymDIFFUSION -q / (2 a).

CRAN-era ctsem summary.ctsemFit.R comments out TDPREDVAR / TDPREDVARstd and does not form a TDPREDMEANSstd matrix. Page 22 does not report standardised TDPRED estimates when there is no modeled predictor variance. This crate therefore owns the footnote-4 standardisation of that named mean after a modeled v.

JSS PDF re-opened 2026-08-31T03:00Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104.

Map

Form strictly positive v first, then divide μ_x by √v:

TDPREDMEANSstd = μ_x / √v

A zero mean is exactly zero. Overflow of the ratio fails closed.

Claim boundary

• Unstandardised TDPREDMEANS μ_x is defined for a zero predictor variance and is not TDPREDMEANSstd.
• TDPREDVARstd v / v = 1 recovers the same number when μ_x = √v and remains a distinct named quantity. This crate does not currently export TDPREDVARstd; the refuse still names that quantity.
• μ_x / √asymDIFFUSION uses process-dynamics variance and is not this predictor map.

Event time only. Zero v has no positive SD and fails closed. TDPREDMEANS does not require stable a < 0. Negative means remain valid signed locations.

Still not a Kalman filter, not a matrix expm, not ESEM estimation, not DSEM, and not ctsem estimation.

Meredith (1993) remains unread (Unpaywall historically is_oa: false; Springer content/pdf is an HTML stub). Mislevy (1991, Psychometrika, 56, 177–196) remains unread on the same terms (DOI 10.1007/bf02294457).

Verification

• cargo test -p psychometric_core (full crate, including the new unit, recovery, and claim-boundary tests)
• cargo clippy -p psychometric_core --all-targets -- -D warnings
• cargo fmt -p psychometric_core -- --check
• RUSTDOCFLAGS='-D warnings' cargo doc -p psychometric_core --no-deps

Do not merge without independent non-author APPROVE and exact-head required-check success. Do not convert #310. Do not self-approve.

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[seonghobae]

Independent review requested on exact head 26e163a714886cb35dda4ee779328c2f059f7e6e. Do not self-approve. Do not merge without independent non-author APPROVE and exact-head required-check success.

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[coderabbitai]

@seonghobae: I will review pull request #338 at exact head 26e163a714886cb35dda4ee779328c2f059f7e6e. I will not self-approve or merge it.

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[seonghobae]

Restack on protected main (a243f18)

Non-force merge of origin/main (merge commit 82b02ccc); the only conflict was the CHANGELOG.md append, both entries kept.

Local evidence on the pushed head (toolchain 1.98.0): cargo test -p psychometric_core 368 passed / 0 failed, clippy -D warnings clean, cargo fmt --all --check clean, documentation/workspace/docstring contracts PASS, git diff --check clean.

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