feat(psychometric): recover Driver lagged covariance of predetermined T0VAR on main

CHANGELOG.md

@@ -38,6 +38,8 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 
 ## [Unreleased]
 
+- `psychometric_core` recovers the lagged covariance of §4.3 predetermined `T0VAR` independently on current main (register item 47). Driver, Oud, and Voelkle (2017, Eq. 3–4, pp. 4–5; §4.3, pp. 9–10; Table 2, p. 12; p. 16; §7.2, pp. 20–21; JSS PDF re-opened 2026-08-31T10:02Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) treat the first time point as predetermined when no assumptions are made about the process prior to `T0`: free first-occasion variance `p_0` is estimated. Equation 3 writes `η(t) = exp(A Δt) η(t0) + …`. Equation 4 writes `cov(η_t, η_{t-1}) = A_Δt cov(η_{t-1})`. Trait variance and `addedTIPREDVAR` are time-invariant between-subject and do not decay with `e^{a Δt}`. The lagged composition is `trait + e^{a Δt} p_0 + (B / a)² v`. Form the lagged free first-occasion covariance INLINE from on-main `recover_trait_plus_state_lagged_covariance` and `recover_asymptotic_time_independent_predictor_variance`; do not import unpublished `#363` later-occasion helpers or unpublished `#365` observed maps. Setting `p_0 = −q / (2 a)` recovers the stationary lagged map. Stationary lagged covariance uses `−q / (2 a)` in place of free `p_0` and is not this map when `p_0` is free. Later-occasion variance includes `Q_Δt` and is not this lagged map. Evolving `trait + p_0 + (B / a)² v` as if it were all state is not this map. Free `p_0` is not this map. A zero-diffusion carry with `a ≥ 0` is `e^{a Δt} p_0` and is kept. Nonzero TI extra still requires `a < 0`. Event-time-only clocks, non-positive `Δt`, and invalid numeric input fail closed. Meredith (1993) remains unread (Unpaywall 2026-08-31T10:02Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*; Springer `content/pdf` historically an HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196, DOI `10.1007/bf02294457`) remains unread (Unpaywall 2026-08-31T10:02Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*). The 1988 ETS RR of the same title is OA-flagged by Unpaywall (`10.1002/j.2330-8516.1988.tb00310.x`) but Wiley `pdfdirect` returned Cloudflare 403; it is not the 1991 journal article. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.
+
 - `event_core` adds bounded Allen interval-consistency classification, atomic path-consistency closure, contradiction/resource refusals, and an explicit dependency-error fallback without claiming unrestricted global satisfiability.
 
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 2, p. 12 `MANIFESTTRAITVAR`; §7.1, p. 19; p. 16 `MANIFESTTRAITVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-27T14:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised manifest-trait variance on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 83–84). Table 2 names `MANIFESTTRAITVAR` `Ψ_τ` the additional time-invariant variance-covariance on the measurement level and sets it `NULL` when there is no manifest trait. Equation 5 writes `Γ ~ N(τ, Ψ)` and names that covariance the manifest traits. Section 7.1 names manifest traits stable individual differences in indicator levels, distinct from process-level `TRAITVAR` `φ_ξ`. Page 16 prints standardised matrices with the suffix `std` when appropriate. The printed example on p. 16 is `discreteDRIFTstd`, not `MANIFESTTRAITVARstd`. Footnote 4 standardises using only the relevant variance, not the total. The relevant variance for that named indicator-level correlation is `MANIFESTTRAITVAR`, not process-level `TRAITVAR` and not residual `MANIFESTVAR` `θ`. The 2017-era source forms `MANIFESTTRAITVARstd` only when `MANIFESTTRAITVAR != 0`, as `solve(sqrt(diag(MANIFESTTRAITVAR) + ridging)) %&% MANIFESTTRAITVAR` when `verbose = TRUE`. OpenMx `%&%` is `t(A) %*% B %*% A`. Unlike `TRAITVARstd`, that formation adds `diag(c(ridging), n.manifest)`. 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 `ψ / ψ = 1` after strictly positive `MANIFESTTRAITVAR`. Form strictly positive `ψ` first, then `1 / √ψ`, then `(1 / √ψ) ψ (1 / √ψ)`. Unstandardised `MANIFESTTRAITVAR` is defined for a zero trait; standardised `MANIFESTTRAITVAR` is not. Zero `MANIFESTTRAITVAR` skips forming `MANIFESTTRAITVARstd` in the 2017-era source and fails closed here. Indicator-level trait variance is an event-time structural quantity, so a non-event clock fails closed. `MANIFESTTRAITVAR` does not require stable `a < 0`. Distinct positive `ψ` recover the same 1. `trait / trait = 1` is `TRAITVARstd` and recovers the same number and remains a distinct named quantity. `θ` is `MANIFESTVAR` and is measurement error, not this correlation. Meredith (1993) remains unread (web search 2026-08-27T14:20Z: Springer/Cambridge Core paywalled; 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`). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.

crates/psychometric_core/src/error.rs

@@ -504,6 +504,18 @@ pub enum PsychometricError {
     /// later-occasion stationary observed variance. Lagged covariance
     /// omits `Q_Δt` and `θ`.
     StationaryLaggedObservedCovarianceIsNotStationaryLaterObservedVariance,
+    /// Driver §4.3 predetermined lagged covariance was treated as
+    /// stationary lagged covariance. Stationary lagged uses
+    /// `−q / (2 a)` in place of free `p_0`.
+    StationaryLaggedLatentCovarianceIsNotPredeterminedLaggedLatentCovariance,
+    /// Driver §4.3 predetermined later-occasion variance was treated
+    /// as predetermined lagged covariance. Later-occasion variance
+    /// includes `Q_Δt`; lagged covariance omits it.
+    PredeterminedLaterLatentVarianceIsNotPredeterminedLaggedLatentCovariance,
+    /// Driver §4.3 predetermined lagged covariance was treated as
+    /// `e^{a Δt}` of `trait + p_0 + (B / a)² v`. Trait variance and
+    /// `addedTIPREDVAR` do not decay.
+    DecayedPredeterminedTotalIsNotPredeterminedLaggedLatentCovariance,
     /// Driver p. 16 `CINTstd` was requested without a strictly positive
     /// `asymDIFFUSION`. Footnote 4 standardises using only the
     /// relevant variance; zero `q` has no positive process SD.
@@ -1105,6 +1117,15 @@ impl fmt::Display for PsychometricError {
             Self::StationaryLaggedObservedCovarianceIsNotStationaryLaterObservedVariance => {
                 "stationary lagged observed covariance is not the stationary later-occasion observed variance"
             }
+            Self::StationaryLaggedLatentCovarianceIsNotPredeterminedLaggedLatentCovariance => {
+                "stationary lagged latent covariance is not the predetermined lagged latent covariance"
+            }
+            Self::PredeterminedLaterLatentVarianceIsNotPredeterminedLaggedLatentCovariance => {
+                "predetermined later-occasion latent variance is not the predetermined lagged latent covariance"
+            }
+            Self::DecayedPredeterminedTotalIsNotPredeterminedLaggedLatentCovariance => {
+                "decayed predetermined total is not the predetermined lagged latent covariance"
+            }
             Self::StandardisedContinuousInterceptRequiresPositiveStationaryVariance => {
                 "standardised continuous intercept requires strictly positive stationary within-subject variance"
             }
@@ -1850,6 +1871,21 @@ mod tests {
                 .to_string(),
             "stationary lagged observed covariance is not the stationary later-occasion observed variance"
         );
+        assert_eq!(
+            PsychometricError::StationaryLaggedLatentCovarianceIsNotPredeterminedLaggedLatentCovariance
+                .to_string(),
+            "stationary lagged latent covariance is not the predetermined lagged latent covariance"
+        );
+        assert_eq!(
+            PsychometricError::PredeterminedLaterLatentVarianceIsNotPredeterminedLaggedLatentCovariance
+                .to_string(),
+            "predetermined later-occasion latent variance is not the predetermined lagged latent covariance"
+        );
+        assert_eq!(
+            PsychometricError::DecayedPredeterminedTotalIsNotPredeterminedLaggedLatentCovariance
+                .to_string(),
+            "decayed predetermined total is not the predetermined lagged latent covariance"
+        );
     }
 
     #[test]