feat(psychometric): restore Driver p.16 TDPREDVARstd v/v=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, Table 2, p. 12 `TDPREDVAR`; p. 16 `TDPREDVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-31T01:16Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised time-dependent predictor variance on current main (register items 106–107). Table 2 names `TDPREDVAR` the variance / covariance matrix of time dependent predictors and defaults it to 0. Page 16 prints standardised matrices with the suffix `std` when appropriate. The printed example on p. 16 is `discreteDRIFTstd`, not `TDPREDVARstd`. Footnote 4 standardises using only the relevant variance, not the total. The relevant variance for that named time-dependent predictor correlation is `TDPREDVAR` itself, not `TIPREDVAR` and not residual `MANIFESTVAR`. The 2017-era source forms `TDPREDVARstd` whenever `verbose = TRUE` and `n.TDpred > 0`, as `solve(sqrt(TDPREDVARdiag)) %&% TDPREDVAR` with `TDPREDVARdiag = diag((diag(TDPREDVAR))+diag(ridging,n.TDpred))`. OpenMx `%&%` is `t(A) %*% B %*% A`. Unlike `TRAITVARstd`, that formation adds `diag(ridging, n.TDpred)`. The default `ridging = FALSE` adds 0, not `0.0001`; that ridge is a numerical hack and is not this exact map. The 2017-era source assigns `dimnames(TDPREDVARstd)` to `TDpredNames`. The ridge length `n.TDpred` rather than `n.TDpred × Tpoints` is a source bug when the predictor matrix is stacked over occasions and is not this exact map. The scalar correlation is `v / v = 1` after strictly positive `TDPREDVAR`. Form strictly positive `v` first, then `1 / √v`, then `(1 / √v) v (1 / √v)`. Unstandardised `TDPREDVAR` is defined for a zero predictor; standardised `TDPREDVAR` is not. Zero `v` makes `solve(sqrt(0))` fail in the 2017-era source and fails closed here. Unlike `TRAITVAR` / `MANIFESTTRAITVAR`, that source does not skip forming `TDPREDVARstd` when `v = 0`. Time-dependent predictor variance is an event-time structural quantity, so a non-event clock fails closed. `TDPREDVAR` does not require stable `a < 0`. Distinct positive `v` recover the same 1. `v / v = 1` is `TIPREDVARstd` and recovers the same number and remains a distinct named quantity. `θ / θ = 1` is `MANIFESTVARstd` and recovers the same number and remains a distinct named quantity. Meredith (1993) remains unread as a cited source for this slice. 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 +710,31 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+
+    /// Driver p. 16 `TDPREDVARstd` was requested with a non-positive
+    /// time-dependent predictor variance. Unlike `TRAITVAR` /
+    /// `MANIFESTTRAITVAR`, the 2017-era source still forms
+    /// `TDPREDVARstd` when `TDPREDVAR == 0`; `solve(sqrt(0))`
+    /// fails. Footnote 4 standardisation requires strictly
+    /// positive `TDPREDVAR`.
+    StandardisedTimeDependentPredictorVarianceRequiresPositivePredictorVariance,
+    /// Driver Table 2 unstandardised `TDPREDVAR` was treated as
+    /// p. 16 `TDPREDVARstd`. Unstandardised time-dependent
+    /// predictor variance is defined for a zero predictor;
+    /// standardised `TDPREDVAR` is not.
+    UnstandardisedTimeDependentPredictorVarianceIsNotStandardisedTimeDependentPredictorVariance,
+    /// Driver p. 16 `TIPREDVARstd` was treated as p. 16
+    /// `TDPREDVARstd`. Equal numbers when both correlations equal
+    /// 1 are still distinct named quantities. `TIPREDVAR` is the
+    /// time-independent predictor covariance; `TDPREDVAR` is the
+    /// time-dependent predictor covariance.
+    StandardisedTimeIndependentPredictorVarianceIsNotStandardisedTimeDependentPredictorVariance,
+    /// Driver p. 16 `MANIFESTVARstd` was treated as p. 16
+    /// `TDPREDVARstd`. Equal numbers when both correlations equal
+    /// 1 are still distinct named quantities. `MANIFESTVAR` is
+    /// contemporaneous measurement error; `TDPREDVAR` is the
+    /// time-dependent predictor covariance.
+    StandardisedManifestVarianceIsNotStandardisedTimeDependentPredictorVariance,
 }
 
 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::StandardisedTimeDependentPredictorVarianceRequiresPositivePredictorVariance => {
+                "standardised time-dependent predictor variance requires strictly positive time-dependent predictor variance"
+            }
+            Self::UnstandardisedTimeDependentPredictorVarianceIsNotStandardisedTimeDependentPredictorVariance => {
+                "unstandardised time-dependent predictor variance is not standardised time-dependent predictor variance"
+            }
+            Self::StandardisedTimeIndependentPredictorVarianceIsNotStandardisedTimeDependentPredictorVariance => {
+                "standardised time-independent predictor variance is not standardised time-dependent predictor variance"
+            }
+            Self::StandardisedManifestVarianceIsNotStandardisedTimeDependentPredictorVariance => {
+                "standardised measurement-error variance is not standardised time-dependent predictor variance"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2110,28 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn standardised_time_dependent_predictor_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedTimeDependentPredictorVarianceRequiresPositivePredictorVariance
+                .to_string(),
+            "standardised time-dependent predictor variance requires strictly positive time-dependent predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedTimeDependentPredictorVarianceIsNotStandardisedTimeDependentPredictorVariance
+                .to_string(),
+            "unstandardised time-dependent predictor variance is not standardised time-dependent predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedTimeIndependentPredictorVarianceIsNotStandardisedTimeDependentPredictorVariance
+                .to_string(),
+            "standardised time-independent predictor variance is not standardised time-dependent predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedManifestVarianceIsNotStandardisedTimeDependentPredictorVariance
+                .to_string(),
+            "standardised measurement-error variance is not standardised time-dependent predictor variance"
+        );
+    }
 }

crates/psychometric_core/src/event_time.rs

@@ -41,7 +41,13 @@
 //! (`T0MEANS` is not `μ_t`; `CINT` is not that discrete increment). Equation 3's
 //! fourth summand is the contemporaneous Dirac impulse `M x` (Table 2
 //! `TDPREDEFFECT` is `M`, not `CINT`, not `TIPREDEFFECT`, and not
-//! Voelkle et al., 2012, Eq. 14). Equations 1–2 plus the Eq. 3
+//! Voelkle et al., 2012, Eq. 14). Table 2 names `TDPREDVAR` the
+//! variance / covariance of those time-dependent predictors.
+//! Page 16 `TDPREDVARstd` is `v / v = 1` after strictly positive
+//! `TDPREDVAR` (footnote 4; 2017-era `summary.ctsemFit.R`; JSS PDF
+//! re-opened 2026-08-31T01:16Z). Unstandardised `TDPREDVAR` is not
+//! that correlation. `TIPREDVARstd` and `MANIFESTVARstd` recover
+//! the same 1 and remain distinct named quantities. Equations 1–2 plus the Eq. 3
 //! exponential map a time-dependent impulse that occurred strictly
 //! inside `(t0, t)` as `e^{A(t−u)} M x` (`t0 < u < t`). That carry
 //! is not the contemporaneous Dirac, not `CINT`, not `TIPREDEFFECT`,
@@ -1630,6 +1636,156 @@ pub fn refuse_observed_variance_as_standardised_manifest_variance(
     Err(PsychometricError::ObservedVarianceIsNotStandardisedManifestVariance)
 }
 
+/// Exact scalar p. 16 `TDPREDVARstd` after strictly positive
+/// `TDPREDVAR`.
+///
+/// Driver, Oud, and Voelkle (2017, Table 2, p. 12; p. 16; footnote
+/// 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened
+/// 2026-08-31T01:16Z from
+/// <https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104>)
+/// name `TDPREDVAR` the variance / covariance matrix of time
+/// dependent predictors and default it to 0. Page 16 prints
+/// standardised matrices with the suffix `std` when appropriate.
+/// The printed example on p. 16 is `discreteDRIFTstd`, not
+/// `TDPREDVARstd`. Footnote 4: standardisations use only the
+/// relevant variance, not the total. The relevant variance for
+/// that named time-dependent predictor correlation is `TDPREDVAR`
+/// itself, not `TIPREDVAR` and not residual `MANIFESTVAR`. The
+/// 2017-era `summary.ctsemFit.R` forms `TDPREDVARstd` whenever
+/// `verbose = TRUE` and `n.TDpred > 0`, as
+/// `solve(sqrt(TDPREDVARdiag)) %&% TDPREDVAR` with
+/// `TDPREDVARdiag = diag((diag(TDPREDVAR))+diag(ridging,n.TDpred))`.
+/// `OpenMx` `%&%` is the quadratic form `t(A) %*% B %*% A`. Unlike
+/// `TRAITVARstd`, that formation adds `diag(ridging, n.TDpred)`.
+/// The default `ridging = FALSE` adds 0, not `0.0001`; that ridge
+/// is a numerical hack and is not this exact map. The 2017-era
+/// source assigns `dimnames(TDPREDVARstd)` to `TDpredNames`. The
+/// ridge length `n.TDpred` rather than `n.TDpred × Tpoints` is a
+/// source bug when the predictor matrix is stacked over occasions
+/// and is not this exact map. The scalar correlation is
+/// `v / v = 1` after strictly positive `TDPREDVAR`. Form strictly
+/// positive `v` first, then `1 / √v`, then `(1 / √v) v (1 / √v)`.
+/// Unstandardised `TDPREDVAR` is defined for a zero predictor;
+/// standardised `TDPREDVAR` is not. Zero `v` makes
+/// `solve(sqrt(0))` fail in the 2017-era source and fails closed
+/// here. Unlike `TRAITVAR` / `MANIFESTTRAITVAR`, that source does
+/// not skip forming `TDPREDVARstd` when `v = 0`; the quadratic
+/// still fails. Time-dependent predictor variance is an event-time
+/// structural quantity, so a non-event clock fails closed.
+/// `TDPREDVAR` does not require stable `a < 0`. Distinct positive
+/// `v` recover the same 1. `TIPREDVARstd` `v / v = 1` recovers the
+/// same number and remains a distinct named quantity. This crate
+/// does not currently export `TIPREDVARstd`; the refuse still
+/// names that quantity. `MANIFESTVARstd` `θ / θ = 1` recovers the
+/// same number and remains a distinct named quantity. 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,
+/// [`PsychometricError::StandardisedTimeDependentPredictorVarianceRequiresPositivePredictorVariance`]
+/// when `TDPREDVAR` is zero, and
+/// [`PsychometricError::InvalidNumericInput`] when the variance is
+/// non-finite, negative, or the quadratic form overflows.
+pub fn recover_standardised_time_dependent_predictor_variance(
+    time_dependent_predictor_variance: f64,
+    clock: LagClock,
+) -> Result<f64, PsychometricError> {
+    if !clock.admits_structural_lag() {
+        return Err(PsychometricError::EventTimeRequired);
+    }
+    if !time_dependent_predictor_variance.is_finite() || time_dependent_predictor_variance < 0.0 {
+        return Err(PsychometricError::InvalidNumericInput);
+    }
+    if time_dependent_predictor_variance == 0.0 {
+        return Err(
+            PsychometricError::StandardisedTimeDependentPredictorVarianceRequiresPositivePredictorVariance,
+        );
+    }
+    let process_sd = time_dependent_predictor_variance.sqrt();
+    let inverse_sd = require_finite(1.0 / process_sd)?;
+    let scaled = require_finite(inverse_sd * time_dependent_predictor_variance)?;
+    require_finite(scaled * inverse_sd)
+}
+
+/// Refuse treating unstandardised `TDPREDVAR` as p. 16
+/// `TDPREDVARstd`.
+///
+/// Unstandardised `TDPREDVAR` is defined for a zero predictor.
+/// Footnote 4 `TDPREDVARstd` requires strictly positive
+/// `TDPREDVAR`. Equal numbers when `v = 1` are still distinct
+/// named quantities.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::UnstandardisedTimeDependentPredictorVarianceIsNotStandardisedTimeDependentPredictorVariance`].
+pub fn refuse_unstandardised_time_dependent_predictor_variance_as_standardised_time_dependent_predictor_variance(
+    unstandardised_time_dependent_predictor_variance: f64,
+    standardised_time_dependent_predictor_variance: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (
+        unstandardised_time_dependent_predictor_variance,
+        standardised_time_dependent_predictor_variance,
+    );
+    Err(
+        PsychometricError::UnstandardisedTimeDependentPredictorVarianceIsNotStandardisedTimeDependentPredictorVariance,
+    )
+}
+
+/// Refuse treating p. 16 `TIPREDVARstd` as p. 16 `TDPREDVARstd`.
+///
+/// Both scalar correlations equal 1 after strictly positive
+/// variances. `TIPREDVARstd` standardises time-independent
+/// predictor variance. `TDPREDVARstd` standardises time-dependent
+/// predictor variance. Equal numbers remain distinct named
+/// quantities. This crate does not currently export
+/// `TIPREDVARstd`; the refuse still names that quantity.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::StandardisedTimeIndependentPredictorVarianceIsNotStandardisedTimeDependentPredictorVariance`].
+pub fn refuse_standardised_time_independent_predictor_variance_as_standardised_time_dependent_predictor_variance(
+    standardised_time_independent_predictor_variance: f64,
+    standardised_time_dependent_predictor_variance: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (
+        standardised_time_independent_predictor_variance,
+        standardised_time_dependent_predictor_variance,
+    );
+    Err(
+        PsychometricError::StandardisedTimeIndependentPredictorVarianceIsNotStandardisedTimeDependentPredictorVariance,
+    )
+}
+
+/// Refuse treating p. 16 `MANIFESTVARstd` as p. 16 `TDPREDVARstd`.
+///
+/// Both scalar correlations equal 1 after strictly positive
+/// variances. `MANIFESTVARstd` standardises contemporaneous
+/// measurement error `Θ`. `TDPREDVARstd` standardises
+/// time-dependent predictor variance. Equal numbers remain
+/// distinct named quantities.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::StandardisedManifestVarianceIsNotStandardisedTimeDependentPredictorVariance`].
+pub fn refuse_standardised_manifest_variance_as_standardised_time_dependent_predictor_variance(
+    standardised_manifest_variance: f64,
+    standardised_time_dependent_predictor_variance: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (
+        standardised_manifest_variance,
+        standardised_time_dependent_predictor_variance,
+    );
+    Err(
+        PsychometricError::StandardisedManifestVarianceIsNotStandardisedTimeDependentPredictorVariance,
+    )
+}
+
 /// Refuse treating `τ / √(λ² Var(η) + θ)` as p. 16
 /// `MANIFESTMEANSstd`.
 ///