feat(psychometric): recover Eq. 5 of 2017-era three-term asymTOTALVAR 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 Equation 5 of 2017-era commented three-term `asymTOTALVAR` as `λ²(−q / (2 a) + trait / a² + (B / a)² v) + θ` on current main (Driver, Oud, & Voelkle, 2017, Eq. 1, p. 4; Eq. 4–5, p. 5; Table 2, p. 12; §4.3, p. 9; §7.2, pp. 20–21; p. 16; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-31T05:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104). Page 16 names `asymDIFFUSION` `-q / (2 a)`. Section 4.3 adds a stable trait whose process-mean variance is `trait / a²`. Section 7.2 names `addedTIPREDVAR` `(B / a)² v`. The 2017-era source comments `asymTOTALVAR <- asymDIFFUSION + asymTRAITVAR` then `+ addedTIPREDVAR` (not in the active `outlist`). Form that three-term total inline, then `λ²` of it plus `θ`. Do not export the unstandardised total. Do not import unpublished `asymTRAITVAR` / `asymTOTALVAR` helpers. `ψ = 0` this slice. A zero loading is exactly `θ`. All-zero latent contributions return `θ` even if `a ≥ 0`. `a ≥ 0` with any nonzero contribution fails closed. Numeric: `a = −0.5`, `trait = 1`, `q = 0.4`, `B = 0.5`, `v = 1`, `λ = 2`, `θ = 0.3` recovers 21.9, distinct from Eq. 5 of stationary `T0VAR` 9.9 (`TRAITVAR` is not `trait / a²`). `MANIFESTVAR` is not `Var(y)`. The unstandardised three-term total is not `Var(y)`. A non-event clock fails closed. Meredith (1993) remains unread (Springer/Cambridge paywalled; Unpaywall historically `is_oa: false`). Mislevy (1991, *Psychometrika, 56*, 177–196, DOI 10.1007/bf02294457) remains unread on the same terms. 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

@@ -710,6 +710,25 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+    /// Equation 5 of 2017-era three-term `asymTOTALVAR` was requested
+    /// with a non-strictly-negative drift and a nonzero latent
+    /// contribution. Lasting `−q / (2 a) + trait / a² + (B / a)² v`
+    /// requires stable `a < 0`. All-zero contributions remain `θ`.
+    AsymptoticTotalObservedVarianceRequiresStableDrift,
+    /// Unstandardised 2017-era three-term `asymTOTALVAR`
+    /// `−q / (2 a) + trait / a² + (B / a)² v` was treated as Eq. 5 of
+    /// that total. The latent total is not `Var(y)`.
+    UnstandardisedAsymptoticTotalVarianceIsNotAsymptoticTotalObservedVariance,
+    /// Equation 5 of §4.3 stationary `T0VAR`
+    /// `λ²(trait + −q / (2 a) + (B / a)² v) + θ` was treated as
+    /// Eq. 5 of 2017-era three-term `asymTOTALVAR`. Stationary
+    /// `T0VAR` uses untransformed `TRAITVAR`; `asymTRAITVAR` is
+    /// `trait / a²`.
+    StationaryInitialObservedVarianceIsNotAsymptoticTotalObservedVariance,
+    /// Driver Table 2 `MANIFESTVAR` `θ` was treated as Eq. 5 of
+    /// 2017-era three-term `asymTOTALVAR`. Measurement error is not
+    /// `λ²` of that latent total plus `θ`.
+    MeasurementErrorIsNotAsymptoticTotalObservedVariance,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1235,6 +1254,18 @@ impl fmt::Display for PsychometricError {
             Self::ObservedVarianceIsNotStandardisedManifestVariance => {
                 "observed-indicator variance is not standardised measurement-error variance"
             }
+            Self::AsymptoticTotalObservedVarianceRequiresStableDrift => {
+                "asymptotic total observed variance requires stable drift"
+            }
+            Self::UnstandardisedAsymptoticTotalVarianceIsNotAsymptoticTotalObservedVariance => {
+                "unstandardised asymptotic total variance is not asymptotic total observed variance"
+            }
+            Self::StationaryInitialObservedVarianceIsNotAsymptoticTotalObservedVariance => {
+                "stationary initial observed variance is not asymptotic total observed variance"
+            }
+            Self::MeasurementErrorIsNotAsymptoticTotalObservedVariance => {
+                "measurement error is not asymptotic total observed variance"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2104,26 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn asymptotic_total_observed_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::AsymptoticTotalObservedVarianceRequiresStableDrift.to_string(),
+            "asymptotic total observed variance requires stable drift"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedAsymptoticTotalVarianceIsNotAsymptoticTotalObservedVariance
+                .to_string(),
+            "unstandardised asymptotic total variance is not asymptotic total observed variance"
+        );
+        assert_eq!(
+            PsychometricError::StationaryInitialObservedVarianceIsNotAsymptoticTotalObservedVariance
+                .to_string(),
+            "stationary initial observed variance is not asymptotic total observed variance"
+        );
+        assert_eq!(
+            PsychometricError::MeasurementErrorIsNotAsymptoticTotalObservedVariance.to_string(),
+            "measurement error is not asymptotic total observed variance"
+        );
+    }
 }