Restore Driver Table 2 T0TDPREDCOV as t0_m·v

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, Table 2, p. 12 `T0TDPREDCOV`; Table 3, p. 13 `T0TDPREDEFFECT`; 2017-era ctsem `ctModel.R` / `ctFit.R`; JSS PDF re-opened 2026-08-30T16:40Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar first-occasion time-dependent predictor covariance on current main (register items 110–111). Table 2 names `T0TDPREDCOV` the `n.latent × (Tpoints × n.TDpred)` covariance matrix between latents at `T0` and time-dependent predictors and defaults it to 0. The 2017-era `ctFit.R` places that matrix in the OpenMx `S` covariance block. Table 3 names `T0TDPREDEFFECT` the first-occasion TD *effect* (a regression). The SEM conversion is `T0TDPREDEFFECT = T0TDPREDCOV * solve(TDPREDVAR)`, so the scalar covariance is `t0_m · v` after finite `t0_m` and `v ≥ 0`. Form `t0_m` first, then multiply by `v`. A zero coefficient or zero predictor variance is exactly zero. A signed coefficient is a signed covariance. `t0_m` is `T0TDPREDEFFECT`, not this covariance; equal numbers when `v = 1` remain distinct named quantities. Analog extra `t0_m² v` is the analog of `addedT0TIPREDVAR`; Table 2 names `T0TDPREDCOV` the covariance, not that extra; equal numbers when `t0_m = 1` remain distinct named quantities. The 2017-era `summary.ctsemFit.R` comments out `TDPREDVAR` / `TDPREDVARstd` and does not form `T0TDPREDCOV` or `addedT0TDPREDVAR` in summary. This crate does not invent `TDPREDVARstd`. `t0_b · v` is the TI analog covariance and is not this map even when `t0_m = t0_b`. Process `m · v` is `TDPREDEFFECT × TDPREDVAR` and is not this first-occasion map even when `t0_m = m`. `v < 0` fails closed. `T0` is an event-time occasion, so a non-event clock fails closed. An overflowing product fails closed. Free first-occasion covariance does not require stable `a < 0`. 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.
+
 - `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 +710,31 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+
+    /// Driver Table 3 `T0TDPREDEFFECT` `t0_m` was treated as Table 2
+    /// `T0TDPREDCOV`. The coefficient is the first-occasion effect;
+    /// the covariance is `t0_m · v`. Equal numbers when `v = 1`
+    /// remain distinct named quantities.
+    InitialTimeDependentEffectIsNotInitialTimeDependentCovariance,
+    /// The analog extra first-occasion TD variance `t0_m² v` was
+    /// treated as Table 2 `T0TDPREDCOV`. That quadratic form is the
+    /// analog of `addedT0TIPREDVAR`; Table 2 names `T0TDPREDCOV` the
+    /// covariance, not that extra variance. Equal numbers when
+    /// `t0_m = 1` remain distinct named quantities. The 2017-era
+    /// source does not form `addedT0TDPREDVAR`.
+    InitialTimeDependentExtraVarianceIsNotInitialTimeDependentCovariance,
+    /// The first-occasion TI analog covariance `t0_b · v` was treated
+    /// as Table 2 `T0TDPREDCOV`. Table 3 names `T0TIPREDEFFECT` a
+    /// regression; Table 2 names `T0TDPREDCOV` the TD covariance.
+    /// Equal numbers when `t0_m = t0_b` remain distinct named
+    /// quantities.
+    InitialTimeIndependentCovarianceIsNotInitialTimeDependentCovariance,
+    /// Process `TDPREDEFFECT × TDPREDVAR` `m · v` was treated as
+    /// Table 2 `T0TDPREDCOV`. Table 2 / Table 3 name `TDPREDEFFECT`
+    /// `M` the process coefficient. `T0TDPREDCOV` is the first
+    /// occasion. Equal numbers when `t0_m = m` remain distinct
+    /// named quantities.
+    TimeDependentEffectCovarianceIsNotInitialTimeDependentCovariance,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1235,6 +1260,18 @@ impl fmt::Display for PsychometricError {
             Self::ObservedVarianceIsNotStandardisedManifestVariance => {
                 "observed-indicator variance is not standardised measurement-error variance"
             }
+            Self::InitialTimeDependentEffectIsNotInitialTimeDependentCovariance => {
+                "first-occasion time-dependent predictor effect is not the first-occasion time-dependent predictor covariance"
+            }
+            Self::InitialTimeDependentExtraVarianceIsNotInitialTimeDependentCovariance => {
+                "first-occasion time-dependent extra predictor variance is not the first-occasion time-dependent predictor covariance"
+            }
+            Self::InitialTimeIndependentCovarianceIsNotInitialTimeDependentCovariance => {
+                "first-occasion time-independent predictor covariance is not the first-occasion time-dependent predictor covariance"
+            }
+            Self::TimeDependentEffectCovarianceIsNotInitialTimeDependentCovariance => {
+                "time-dependent predictor effect covariance is not the first-occasion time-dependent predictor covariance"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2110,28 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn initial_time_dependent_covariance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::InitialTimeDependentEffectIsNotInitialTimeDependentCovariance
+                .to_string(),
+            "first-occasion time-dependent predictor effect is not the first-occasion time-dependent predictor covariance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTimeDependentExtraVarianceIsNotInitialTimeDependentCovariance
+                .to_string(),
+            "first-occasion time-dependent extra predictor variance is not the first-occasion time-dependent predictor covariance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTimeIndependentCovarianceIsNotInitialTimeDependentCovariance
+                .to_string(),
+            "first-occasion time-independent predictor covariance is not the first-occasion time-dependent predictor covariance"
+        );
+        assert_eq!(
+            PsychometricError::TimeDependentEffectCovarianceIsNotInitialTimeDependentCovariance
+                .to_string(),
+            "time-dependent predictor effect covariance is not the first-occasion time-dependent predictor covariance"
+        );
+    }
 }