feat(psychometric): restore Driver 2017-era T0TOTALVAR extra+p_0 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, Table 2, p. 12 `TRAITVAR` / `T0VAR`; §7.1, pp. 18–19; p. 16; 2017-era ctsem `summary.ctsemFit.R` lines 322–339; JSS PDF re-opened 2026-08-30T18:50Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar 2017-era `T0TOTALVAR` on current main (register items 110–111). Independent of open `#321` unstandardised `T0TRAITVAR` and `#322` `T0TRAITVARstd`. This crate does not currently export `recover_initial_trait_variance`; form the quadratic `t0_trait² · trait` directly, then add free first-occasion `T0VAR` `p_0`. Table 2 names `TRAITVAR` `φ_ξ` the latent trait variance/covariance and `T0VAR` the latent process initial variance/covariance. Section 7.1 names traits the stable between-subject differences (unit-level unobserved heterogeneity). `T0TRAITEFFECT` is not in Table 2 or Table 3. The 2017-era `summary.ctsemFit.R` (ctsem 2.5.0, lines 322–339) comments `T0TRAITVAR <- T0TRAITEFFECT %*% TRAITVAR %*% t(T0TRAITEFFECT)` with `#is this valid?`, then `T0TOTALVAR <- T0TRAITVAR + T0VAR`. The scalar analog extra is `t0_trait² · trait`. The scalar total is `extra + p_0`. Form the extra first, then add free `p_0`. A zero extra or zero `p_0` is kept. A zero extra and a zero `p_0` is exactly zero. `trait < 0` or `p_0 < 0` fails closed. `T0` is an event-time occasion, so a non-event clock fails closed. Free `T0TRAITEFFECT` and free `T0VAR` do not require stable `a < 0`. `t0_trait² · trait` is `T0TRAITVAR` and equals this total when `p_0 = 0` and remains a distinct named quantity. Free `p_0` is `T0VAR` and equals this total when the extra is 0 and remains a distinct named quantity. `TRAITVAR` equals this total when `T0TRAITEFFECT = I` and `p_0 = 0` and remains a distinct named quantity. `t0_b² v` is `addedT0TIPREDVAR` and is extra first-occasion TI variance, not this total. Meredith (1993) remains unread (Unpaywall 2026-08-30T18:40Z: `is_oa: false`; OpenAlex closed; Springer `content/pdf` is an HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`; Unpaywall `is_oa: false`). 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 +710,23 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+    /// Driver 2017-era `T0TOTALVAR` `t0_trait² · trait + p_0` was
+    /// treated as unstandardised `T0TRAITVAR` `t0_trait² · trait`.
+    /// Equal numbers when `p_0 = 0` are still distinct named
+    /// quantities.
+    InitialTotalVarianceIsNotInitialTraitVariance,
+    /// Driver 2017-era `T0TOTALVAR` was treated as free first-occasion
+    /// `T0VAR` `p_0`. Equal numbers when the trait extra is 0 are
+    /// still distinct named quantities.
+    InitialTotalVarianceIsNotInitialLatentVariance,
+    /// Driver 2017-era `T0TOTALVAR` was treated as Table 2 `TRAITVAR`.
+    /// Equal numbers when `T0TRAITEFFECT = I` and `p_0 = 0` are still
+    /// distinct named quantities.
+    InitialTotalVarianceIsNotTraitVariance,
+    /// Driver 2017-era `T0TOTALVAR` was treated as 2017-era
+    /// `addedT0TIPREDVAR` `t0_b² v`. Extra first-occasion TI variance
+    /// is not the first-occasion trait-plus-state total.
+    InitialTotalVarianceIsNotInitialTimeIndependentVariance,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1235,6 +1252,18 @@ impl fmt::Display for PsychometricError {
             Self::ObservedVarianceIsNotStandardisedManifestVariance => {
                 "observed-indicator variance is not standardised measurement-error variance"
             }
+            Self::InitialTotalVarianceIsNotInitialTraitVariance => {
+                "initial total variance is not initial trait variance"
+            }
+            Self::InitialTotalVarianceIsNotInitialLatentVariance => {
+                "initial total variance is not initial latent variance"
+            }
+            Self::InitialTotalVarianceIsNotTraitVariance => {
+                "initial total variance is not trait variance"
+            }
+            Self::InitialTotalVarianceIsNotInitialTimeIndependentVariance => {
+                "initial total variance is not initial time-independent predictor variance"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2102,24 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn initial_total_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::InitialTotalVarianceIsNotInitialTraitVariance.to_string(),
+            "initial total variance is not initial trait variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTotalVarianceIsNotInitialLatentVariance.to_string(),
+            "initial total variance is not initial latent variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTotalVarianceIsNotTraitVariance.to_string(),
+            "initial total variance is not trait variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTotalVarianceIsNotInitialTimeIndependentVariance.to_string(),
+            "initial total variance is not initial time-independent predictor variance"
+        );
+    }
 }