Restore 2017-era T0TRAITEFFECT Eq.3 carry as e^{aΔt} t0_trait·trait

CHANGELOG.md

@@ -40,6 +40,8 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 
 - `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, Eq. 3 first summand, p. 5; §4.3, pp. 9–10; §7.1, pp. 18–19; 2017-era ctsem `ctModel.R` / `ctFit.R` / `ctGenerate.R`; JSS PDF re-opened 2026-08-31T01:40Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar Eq. 3 first-summand carry of 2017-era `T0TRAITEFFECT` as `e^{A Δt} t0_trait · trait` (register items 114–115). Paper §4.3 / §7.1 name traits the between-subject process. Table 2 / Table 3 do not print `T0TRAITEFFECT`. The 2017-era `ctFit.R` places that matrix in the `OpenMx` `A` regression block from trait latents to process latents at `T0`; `ctGenerate.R` writes `T0MEANS = T0MEANS + T0TRAITEFFECT %*% traits` and then integrates the SDE, so that product is already in `η(t0)`. Equation 3's first summand is `e^{A(t−t0)} η_i(t0)`, so the carry is `e^{A Δt} t0_trait · trait`. Form `t0_trait` first, then multiply by the trait score, then `e^{a Δt}` of that product. A zero coefficient or zero trait is exactly zero. A zero drift is the first-occasion product with no dissipation. Binary64 underflow of `e^{a Δt}` to `+0` is a vanishing carry and is kept. Overflow of a finite `a Δt` rewrites as `sign(shift) exp(ln|shift| + a Δt)`. `t0_trait · trait` is the first-occasion shift and is not this carry even when `a = 0`. `e^{A Δt} t0_b z` is `T0TIPREDEFFECT` carry and is not this carry even when the numbers equal. `e^{A Δt} t0_m x0` is `T0TDPREDEFFECT` carry and is not this carry even when the numbers equal. `A^{-1}[e^{A Δt} − I] B z` is `TIPREDEFFECT` and is not this carry. This crate does not invent `T0TRAITVAR`. Free `T0TRAITEFFECT` does not require `a < 0`. Independent of open sibling PRs (`#299`–`#318`). Meredith (1993) remains unread (web search 2026-08-31T01:40Z: Springer/Cambridge Core paywalled; Unpaywall historically `is_oa: false`). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`; ERIC ED268155 is Mislevy 1985 ETS RR-85-41, not the 1991 journal article). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.
+
 - `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.
 
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 2, p. 12 `TRAITVAR`; §7.1, pp. 18–19; p. 16 `TRAITVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-26T17:45Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised trait variance on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 81–82). Table 2 names `TRAITVAR` `φ_ξ` the latent trait variance/covariance and sets it `NULL` when there is no trait. Section 7.1 names traits the stable between-subject differences (unit-level unobserved heterogeneity). Page 16 prints standardised matrices with the suffix `std` when appropriate. The printed example on p. 16 is `discreteDRIFTstd`, not `TRAITVARstd`. Footnote 4 standardises using only the relevant variance, not the total. The relevant variance for that named between-subject correlation is `TRAITVAR`, not free first-occasion `T0VAR` and not process-dynamics `asymDIFFUSION`. The 2017-era source forms `TRAITVARstd` only when `TRAITVAR != 0`, as `solve(sqrt(diag(TRAITVAR))) %&% TRAITVAR` when `verbose = TRUE`. OpenMx `%&%` is `t(A) %*% B %*% A`. Unlike `T0VARstd`, that formation uses `diag(diag(TRAITVAR))` and does not add `diag(c(ridging))`. The ridge is a `T0VAR` numerical hack and is not this exact map. The scalar correlation is `trait / trait = 1` after strictly positive `TRAITVAR`. Form strictly positive `trait` first, then `1 / √trait`, then `(1 / √trait) trait (1 / √trait)`. Unstandardised `TRAITVAR` is defined for a zero trait; standardised `TRAITVAR` is not. Zero `TRAITVAR` skips forming `TRAITVARstd` in the 2017-era source and fails closed here. Between-subject variance is an event-time structural quantity, so a non-event clock fails closed. `TRAITVAR` does not require stable `a < 0`. Distinct positive `trait` recover the same 1. `p_0 / p_0 = 1` is `T0VARstd` and recovers the same number and remains a distinct named quantity. `t0_b² v` is `addedT0TIPREDVAR` and is extra first-occasion TI variance, not this correlation. Meredith (1993) remains unread (Unpaywall 2026-08-26T17:20Z: `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.

crates/psychometric_core/src/error.rs

@@ -710,6 +710,22 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+    /// 2017-era `T0TRAITEFFECT` first-occasion shift was treated as
+    /// the Eq. 3 first-summand carry. `t0_trait · trait` is not
+    /// `e^{A Δt} t0_trait · trait`.
+    InitialTraitEffectIsNotInitialTraitCarry,
+    /// Driver Eq. 3 carry of Table 3 `T0TIPREDEFFECT` was treated as
+    /// the Eq. 3 carry of 2017-era `T0TRAITEFFECT`. `e^{A Δt} t0_b z`
+    /// is not `e^{A Δt} t0_trait · trait`.
+    InitialTimeIndependentCarryIsNotInitialTraitCarry,
+    /// Driver Eq. 3 carry of Table 3 `T0TDPREDEFFECT` was treated as
+    /// the Eq. 3 carry of 2017-era `T0TRAITEFFECT`. `e^{A Δt} t0_m x0`
+    /// is not `e^{A Δt} t0_trait · trait`.
+    InitialTimeDependentCarryIsNotInitialTraitCarry,
+    /// Driver Eq. 3 second-summand `TIPREDEFFECT` increment was treated
+    /// as the Eq. 3 carry of 2017-era `T0TRAITEFFECT`.
+    /// `A^{-1}[e^{A Δt} − I] B z` is not `e^{A Δt} t0_trait · trait`.
+    TimeIndependentIncrementIsNotInitialTraitCarry,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1235,6 +1251,18 @@ impl fmt::Display for PsychometricError {
             Self::ObservedVarianceIsNotStandardisedManifestVariance => {
                 "observed-indicator variance is not standardised measurement-error variance"
             }
+            Self::InitialTraitEffectIsNotInitialTraitCarry => {
+                "first-occasion trait effect is not the first-occasion trait carry"
+            }
+            Self::InitialTimeIndependentCarryIsNotInitialTraitCarry => {
+                "first-occasion time-independent predictor carry is not the first-occasion trait carry"
+            }
+            Self::InitialTimeDependentCarryIsNotInitialTraitCarry => {
+                "first-occasion time-dependent predictor carry is not the first-occasion trait carry"
+            }
+            Self::TimeIndependentIncrementIsNotInitialTraitCarry => {
+                "time-independent predictor increment is not the first-occasion trait carry"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2101,24 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn initial_trait_carry_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::InitialTraitEffectIsNotInitialTraitCarry.to_string(),
+            "first-occasion trait effect is not the first-occasion trait carry"
+        );
+        assert_eq!(
+            PsychometricError::InitialTimeIndependentCarryIsNotInitialTraitCarry.to_string(),
+            "first-occasion time-independent predictor carry is not the first-occasion trait carry"
+        );
+        assert_eq!(
+            PsychometricError::InitialTimeDependentCarryIsNotInitialTraitCarry.to_string(),
+            "first-occasion time-dependent predictor carry is not the first-occasion trait carry"
+        );
+        assert_eq!(
+            PsychometricError::TimeIndependentIncrementIsNotInitialTraitCarry.to_string(),
+            "time-independent predictor increment is not the first-occasion trait carry"
+        );
+    }
 }