feat(psychometric): restore Driver Eq. 5 of addedTIPREDVAR λ² (B/a)² v 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 Driver, Oud, and Voelkle (2017, Eq. 5, p. 5; Table 2, p. 12 `LAMBDA`/`MANIFESTVAR`/`TIPREDEFFECT`; §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 §7.2 `addedTIPREDVAR` on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 73–74). Equation 5 writes `y_i(t) = Γ + Λ η_i(t) + ζ_i(t)` with `ζ ~ N(0, Θ)` and `Γ ~ N(τ, Ψ)`. Section 7.2 names `addedTIPREDVAR` the stable between-subject variance accounted for by time-independent predictors. The 2017-era `summary.ctsemFit.R` forms that latent extra as `asymTIPREDEFFECT %*% TIPREDVAR %*% t(asymTIPREDEFFECT)`. The scalar analog 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. A non-event clock fails closed. `a ≥ 0` with a nonzero extra fails closed. `(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 `λ² t0_b² v` is Eq. 5 of `addedT0TIPREDVAR`, not this asymptotic observed extra; unpublished `#308` is not a dependency and that first-occasion map is compared inline. `λ² p + θ` is stationary observed variance, not this extra. `MANIFESTVAR` `θ` is measurement error, not this extra. 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.
+
 - `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

@@ -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 §7.2 `addedTIPREDVAR` `λ² (B / a)² v` was
+    /// treated as the latent extra `(B / a)² v`. The observed extra
+    /// is not the latent extra.
+    AsymptoticTimeIndependentObservedVarianceIsNotAsymptoticTimeIndependentVariance,
+    /// Driver Eq. 5 of §7.2 `addedTIPREDVAR` `λ² (B / a)² v` was
+    /// treated as Eq. 5 of `addedT0TIPREDVAR` `λ² t0_b² v`. The
+    /// asymptotic observed extra uses `-B / a`, not free
+    /// `T0TIPREDEFFECT`.
+    AsymptoticTimeIndependentObservedVarianceIsNotInitialTimeIndependentObservedVariance,
+    /// Driver Eq. 5 of §7.2 `addedTIPREDVAR` `λ² (B / a)² v` was
+    /// treated as stationary observed variance `λ² p + θ`. The extra
+    /// is not the full stationary `Var(y)`.
+    AsymptoticTimeIndependentObservedVarianceIsNotStationaryObservedVariance,
+    /// Driver Eq. 5 of §7.2 `addedTIPREDVAR` `λ² (B / a)² v` was
+    /// treated as `MANIFESTVAR` `θ`. Measurement error is not extra
+    /// observed TI variance.
+    AsymptoticTimeIndependentObservedVarianceIsNotMeasurementError,
 
     /// 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::AsymptoticTimeIndependentObservedVarianceIsNotAsymptoticTimeIndependentVariance => {
+                "asymptotic time-independent observed variance is not asymptotic time-independent predictor variance"
+            }
+            Self::AsymptoticTimeIndependentObservedVarianceIsNotInitialTimeIndependentObservedVariance => {
+                "asymptotic time-independent observed variance is not initial time-independent observed variance"
+            }
+            Self::AsymptoticTimeIndependentObservedVarianceIsNotStationaryObservedVariance => {
+                "asymptotic time-independent observed variance is not stationary observed variance"
+            }
+            Self::AsymptoticTimeIndependentObservedVarianceIsNotMeasurementError => {
+                "asymptotic time-independent observed variance is not measurement-error variance"
+            }
 
 
 
@@ -2002,6 +2031,30 @@ mod tests {
         );
     }
 
+    #[test]
+    fn asymptotic_time_independent_observed_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::AsymptoticTimeIndependentObservedVarianceIsNotAsymptoticTimeIndependentVariance
+                .to_string(),
+            "asymptotic time-independent observed variance is not asymptotic time-independent predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::AsymptoticTimeIndependentObservedVarianceIsNotInitialTimeIndependentObservedVariance
+                .to_string(),
+            "asymptotic time-independent observed variance is not initial time-independent observed variance"
+        );
+        assert_eq!(
+            PsychometricError::AsymptoticTimeIndependentObservedVarianceIsNotStationaryObservedVariance
+                .to_string(),
+            "asymptotic time-independent observed variance is not stationary observed variance"
+        );
+        assert_eq!(
+            PsychometricError::AsymptoticTimeIndependentObservedVarianceIsNotMeasurementError
+                .to_string(),
+            "asymptotic time-independent observed variance is not measurement-error variance"
+        );
+    }
+
     #[test]
 
     fn standardised_discrete_continuous_intercept_boundary_messages_are_stable() {