feat(psychometric): restore Driver p.16 addedTIPREDVARstd extra/extra=1 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, p. 16 `addedTIPREDVARstd`; §7.2, pp. 20–21; Table 2, p. 12; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-30T12:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised extra time-independent predictor variance on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 106–107). Page 16 prints standardised matrices with the suffix `std` when appropriate. The printed example on p. 16 is `discreteDRIFTstd`, not `addedTIPREDVARstd`. Footnote 4 standardises using only the relevant variance, not the total. The relevant variance for that named extra-process correlation is `addedTIPREDVAR` itself, not `TRAITVAR`, not `TIPREDVAR`, and not `asymDIFFUSION`. Section 7.2 names `addedTIPREDVAR` the stable between-subject variance accounted for by time-independent predictors. After `addedTIPREDVAR` as `asymTIPREDEFFECT %*% TIPREDVAR %*% t(asymTIPREDEFFECT)`, the 2017-era source forms `addedTIPREDVARstd` whenever `verbose = TRUE` and `n.TIpred > 0`, as `solve(sqrt(diag(addedTIPREDVAR) + ridging)) %&% addedTIPREDVAR`. OpenMx `%&%` is `t(A) %*% B %*% A`. That formation adds `diag(c(ridging), n.latent)`. 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 `extra / extra = 1` after strictly positive extra. Form `addedTIPREDVAR` first, then `1 / √extra`, then `(1 / √extra) extra (1 / √extra)`. Unstandardised `(B / a)² v` is defined for a zero coefficient and for zero predictor variance; standardised `addedTIPREDVAR` is not. Zero extra makes `solve(sqrt(0))` fail in the 2017-era source and fails closed here. Unlike `TRAITVAR` / `MANIFESTTRAITVAR`, that source does not skip forming `addedTIPREDVARstd` when extra is 0. Extra process variance is an event-time structural quantity, so a non-event clock fails closed. Lasting extra requires stable `a < 0` when the extra is nonzero. Distinct positive extra recover the same 1. `trait / trait = 1` is `TRAITVARstd` and recovers the same number and remains a distinct named quantity. `t0_b² v` is 2017-era `addedT0TIPREDVAR` and is extra first-occasion TI variance, not this correlation. `λ² (B / a)² v` is Eq. 5 of the extra, not this correlation. The printed 2-latent `addedTIPREDVAR` 2.838 is not this scalar 1. Meredith (1993) remains unread (web search 2026-08-30T12:20Z: 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.
+
 - `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 +710,30 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+    /// Driver p. 16 `addedTIPREDVARstd` was requested without a
+    /// strictly positive extra. Unlike `TRAITVAR` /
+    /// `MANIFESTTRAITVAR`, the 2017-era source still forms
+    /// `addedTIPREDVARstd` when extra is 0; `solve(sqrt(0))` fails.
+    /// Footnote 4 standardisation requires strictly positive
+    /// `addedTIPREDVAR`.
+    StandardisedAsymptoticTimeIndependentVarianceRequiresPositiveAddedVariance,
+    /// Driver §7.2 unstandardised `addedTIPREDVAR` `(B / a)² v` was
+    /// treated as p. 16 `addedTIPREDVARstd`. Unstandardised extra is
+    /// defined for a zero coefficient and for zero predictor
+    /// variance; standardised `addedTIPREDVAR` is not.
+    UnstandardisedAsymptoticTimeIndependentVarianceIsNotStandardisedAsymptoticTimeIndependentVariance,
+    /// Driver p. 16 `TRAITVARstd` was treated as p. 16
+    /// `addedTIPREDVARstd`. Equal numbers when both correlations
+    /// equal 1 are still distinct named quantities.
+    /// `addedTIPREDVARstd` is the correlation form of extra TI
+    /// process variance; `TRAITVARstd` is the correlation form of
+    /// between-subject `TRAITVAR`.
+    StandardisedTraitVarianceIsNotStandardisedAsymptoticTimeIndependentVariance,
+    /// Driver 2017-era `addedT0TIPREDVAR` `t0_b² v` was treated as
+    /// p. 16 `addedTIPREDVARstd`. Extra first-occasion TI variance
+    /// is not the correlation form of asymptotic extra
+    /// `addedTIPREDVAR`.
+    InitialTimeIndependentVarianceIsNotStandardisedAsymptoticTimeIndependentVariance,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1235,6 +1259,18 @@ impl fmt::Display for PsychometricError {
             Self::ObservedVarianceIsNotStandardisedManifestVariance => {
                 "observed-indicator variance is not standardised measurement-error variance"
             }
+            Self::StandardisedAsymptoticTimeIndependentVarianceRequiresPositiveAddedVariance => {
+                "standardised added time-independent predictor variance requires strictly positive extra variance"
+            }
+            Self::UnstandardisedAsymptoticTimeIndependentVarianceIsNotStandardisedAsymptoticTimeIndependentVariance => {
+                "unstandardised added time-independent predictor variance is not standardised added time-independent predictor variance"
+            }
+            Self::StandardisedTraitVarianceIsNotStandardisedAsymptoticTimeIndependentVariance => {
+                "standardised trait variance is not standardised added time-independent predictor variance"
+            }
+            Self::InitialTimeIndependentVarianceIsNotStandardisedAsymptoticTimeIndependentVariance => {
+                "initial time-independent predictor variance is not standardised added time-independent predictor variance"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2109,28 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn standardised_added_time_independent_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedAsymptoticTimeIndependentVarianceRequiresPositiveAddedVariance
+                .to_string(),
+            "standardised added time-independent predictor variance requires strictly positive extra variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedAsymptoticTimeIndependentVarianceIsNotStandardisedAsymptoticTimeIndependentVariance
+                .to_string(),
+            "unstandardised added time-independent predictor variance is not standardised added time-independent predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedTraitVarianceIsNotStandardisedAsymptoticTimeIndependentVariance
+                .to_string(),
+            "standardised trait variance is not standardised added time-independent predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTimeIndependentVarianceIsNotStandardisedAsymptoticTimeIndependentVariance
+                .to_string(),
+            "initial time-independent predictor variance is not standardised added time-independent predictor variance"
+        );
+    }
 }