feat(psychometric): restore Driver 2017-era T0TRAITVAR t0_trait² · trait 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`; §7.1, pp. 18–19; 2017-era ctsem `ctFit.R` / `summary.ctsemFit.R` / `ctGenerate.R`; JSS PDF re-opened 2026-08-30T18:50Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar 2017-era `T0TRAITVAR` on current main (register items 106–107). 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). `T0TRAITEFFECT` is not in Table 2 or Table 3. The 2017-era `ctFit.R` (ctsem 2.5.0, lines 693–696) places it as the OpenMx `A` path from the trait latent onto the process at `T0`. When `'T0TRAITEFFECT'` is in `stationary` (lines 1494–1508) that path is the identity. The 2017-era `summary.ctsemFit.R` (lines 322–331) comments `T0TRAITVAR <- T0TRAITEFFECT %*% TRAITVAR %*% t(T0TRAITEFFECT)` with `#is this valid?` — the same comment as `addedT0TIPREDVAR`. The scalar analog of that quadratic form is `t0_trait² · trait`. Form `t0_trait` first, then square, then multiply by `trait`. A zero coefficient or zero trait is exactly zero. `trait < 0` fails closed. `T0` is an event-time occasion, so a non-event clock fails closed. Free `T0TRAITEFFECT` does not require stable `a < 0`. Stationary `T0TRAITEFFECT = I` makes `T0TRAITVAR` equal `TRAITVAR` numerically; those remain distinct named quantities. `t0_b² v` is `addedT0TIPREDVAR` and is not this trait extra. `(B / a)² v` is `addedTIPREDVAR` and is not this first-occasion map. Free `T0VAR` `p_0` is not this extra. `ctGenerate.R` (lines 113–116) draws traits from `N(0, I)` and adds `T0TRAITEFFECT %*% traits` to `T0MEANS`, so the generate extra at `T0` is `t0_trait²`, not `t0_trait² · trait`. This crate does not currently export `recover_initial_trait_effect`; form the quadratic directly. 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

@@ -710,6 +710,28 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+    /// Driver 2017-era `T0TRAITVAR` `t0_trait² · trait` was treated
+    /// as Table 2 `TRAITVAR`. When `T0TRAITEFFECT` is the
+    /// stationary identity those numbers equal and remain distinct
+    /// named quantities.
+    InitialTraitVarianceIsNotTraitVariance,
+    /// Driver 2017-era `T0TRAITVAR` `t0_trait² · trait` was treated
+    /// as 2017-era `addedT0TIPREDVAR` `t0_b² v`. Trait loadings
+    /// are not time-independent predictor effects.
+    InitialTraitVarianceIsNotInitialTimeIndependentVariance,
+    /// Driver 2017-era `T0TRAITVAR` `t0_trait² · trait` was treated
+    /// as §7.2 `addedTIPREDVAR` `(B / a)² v`. First-occasion trait
+    /// extra is not asymptotic TI extra.
+    InitialTraitVarianceIsNotAsymptoticTimeIndependentVariance,
+    /// Driver 2017-era `T0TRAITVAR` `t0_trait² · trait` was treated
+    /// as free `T0VAR` `p_0`. Trait extra at `T0` is not the
+    /// first-occasion state.
+    InitialTraitVarianceIsNotInitialLatentVariance,
+    /// Driver 2017-era `T0TRAITVAR` `t0_trait² · trait` was treated
+    /// as the ctGenerate unit-normal extra `t0_trait²`. Generate
+    /// draws traits from `N(0, I)` at `T0`; SEM path-tracing uses
+    /// `TRAITVAR`.
+    InitialTraitVarianceIsNotUnitTraitGenerateVariance,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1235,6 +1257,21 @@ impl fmt::Display for PsychometricError {
             Self::ObservedVarianceIsNotStandardisedManifestVariance => {
                 "observed-indicator variance is not standardised measurement-error variance"
             }
+            Self::InitialTraitVarianceIsNotTraitVariance => {
+                "initial trait variance is not trait variance"
+            }
+            Self::InitialTraitVarianceIsNotInitialTimeIndependentVariance => {
+                "initial trait variance is not initial time-independent predictor variance"
+            }
+            Self::InitialTraitVarianceIsNotAsymptoticTimeIndependentVariance => {
+                "initial trait variance is not asymptotic time-independent predictor variance"
+            }
+            Self::InitialTraitVarianceIsNotInitialLatentVariance => {
+                "initial trait variance is not initial latent variance"
+            }
+            Self::InitialTraitVarianceIsNotUnitTraitGenerateVariance => {
+                "initial trait variance is not unit-trait generate variance"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2110,29 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn initial_trait_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::InitialTraitVarianceIsNotTraitVariance.to_string(),
+            "initial trait variance is not trait variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTraitVarianceIsNotInitialTimeIndependentVariance.to_string(),
+            "initial trait variance is not initial time-independent predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTraitVarianceIsNotAsymptoticTimeIndependentVariance
+                .to_string(),
+            "initial trait variance is not asymptotic time-independent predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTraitVarianceIsNotInitialLatentVariance.to_string(),
+            "initial trait variance is not initial latent variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTraitVarianceIsNotUnitTraitGenerateVariance.to_string(),
+            "initial trait variance is not unit-trait generate variance"
+        );
+    }
 }

crates/psychometric_core/src/event_time.rs

@@ -61,6 +61,14 @@
 //! accounted for by those predictors. The scalar map is `(B / a)² v`
 //! for predictor variance `v ≥ 0`. That variance is not `TRAITVAR`,
 //! not `asymDIFFUSION`, and not the expected total change `-B z / a`.
+//! The 2017-era `summary.ctsemFit.R` (ctsem 2.5.0, lines 322–331)
+//! comments the SEM path-tracing
+//! `T0TRAITVAR <- T0TRAITEFFECT %*% TRAITVAR %*% t(T0TRAITEFFECT)`
+//! with `#is this valid?`. The scalar analog is `t0_trait² · trait`.
+//! That first-occasion trait extra is not `TRAITVAR` even when
+//! stationary `T0TRAITEFFECT = I` so they equal, not `addedT0TIPREDVAR`
+//! `t0_b² v`, not `addedTIPREDVAR` `(B / a)² v`, not free `T0VAR`,
+//! and not the ctGenerate unit-normal extra `t0_trait²`.
 //! Table 2 (p. 12) names `asymCINT` the asymptotic (`Δt = ∞`)
 //! expected change in processes for a 1 unit change in intercept
 //! (`CINT`). Equation 3 maps a finite event interval as
@@ -6795,6 +6803,154 @@ pub fn recover_irregular_centered_residual_log_rate(
     require_finite(sum / count)
 }
 
+/// Exact scalar 2017-era `T0TRAITVAR`.
+///
+/// Driver, Oud, and Voelkle (2017, Table 2, p. 12 `TRAITVAR`; §7.1,
+/// pp. 18–19; 2017-era ctsem `ctFit.R` / `summary.ctsemFit.R` /
+/// `ctGenerate.R`; JSS PDF re-opened 2026-08-30T18:50Z from
+/// <https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104>)
+/// name `TRAITVAR` `φ_ξ` the latent trait variance. `T0TRAITEFFECT`
+/// is not in Table 2 or Table 3. The 2017-era `ctFit.R` (ctsem 2.5.0,
+/// lines 693–696) places it as the `OpenMx` `A` path from the trait
+/// latent onto the process at `T0`. When `'T0TRAITEFFECT'` is in
+/// `stationary` (lines 1494–1508) that path is the identity. The
+/// 2017-era `summary.ctsemFit.R` (lines 322–331) comments
+/// `T0TRAITVAR <- T0TRAITEFFECT %*% TRAITVAR %*% t(T0TRAITEFFECT)`
+/// with `#is this valid?` — the same comment as `addedT0TIPREDVAR`.
+/// The scalar analog of that quadratic form is `t0_trait² · trait`.
+/// Form `t0_trait` first, then square, then multiply by `trait`. A
+/// zero coefficient or zero trait is exactly zero. `trait < 0` fails
+/// closed. `T0` is an event-time occasion, so a non-event clock fails
+/// closed. Free `T0TRAITEFFECT` does not require stable `a < 0`.
+/// Stationary `T0TRAITEFFECT = I` makes `T0TRAITVAR` equal `TRAITVAR`
+/// numerically; those remain distinct named quantities. `t0_b² v` is
+/// `addedT0TIPREDVAR` and is not this trait extra. `(B / a)² v` is
+/// `addedTIPREDVAR` and is not this first-occasion map. Free `T0VAR`
+/// `p_0` is not this extra. `ctGenerate.R` (lines 113–116) draws
+/// traits from `N(0, I)` and adds `T0TRAITEFFECT %*% traits` to
+/// `T0MEANS`, so the generate extra at `T0` is `t0_trait²`, not
+/// `t0_trait² · trait`. This crate does not currently export
+/// `recover_initial_trait_effect`; form the quadratic directly. This
+/// is not a Kalman filter, not a matrix `expm`, not DSEM, and not
+/// ctsem estimation.
+///
+/// # Errors
+///
+/// Returns [`PsychometricError::EventTimeRequired`] for any
+/// non-event clock and
+/// [`PsychometricError::InvalidNumericInput`] when an input is
+/// non-finite, the trait variance is negative, or the product
+/// overflows.
+pub fn recover_initial_trait_variance(
+    initial_trait_effect: f64,
+    trait_variance: f64,
+    clock: LagClock,
+) -> Result<f64, PsychometricError> {
+    if !clock.admits_structural_lag() {
+        return Err(PsychometricError::EventTimeRequired);
+    }
+    if !initial_trait_effect.is_finite() || !trait_variance.is_finite() || trait_variance < 0.0 {
+        return Err(PsychometricError::InvalidNumericInput);
+    }
+    if initial_trait_effect == 0.0 || trait_variance == 0.0 {
+        return Ok(0.0);
+    }
+    let squared = require_finite(initial_trait_effect * initial_trait_effect)?;
+    require_finite(squared * trait_variance)
+}
+
+/// Refuse treating 2017-era `T0TRAITVAR` as Table 2 `TRAITVAR`.
+///
+/// `t0_trait² · trait` is extra first-occasion trait variance.
+/// `TRAITVAR` is the between-subject process. Stationary
+/// `T0TRAITEFFECT = I` makes the numbers equal; they remain
+/// distinct named quantities.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::InitialTraitVarianceIsNotTraitVariance`].
+pub fn refuse_initial_trait_variance_as_trait_variance(
+    initial_trait_variance: f64,
+    trait_variance: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (initial_trait_variance, trait_variance);
+    Err(PsychometricError::InitialTraitVarianceIsNotTraitVariance)
+}
+
+/// Refuse treating 2017-era `T0TRAITVAR` as 2017-era `addedT0TIPREDVAR`.
+///
+/// `t0_trait² · trait` is extra first-occasion trait variance.
+/// `t0_b² v` is extra first-occasion TI predictor variance. This
+/// crate does not currently export `addedT0TIPREDVAR`; the refuse
+/// still names that quantity.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::InitialTraitVarianceIsNotInitialTimeIndependentVariance`].
+pub fn refuse_initial_trait_variance_as_initial_time_independent_variance(
+    initial_trait_variance: f64,
+    initial_predictor_variance: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (initial_trait_variance, initial_predictor_variance);
+    Err(PsychometricError::InitialTraitVarianceIsNotInitialTimeIndependentVariance)
+}
+
+/// Refuse treating 2017-era `T0TRAITVAR` as §7.2 `addedTIPREDVAR`.
+///
+/// `t0_trait² · trait` is extra first-occasion trait variance.
+/// `(B / a)² v` is the asymptotic TI extra. Those are not the
+/// same map.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::InitialTraitVarianceIsNotAsymptoticTimeIndependentVariance`].
+pub fn refuse_initial_trait_variance_as_asymptotic_time_independent_variance(
+    initial_trait_variance: f64,
+    asymptotic_predictor_variance: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (initial_trait_variance, asymptotic_predictor_variance);
+    Err(PsychometricError::InitialTraitVarianceIsNotAsymptoticTimeIndependentVariance)
+}
+
+/// Refuse treating 2017-era `T0TRAITVAR` as free `T0VAR`.
+///
+/// `t0_trait² · trait` is extra first-occasion trait variance.
+/// Free `T0VAR` `p_0` is the first-occasion state. Those are not
+/// the same map.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::InitialTraitVarianceIsNotInitialLatentVariance`].
+pub fn refuse_initial_trait_variance_as_initial_latent_variance(
+    initial_trait_variance: f64,
+    initial_latent_variance: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (initial_trait_variance, initial_latent_variance);
+    Err(PsychometricError::InitialTraitVarianceIsNotInitialLatentVariance)
+}
+
+/// Refuse treating 2017-era `T0TRAITVAR` as the ctGenerate unit extra.
+///
+/// `ctGenerate.R` draws traits from `N(0, I)` and adds
+/// `T0TRAITEFFECT %*% traits` to `T0MEANS`, so the generate extra
+/// at `T0` is `t0_trait²`. SEM path-tracing uses `TRAITVAR`.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::InitialTraitVarianceIsNotUnitTraitGenerateVariance`].
+pub fn refuse_initial_trait_variance_as_unit_trait_generate_variance(
+    initial_trait_variance: f64,
+    unit_generate_variance: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (initial_trait_variance, unit_generate_variance);
+    Err(PsychometricError::InitialTraitVarianceIsNotUnitTraitGenerateVariance)
+}
+
 /// Least-squares scalar log-rate for already-formed residual pairs.
 ///
 /// Pair-wise logs initialize Newton. This helper is crate-visible so overflow

crates/psychometric_core/src/lib.rs

@@ -379,6 +379,8 @@ pub use event_time::recover_initial_time_dependent_predictor_effect;
 pub use event_time::recover_initial_time_independent_predictor_carry;
 /// Exact scalar first-occasion `T0TIPREDEFFECT` shift `t0_b z`.
 pub use event_time::recover_initial_time_independent_predictor_effect;
+/// Exact scalar 2017-era `T0TRAITVAR` `t0_trait² · trait`.
+pub use event_time::recover_initial_trait_variance;
 /// Mean exact log-rate on already-centered irregular residuals.
 pub use event_time::recover_irregular_centered_residual_log_rate;
 /// Exact scalar §7.2 level-change `CINT` `κ = −a m x`.
@@ -572,6 +574,16 @@ pub use event_time::refuse_initial_time_independent_effect_as_time_dependent_imp
 pub use event_time::refuse_initial_time_independent_observed_mean_as_initial_time_dependent_observed_mean;
 /// Refuse treating 2017-era `addedT0TIPREDVAR` as p. 16 `TRAITVARstd`.
 pub use event_time::refuse_initial_time_independent_variance_as_standardised_trait_variance;
+/// Refuse treating 2017-era `T0TRAITVAR` as §7.2 `addedTIPREDVAR`.
+pub use event_time::refuse_initial_trait_variance_as_asymptotic_time_independent_variance;
+/// Refuse treating 2017-era `T0TRAITVAR` as free `T0VAR`.
+pub use event_time::refuse_initial_trait_variance_as_initial_latent_variance;
+/// Refuse treating 2017-era `T0TRAITVAR` as 2017-era `addedT0TIPREDVAR`.
+pub use event_time::refuse_initial_trait_variance_as_initial_time_independent_variance;
+/// Refuse treating 2017-era `T0TRAITVAR` as Table 2 `TRAITVAR`.
+pub use event_time::refuse_initial_trait_variance_as_trait_variance;
+/// Refuse treating 2017-era `T0TRAITVAR` as the ctGenerate unit extra.
+pub use event_time::refuse_initial_trait_variance_as_unit_trait_generate_variance;
 /// Refuse treating Driver Eq. 3–4 lagged latent covariance as `cov(y_t, y_{t-1})`.
 pub use event_time::refuse_latent_lagged_covariance_as_observed_covariance;
 /// Refuse treating Driver Eq. 5 latent mean as `E(y)`.