feat(psychometric): recover Driver p.16 TRAITVARstd after positive TRAITVAR

CHANGELOG.md

@@ -4,6 +4,7 @@ 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; p. 16 `TRAITVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T22:21Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised trait variance. 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 2017-era `summary.ctsemFit.R` forms `TRAITVARstd` only when `TRAITVAR != 0`, as `solve(sqrt(diag(TRAITVAR))) %&% TRAITVAR` when `verbose = TRUE`. OpenMx `%&%` is the quadratic form `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. `T0VARstd` `p_0 / p_0 = 1` recovers the same number and remains a distinct named quantity. `addedT0TIPREDVAR` `t0_b² v` is extra first-occasion TI variance, not this correlation. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T22:21Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T22:21Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*).
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 2, p. 12 `T0VAR`; p. 16 `T0VARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T22:06Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised first-occasion latent variance. Table 2 names `T0VAR` the latent process initial variance/covariance. Page 16 prints standardised matrices with the suffix `std` when appropriate. The 2017-era `summary.ctsemFit.R` forms `T0VARstd` as `solve(sqrt(diag(T0VAR))) %&% T0VAR` when `verbose = TRUE`. OpenMx `%&%` is the quadratic form `t(A) %*% B %*% A`. 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 `p_0 / p_0 = 1` after strictly positive free `T0VAR`. Form strictly positive `p_0` first, then `1 / √p_0`, then `(1 / √p_0) p_0 (1 / √p_0)`. Unstandardised `T0VAR` is defined for a zero first-occasion variance; standardised `T0VAR` is not. Zero `p_0` has no positive SD and fails closed. `T0` is an event-time occasion, so a non-event clock fails closed. Free `T0VAR` does not require stable `a < 0`. Distinct positive `p_0` recover the same 1. `T0TDPREDEFFECTstd` `t0_m · √v / √p_0` depends on `p_0` and is not this correlation. `addedT0TIPREDVAR` `t0_b² v` is extra TI variance, not this correlation. `TRAITVAR` is not the standardisation variance. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T22:06Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T22:06Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*).
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 3, p. 13 `T0TDPREDEFFECTstd`; Table 2, p. 12; p. 16; footnote 4; Eq. 3, p. 5; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T21:34Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised first-occasion time-dependent predictor effect. Table 3 names `T0TDPREDEFFECT` the effect of time-dependent predictors on latents at `T0`. Table 2 names `M` `TDPREDEFFECT` and names `T0TDPREDCOV` the first-occasion covariance, not this coefficient. Page 16 prints standardised matrices with the suffix `std` when appropriate. Footnote 4: standardisations use only the relevant variance, not the total. The affecting variance is time-dependent predictor variance `v`, not `TIPREDVAR`. The affected variance is free first-occasion `T0VAR` `p_0`, not within-subject `asymDIFFUSION` `-q / (2 a)`, because Table 3 is the first occasion, not the process dynamics. Form strictly positive `p_0` first, then strictly positive `v`, then `t0_m · √v / √p_0`. Unstandardised `t0_m` is defined for a zero coefficient and for zero predictor variance; standardised `T0TDPREDEFFECT` is not. Zero `p_0` or zero `v` has no positive SD and fails closed. `T0` is an event-time occasion, so a non-event clock fails closed. Free `T0VAR` does not require stable `a < 0`. The continuous standardisation `m · √v / √(-q / (2 a))` uses `asymDIFFUSION` and is not this first-occasion map. `T0TIPREDEFFECTstd` `t0_b · √v / √p_0` is a different named matrix even when `t0_m = t0_b` and the predictor variances match. Section 7.1 warns that omitting trait variance confounds between- and within-person information. `t0_m · √v / √(trait + p_0 + added)` uses the total, not free `T0VAR`, and is not `T0TDPREDEFFECTstd` when `TRAITVAR` is nonzero. `TRAITVAR` is not the standardisation variance. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T21:34Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T21:34Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*).
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, p. 16 `TDPREDEFFECTstd`; Table 2, p. 12; Eq. 3, p. 5; footnote 4; §7.1, pp. 18–19; JSS PDF re-opened 2026-08-23T21:10Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised continuous time-dependent predictor effect. Page 16 prints continuous-time parameters and, when appropriate, standardised matrices with the suffix `std`. Table 2 names `M` `TDPREDEFFECT`. Footnote 4: standardisations use only the relevant variance, not the total. The affecting variance is time-dependent predictor variance `v`. The affected variance is within-subject `asymDIFFUSION` `-q / (2 a)`, because the process dynamics are individual, or average individual, temporal dynamics. Form strictly positive `asymDIFFUSION` first, then strictly positive `v`, then `m · √v / √(-q / (2 a))`. Unstandardised `M` is defined for a zero coefficient and for zero predictor variance; standardised `TDPREDEFFECT` is not. Zero `asymDIFFUSION` or zero `v` has no positive SD and fails closed. `TIPREDEFFECTstd` `B · √v / √p` is a different named matrix even when `M = B` and the predictor variances match. The finite-interval intercept-style standardisation `A^{-1}[e^{A Δt} − I] M · √v / √p` depends on the event interval and is not this continuous Dirac coefficient. Section 7.1 warns that omitting trait variance confounds between- and within-person information. `m · √v / √(trait + p + added)` uses the total, not `asymDIFFUSION`, and is not `TDPREDEFFECTstd` when `TRAITVAR` is nonzero. `TRAITVAR` is not the standardisation variance. Predecessor `event_time.rs` asymptotic-std `process_sd == 0` / `predictor_sd == 0` gates after already-checked `within == 0` and `v == 0` were unreachable; this slice drops them so stacked line/branch coverage can close. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T21:10Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T21:10Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*).

crates/psychometric_core/src/error.rs

@@ -945,6 +945,23 @@ pub enum PsychometricError {
     /// p. 16 `T0VARstd`. Extra TI variance is not the correlation
     /// form of free `T0VAR`.
     InitialTimeIndependentVarianceIsNotStandardisedInitialLatentVariance,
+    /// Driver p. 16 `TRAITVARstd` was requested with a non-positive
+    /// trait variance. The 2017-era correlation form requires
+    /// strictly positive `TRAITVAR` and is not formed when
+    /// `TRAITVAR` is zero.
+    StandardisedTraitVarianceRequiresPositiveTraitVariance,
+    /// Driver Table 2 unstandardised `TRAITVAR` was treated as
+    /// p. 16 `TRAITVARstd`. Unstandardised trait variance is
+    /// defined for a zero trait; standardised `TRAITVAR` is not.
+    UnstandardisedTraitVarianceIsNotStandardisedTraitVariance,
+    /// Driver p. 16 `T0VARstd` was treated as p. 16 `TRAITVARstd`.
+    /// Equal numbers when both correlations equal 1 are still
+    /// distinct named quantities.
+    StandardisedInitialLatentVarianceIsNotStandardisedTraitVariance,
+    /// Driver 2017-era `addedT0TIPREDVAR` `t0_b² v` was treated as
+    /// p. 16 `TRAITVARstd`. Extra first-occasion TI variance is not
+    /// the correlation form of between-subject `TRAITVAR`.
+    InitialTimeIndependentVarianceIsNotStandardisedTraitVariance,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1644,6 +1661,18 @@ impl fmt::Display for PsychometricError {
             Self::InitialTimeIndependentVarianceIsNotStandardisedInitialLatentVariance => {
                 "initial time-independent predictor variance is not standardised initial latent variance"
             }
+            Self::StandardisedTraitVarianceRequiresPositiveTraitVariance => {
+                "standardised trait variance requires strictly positive trait variance"
+            }
+            Self::UnstandardisedTraitVarianceIsNotStandardisedTraitVariance => {
+                "unstandardised trait variance is not standardised trait variance"
+            }
+            Self::StandardisedInitialLatentVarianceIsNotStandardisedTraitVariance => {
+                "standardised initial latent variance is not standardised trait variance"
+            }
+            Self::InitialTimeIndependentVarianceIsNotStandardisedTraitVariance => {
+                "initial time-independent predictor variance is not standardised trait variance"
+            }
         };
         formatter.write_str(message)
     }
@@ -2834,4 +2863,27 @@ mod tests {
             "initial time-independent predictor variance is not standardised initial latent variance"
         );
     }
+
+    #[test]
+    fn standardised_trait_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedTraitVarianceRequiresPositiveTraitVariance.to_string(),
+            "standardised trait variance requires strictly positive trait variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedTraitVarianceIsNotStandardisedTraitVariance
+                .to_string(),
+            "unstandardised trait variance is not standardised trait variance"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedInitialLatentVarianceIsNotStandardisedTraitVariance
+                .to_string(),
+            "standardised initial latent variance is not standardised trait variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTimeIndependentVarianceIsNotStandardisedTraitVariance
+                .to_string(),
+            "initial time-independent predictor variance is not standardised trait variance"
+        );
+    }
 }