feat(psychometric): recover Driver 2017-era addedTIPREDVARstd after addedTIPREDVAR

[seonghobae]

Stacked on #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. It does not duplicate #195 CINTstd, #197 T0TDPREDEFFECTstd, or #202 TDPREDEFFECTstd.

psychometric_core recovers the Driver, Oud, and Voelkle (2017, p. 16; §7.2, pp. 20–21; Table 2, p. 12; 2017-era ctsem summary.ctsemFit.R; JSS PDF re-opened 2026-08-23T21:22Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised extra time-independent predictor variance addedTIPREDVARstd. Page 16 prints standardised matrices with the suffix std when appropriate. After addedTIPREDVAR as asymTIPREDEFFECT %*% TIPREDVAR %*% t(asymTIPREDEFFECT), the 2017-era summary.ctsemFit.R forms addedTIPREDVARstd = solve(sqrt(diag(addedTIPREDVAR))) %&% addedTIPREDVAR. OpenMx %&% is the quadratic form t(A) %*% B %*% A. The default ridging = FALSE adds 0, not 0.0001; that ridge is a numerical hack and is not this exact map. The scalar correlation is extra / extra = 1 after strictly positive extra. Form addedTIPREDVAR first, then the ratio.

• A zero extra has no positive extra SD and fails closed (StandardisedAsymptoticTimeIndependentVarianceRequiresPositiveExtraVariance).
• v < 0 fails closed (InvalidNumericInput).
• A non-event clock fails closed (EventTimeRequired).
• a ≥ 0 cannot hold a finite process-mean change when the extra is nonzero and fails closed (AsymptoticTimeIndependentEffectRequiresStableDrift).
• Unstandardised (B / a)² v is defined for a zero coefficient and for zero predictor variance; standardised addedTIPREDVAR is not.
• λ² (B / a)² v is Eq. 5 of the extra, not this correlation.
• t0_b² v is addedT0TIPREDVAR, not this asymptotic extra correlation.
• TRAITVAR is not the standardisation variance.
• The printed 2-latent addedTIPREDVAR 2.838 is not this scalar 1.

Still not a Kalman filter, not a matrix expm, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T21:22Z: is_oa: false; title Measurement Invariance, Factor Analysis and Factorial Invariance). Mislevy (1991, Psychometrika, 56, 177–196) remains unread (Unpaywall 2026-08-23T21:22Z: 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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