feat(psychometric): recover Driver Table 3 T0TDPREDEFFECTstd after positive T0VAR

[seonghobae]

Stacked on #202 (a7ce1a0) / #200 (8f42947) / #199 (7a476ed) / #198 (52a9b4c) / #196 (1cb91b4) / #194 (471b115) / #192 (1690c7b) / #190 (adb0bc6) / #189 (0836c35) / #188 (444304d) / #187 (6afd048) / #185 (69ffec6) / #184 (6b93147) / #183 (c10097be) / #182 (2d4d6bf) / #181 (542806b) / #49 (6f95142). ADR 0005 executable slice stays inside psychometric_core. This is not a second invariance crate and does not recreate #78 or #80.

psychometric_core recovers the Driver, Oud, and Voelkle (2017, Table 3, p. 13 T0TDPREDEFFECTstd; Table 2, p. 12; p. 16; footnote 4; Eq. 3, p. 5; 2017-era ctsem summary.ctsemFit.R; JSS PDF re-opened 2026-08-23T21:34Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised first-occasion time-dependent predictor effect. Table 3 names T0TDPREDEFFECT the effect of time-dependent predictors on latents at T0. Table 2 names M TDPREDEFFECT and names T0TDPREDCOV the first-occasion covariance, not this coefficient. Page 16 prints standardised matrices with the suffix std when appropriate. Footnote 4: standardisations use only the relevant variance, not the total. The affecting variance is time-dependent predictor variance v, not TIPREDVAR. The affected variance is free first-occasion T0VAR p_0, not within-subject asymDIFFUSION -q / (2 a), because Table 3 is the first occasion, not the process dynamics. Form strictly positive p_0 first, then strictly positive v, then t0_m · √v / √p_0.

• Unstandardised t0_m is defined for a zero coefficient and for zero predictor variance; standardised T0TDPREDEFFECT is not.
• Zero p_0 or zero v has no positive SD and fails closed.
• T0 is an event-time occasion, so a non-event clock fails closed. Free T0VAR does not require stable a < 0.
• TDPREDEFFECTstd m · √v / √(-q / (2 a)) uses asymDIFFUSION and is not this first-occasion map.
• T0TIPREDEFFECTstd t0_b · √v / √p_0 is a different named matrix even when t0_m = t0_b and the predictor variances match.
• t0_m · √v / √(trait + p_0 + added) uses the total, not free T0VAR, and is not T0TDPREDEFFECTstd when TRAITVAR is nonzero.

Still not a Kalman filter, not a matrix expm, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T21:34Z: is_oa: false; title Measurement Invariance, Factor Analysis and Factorial Invariance). Mislevy (1991, Psychometrika, 56, 177–196) remains unread (Unpaywall 2026-08-23T21:34Z: is_oa: false; title Randomization-Based Inference about Latent Variables from Complex Samples).

Do not merge, self-approve, or request Copilot.

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[seonghobae]

Folded into the consolidation vehicle #231; this draft stays open until the vehicle merges, then closes as superseded-by-consolidation.

[seonghobae]

Superseded by consolidation: this slice's Driver et al. (2017) standardization recovery landed on protected main through the integration vehicles (#231/#232), and its contract coverage is carried by the reconciled suites (multilevel_event_time_recovery_contract, rubin_and_mean_gate_contract) with test-signature repair tracked in #234. The stacked-draft form is retired to keep the delivery queue at review-ready work only; no capability is lost — the exact-head provenance remains in the vehicle PR descriptions and CHANGELOG.