feat(psychometric): restore Driver p.16 T0VARstd p_0/p_0=1 on main

CHANGELOG.md

@@ -36,6 +36,7 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 
 ## [Unreleased]
 
+- `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, p. 16 `T0VARstd`; Table 2, p. 12; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-26T07:17Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised initial latent variance on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 79–80). Page 16 prints standardised matrices with the suffix `std` when appropriate. The printed example on p. 16 is `discreteDRIFTstd`, not `T0VARstd`. Footnote 4 standardises using only the relevant variance, not the total. Table 2 names `T0VAR` the latent process initial variance/covariance. The first-occasion relevant variance is free `T0VAR` `p_0`, not process-dynamics `asymDIFFUSION` `-q / (2 a)`. The 2017-era source forms `T0VARstd` as `solve(sqrt(diag(T0VAR))) %&% T0VAR` when `verbose = TRUE`. OpenMx `%&%` is `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 `p_0`. Form strictly positive `p_0` first, then `1 / √p_0`, then `(1 / √p_0) p_0 (1 / √p_0)`. A zero first-occasion variance 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. `μ_0 / √p_0` is `T0MEANSstd` and recovers the same number when `μ_0 = √p_0` and remains a distinct named quantity. `p / p = 1` is `asymDIFFUSIONstd` and recovers the same number and remains a distinct named quantity. Meredith (1993) remains unread (Unpaywall 2026-08-26T07:17Z: `is_oa: false`; OpenAlex closed; Springer `content/pdf` is a 3038-byte 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.
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, p. 16 `asymCINTstd`; Eq. 3, p. 4; Table 2, p. 12; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-26T00:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised asymptotic continuous intercept on current main after consolidation dropped the pre-consolidation `(-κ / a) / √p` slice. Page 16 prints standardised matrices with the suffix `std` when appropriate, and asymptotic values as `Δt → ∞`. Footnote 4 standardises using only the relevant variance, not the total. Table 2 names `κ` `CINT`. The relevant variance for that process intercept is within-subject `asymDIFFUSION` `p = −q / (2 a)`. The 2017-era source forms unstandardised `asymCINT` whenever `verbose = TRUE` as `-solve(DRIFT) %*% CINT` and does not form an `asymCINTstd` matrix. Form strictly positive `p` first, then the asymptotic intercept, then divide by `√p`. A zero intercept is exactly zero after that positive SD. Zero `q` has no positive process SD and fails closed. Lasting `p` requires stable `a < 0`. A non-event clock fails closed. `κ / √p` is `CINTstd` and is not this total-change map. `A^{-1}[e^{A Δt} − I] κ / √p` is `discreteCINTstd` and depends on the event interval. Meredith (1993) remains unread (Unpaywall 2026-08-25T18:22Z: `is_oa: false`; Springer `content/pdf` is a 3038-byte HTML stub). Mislevy (1991) remains unread on the same terms. 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, p. 16 `T0MEANSstd`; Table 2, p. 12; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-26T04:09Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised initial latent mean on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map. Page 16 prints standardised matrices with the suffix `std` when appropriate. Footnote 4 standardises using only the relevant variance, not the total. Table 2 names `T0MEANS` the `n.latent × 1` matrix of latent process means at the first time point `T0` and names `T0VAR` the latent process initial variance/covariance. The first-occasion relevant variance is free `T0VAR` `p_0`, not process-dynamics `asymDIFFUSION` `-q / (2 a)`. The 2017-era source forms unstandardised `T0MEANS` and does not form a `T0MEANSstd` matrix; the scalar map is `μ_0 / √p_0` after strictly positive `p_0`. A zero mean is exactly zero. Zero `p_0` has no positive SD and fails closed. `T0` is an event-time occasion, so a non-event clock fails closed. Free `T0MEANS` does not require stable `a < 0`. `p_0 / p_0 = 1` recovers the same number when `μ_0 = √p_0` and remains a distinct named quantity. `μ_0 / √asymDIFFUSION` uses process-dynamics variance and is not this first-occasion map. Meredith (1993) remains unread (Unpaywall 2026-08-26T00:22Z: `is_oa: false`; OpenAlex closed; Springer `content/pdf` is a 3038-byte HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms. 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, p. 16 `MANIFESTMEANSstd`; Table 2, p. 12; footnote 4; Eq. 5, p. 5; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-25T11:32Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised manifest mean on current main after `0ce16e8` restored the pre-consolidation unstandardised slice. Page 16 prints standardised matrices with the suffix `std` when appropriate. Footnote 4 standardises using only the relevant variance, not the total. Table 2 names `MANIFESTMEANS` `τ` the `n.manifest × 1` matrix of manifest means and `MANIFESTVAR` `Θ` the residual covariance of the indicators. The relevant variance for that named measurement intercept is residual `θ`, not total observed `Var(y) = λ² Var(η) + θ`. The 2017-era source forms unstandardised `MANIFESTMEANS` and does not form a `MANIFESTMEANSstd` matrix; the scalar map is `τ / √θ` after strictly positive `θ`. A zero mean is exactly zero. Zero `θ` has no positive SD and fails closed. A non-event clock fails closed. `MANIFESTMEANS` does not require stable `a < 0`. `θ / θ = 1` recovers the same number when `τ = √θ` and remains a distinct named quantity. `τ / √(λ² Var(η) + θ)` uses total observed variance and is not this residual map. Meredith (1993) remains unread (Unpaywall 2026-08-25T11:32Z: `is_oa: false`, 0 locations; OpenAlex closed; Springer `content/pdf` is a 3038-byte HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-25T11:32Z: `is_oa: false`, 0 locations). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.

crates/psychometric_core/src/error.rs

@@ -564,6 +564,27 @@ pub enum PsychometricError {
     /// mean using free `T0VAR`, not process-dynamics
     /// `asymDIFFUSION`.
     WithinSubjectScaledInitialLatentMeanIsNotStandardisedInitialLatentMean,
+    /// Driver p. 16 `T0VARstd` was requested with a non-positive
+    /// first-occasion variance. Footnote 4 standardisation of the
+    /// 2017-era `T0VAR` matrix requires strictly positive free
+    /// `T0VAR`.
+    StandardisedInitialLatentVarianceRequiresPositiveInitialLatentVariance,
+    /// Driver Table 2 unstandardised `T0VAR` `p_0` was treated as
+    /// p. 16 `T0VARstd`. Unstandardised `p_0` is defined for a zero
+    /// first-occasion variance; standardised `T0VAR` is not.
+    UnstandardisedInitialLatentVarianceIsNotStandardisedInitialLatentVariance,
+    /// Driver p. 16 `T0MEANSstd` was treated as p. 16 `T0VARstd`.
+    /// Equal numbers when `μ_0 = √p_0` are still distinct named
+    /// quantities. `T0VARstd` is the correlation form of free
+    /// `T0VAR`; `T0MEANSstd` is the first-occasion mean.
+    StandardisedInitialLatentMeanIsNotStandardisedInitialLatentVariance,
+    /// Driver p. 16 `asymDIFFUSIONstd` was treated as p. 16
+    /// `T0VARstd`. Equal numbers of 1 after a strictly positive
+    /// relevant variance are still distinct named quantities.
+    /// `T0VARstd` is the correlation form of free `T0VAR`;
+    /// `asymDIFFUSIONstd` is the correlation form of process-
+    /// dynamics `asymDIFFUSION`.
+    StandardisedAsymptoticDiffusionIsNotStandardisedInitialLatentVariance,
     /// Driver p. 16 `discreteCINTstd` was requested without a strictly
     /// positive `asymDIFFUSION`. Footnote 4 standardises using only the
     /// relevant variance; zero `q` has no positive process SD.
@@ -1030,6 +1051,18 @@ impl fmt::Display for PsychometricError {
             Self::WithinSubjectScaledInitialLatentMeanIsNotStandardisedInitialLatentMean => {
                 "within-subject scaled initial latent mean is not standardised initial latent mean"
             }
+            Self::StandardisedInitialLatentVarianceRequiresPositiveInitialLatentVariance => {
+                "standardised initial latent variance requires strictly positive initial latent variance"
+            }
+            Self::UnstandardisedInitialLatentVarianceIsNotStandardisedInitialLatentVariance => {
+                "unstandardised initial latent variance is not standardised initial latent variance"
+            }
+            Self::StandardisedInitialLatentMeanIsNotStandardisedInitialLatentVariance => {
+                "standardised initial latent mean is not standardised initial latent variance"
+            }
+            Self::StandardisedAsymptoticDiffusionIsNotStandardisedInitialLatentVariance => {
+                "standardised asymptotic diffusion is not standardised initial latent variance"
+            }
             Self::StandardisedDiscreteContinuousInterceptRequiresPositiveStationaryVariance => {
                 "standardised discrete continuous intercept requires strictly positive stationary within-subject variance"
             }
@@ -1745,6 +1778,30 @@ mod tests {
         );
     }
 
+    #[test]
+    fn standardised_initial_latent_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedInitialLatentVarianceRequiresPositiveInitialLatentVariance
+                .to_string(),
+            "standardised initial latent variance requires strictly positive initial latent variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedInitialLatentVarianceIsNotStandardisedInitialLatentVariance
+                .to_string(),
+            "unstandardised initial latent variance is not standardised initial latent variance"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedInitialLatentMeanIsNotStandardisedInitialLatentVariance
+                .to_string(),
+            "standardised initial latent mean is not standardised initial latent variance"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedAsymptoticDiffusionIsNotStandardisedInitialLatentVariance
+                .to_string(),
+            "standardised asymptotic diffusion is not standardised initial latent variance"
+        );
+    }
+
     #[test]
     fn standardised_discrete_continuous_intercept_boundary_messages_are_stable() {
         assert_eq!(