feat(psychometric): restore Driver Eq. 5 of addedT0TIPREDVAR λ² t0_b² v on main

CHANGELOG.md

@@ -38,6 +38,7 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 
 ## [Unreleased]
 
+- `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Eq. 5, p. 5; Table 3, p. 13 `T0TIPREDEFFECT`; Table 2, p. 12 `LAMBDA`/`MANIFESTVAR`; p. 16; §7.2, pp. 20–21; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-30T14:06Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar extra observed-indicator time-independent predictor variance of 2017-era `addedT0TIPREDVAR` on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 71–72). Equation 5 writes `y_i(t) = Γ + Λ η_i(t) + ζ_i(t)` with `ζ ~ N(0, Θ)` and `Γ ~ N(τ, Ψ)`. Immediately after `T0TIPREDEFFECTstd`, the 2017-era `summary.ctsemFit.R` in ctsem 2.1.0 (lines 429–431) forms `addedT0TIPREDVAR = T0TIPREDEFFECT %*% TIPREDVAR %*% t(T0TIPREDEFFECT)` when `verbose = TRUE` and `'TOTIPRED'` is not in `stationary`. That source comments `#is this valid?`. The scalar analog of that quadratic form is `t0_b² v`. Equation 5 of that extra, with `θ = 0` and `ψ = 0`, is `λ² t0_b² v`. Form `t0_b` first, then square, then multiply by `v`, then `(λ extra) λ`. Do not form `λ²` first. A zero loading or zero extra is exactly zero. `v < 0` fails closed. `T0` is an event-time occasion, so a non-event clock fails closed. Free `T0TIPREDEFFECT` does not require stable `a < 0`. The latent extra is formed inline; unpublished `#307` `recover_initial_time_independent_predictor_variance` is not a dependency. `t0_b² v` is the latent extra, not this observed extra. `λ² p_0 + θ` is first-occasion observed variance, not this extra. `λ² (B / a)² v` is Eq. 5 of `addedTIPREDVAR`, not this first-occasion observed extra. `MANIFESTVAR` `θ` is measurement error, not this extra. `Ψ` is intercept variance and is not extra TI. 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`). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.
 - Removed the repository-local hourly PR-maintenance caller now covered by the central required scheduler, retired stale workflow registrations, narrowed documentation triggers, keyed PR concurrency by fixed workflow name, repository, and pull-request number without cancelling non-PR runs, and combined line/branch coverage on one sequential runner while preserving both 100% gates and diagnostics.
 
 - `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.

crates/psychometric_core/src/error.rs

@@ -632,6 +632,23 @@ pub enum PsychometricError {
     /// p. 16 `TRAITVARstd`. Extra first-occasion TI variance is not
     /// the correlation form of between-subject `TRAITVAR`.
     InitialTimeIndependentVarianceIsNotStandardisedTraitVariance,
+    /// Driver Eq. 5 of 2017-era `addedT0TIPREDVAR` `λ² t0_b² v` was
+    /// treated as the latent extra `t0_b² v`. The observed extra is
+    /// not the latent extra.
+    InitialTimeIndependentObservedVarianceIsNotInitialTimeIndependentVariance,
+    /// Driver Eq. 5 of 2017-era `addedT0TIPREDVAR` `λ² t0_b² v` was
+    /// treated as first-occasion observed variance `λ² p_0 + θ`.
+    /// The extra is not the full first-occasion `Var(y_0)`.
+    InitialTimeIndependentObservedVarianceIsNotInitialObservedVariance,
+    /// Driver Eq. 5 of 2017-era `addedT0TIPREDVAR` `λ² t0_b² v` was
+    /// treated as Eq. 5 of `addedTIPREDVAR` `λ² (B / a)² v`. The
+    /// first-occasion observed extra uses free `T0TIPREDEFFECT`,
+    /// not `-B / a`.
+    InitialTimeIndependentObservedVarianceIsNotAsymptoticTimeIndependentObservedVariance,
+    /// Driver Eq. 5 of 2017-era `addedT0TIPREDVAR` `λ² t0_b² v` was
+    /// treated as `MANIFESTVAR` `θ`. Measurement error is not extra
+    /// observed TI variance.
+    InitialTimeIndependentObservedVarianceIsNotMeasurementError,
 
     /// Driver p. 16 `discreteCINTstd` was requested without a strictly
     /// positive `asymDIFFUSION`. Footnote 4 standardises using only the
@@ -1183,6 +1200,18 @@ impl fmt::Display for PsychometricError {
             Self::InitialTimeIndependentVarianceIsNotStandardisedTraitVariance => {
                 "initial time-independent predictor variance is not standardised trait variance"
             }
+            Self::InitialTimeIndependentObservedVarianceIsNotInitialTimeIndependentVariance => {
+                "initial time-independent observed variance is not initial time-independent predictor variance"
+            }
+            Self::InitialTimeIndependentObservedVarianceIsNotInitialObservedVariance => {
+                "initial time-independent observed variance is not initial observed variance"
+            }
+            Self::InitialTimeIndependentObservedVarianceIsNotAsymptoticTimeIndependentObservedVariance => {
+                "initial time-independent observed variance is not asymptotic time-independent observed variance"
+            }
+            Self::InitialTimeIndependentObservedVarianceIsNotMeasurementError => {
+                "initial time-independent observed variance is not measurement-error variance"
+            }
 
 
 
@@ -2002,6 +2031,30 @@ mod tests {
         );
     }
 
+    #[test]
+    fn initial_time_independent_observed_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::InitialTimeIndependentObservedVarianceIsNotInitialTimeIndependentVariance
+                .to_string(),
+            "initial time-independent observed variance is not initial time-independent predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTimeIndependentObservedVarianceIsNotInitialObservedVariance
+                .to_string(),
+            "initial time-independent observed variance is not initial observed variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTimeIndependentObservedVarianceIsNotAsymptoticTimeIndependentObservedVariance
+                .to_string(),
+            "initial time-independent observed variance is not asymptotic time-independent observed variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTimeIndependentObservedVarianceIsNotMeasurementError
+                .to_string(),
+            "initial time-independent observed variance is not measurement-error variance"
+        );
+    }
+
     #[test]
 
     fn standardised_discrete_continuous_intercept_boundary_messages_are_stable() {