feat(psychometric): recover Driver Eq. 5 of addedTIPREDVAR extra observed TI variance

[seonghobae]

Stacked on #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, Eq. 5, p. 5; Table 2, p. 12; §7.2, pp. 20–21; 2017-era ctsem summary.ctsemFit.R; JSS PDF re-opened 2026-08-23T19:23Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar extra observed-indicator time-independent predictor variance of §7.2 addedTIPREDVAR. Equation 5 writes y_i(t) = Γ + Λ η_i(t) + ζ_i(t) with ζ ~ N(0, Θ) and Γ ~ N(τ, Ψ). The 2017-era summary.ctsemFit.R forms the latent extra addedTIPREDVAR as asymTIPREDEFFECT %*% TIPREDVAR %*% t(asymTIPREDEFFECT). The scalar latent extra is (B / a)² v. Equation 5 of that extra, with θ = 0 and ψ = 0, is λ² (B / a)² v.

Form addedTIPREDVAR first, then (λ extra) λ. Do not form λ² first.

• A zero loading or zero extra is exactly zero.
• 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).
• (B / a)² v is the latent extra, not this observed extra.
• λ² t0_b² v is Eq. 5 of addedT0TIPREDVAR, not this asymptotic observed extra.
• λ² p + θ is stationary observed variance, not this extra.
• MANIFESTVAR θ is measurement error, not this extra.

The printed 2-latent addedTIPREDVAR 2.838 is not this scalar map. Still not a Kalman filter, not a matrix expm, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T19:10Z: is_oa: false; title Measurement Invariance, Factor Analysis and Factorial Invariance). Mislevy (1991, Psychometrika, 56, 177–196) remains unread (Unpaywall 2026-08-23T19:10Z: 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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