feat(psychometric): recover Driver p.16 MANIFESTVARstd after positive Θ

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 `MANIFESTVAR`; Eq. 5, p. 5; p. 16 `MANIFESTVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T22:40Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised measurement-error variance. Table 2 names `MANIFESTVAR` `Θ` the residual covariance of the indicators. Equation 5 writes `ζ ~ N(0, Θ)`. Page 16 prints standardised matrices with the suffix `std` when appropriate. The 2017-era `summary.ctsemFit.R` forms `MANIFESTVARstd` whenever `verbose = TRUE`, as `solve(sqrt(diag(MANIFESTVAR) + ridging)) %&% MANIFESTVAR`. OpenMx `%&%` is the quadratic form `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 2017-era source assigns `dimnames(MANIFESTVARstd)` to `latentNames`; the matrix is `n.manifest × n.manifest`. That assignment is a source bug and is not this exact map. The scalar correlation is `θ / θ = 1` after strictly positive `MANIFESTVAR`. Form strictly positive `θ` first, then `1 / √θ`, then `(1 / √θ) θ (1 / √θ)`. Unstandardised `MANIFESTVAR` is defined for a zero residual; standardised `MANIFESTVAR` is not. Zero `θ` makes `solve(sqrt(0))` fail in the 2017-era source and fails closed here. Unlike `TRAITVAR` / `MANIFESTTRAITVAR`, that source does not skip forming `MANIFESTVARstd` when `θ = 0`. Measurement-error variance is an event-time structural quantity, so a non-event clock fails closed. `MANIFESTVAR` does not require stable `a < 0`. Distinct positive `θ` recover the same 1. `MANIFESTTRAITVARstd` `ψ / ψ = 1` recovers the same number and remains a distinct named quantity. Equation 5 `λ² Var(η) + θ` is `Var(y)`, 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 `MANIFESTTRAITVAR`; §7.1, p. 19; p. 16 `MANIFESTTRAITVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T22:28Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised manifest-trait variance. 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. 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 2017-era `summary.ctsemFit.R` forms `MANIFESTTRAITVARstd` only when `MANIFESTTRAITVAR != 0`, as `solve(sqrt(diag(MANIFESTTRAITVAR) + ridging)) %&% MANIFESTTRAITVAR` when `verbose = TRUE`. OpenMx `%&%` is the quadratic form `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. `TRAITVARstd` `trait / trait = 1` recovers the same number and remains a distinct named quantity. `MANIFESTVAR` `θ` is measurement error, 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 `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*).

crates/psychometric_core/src/error.rs

@@ -982,6 +982,26 @@ pub enum PsychometricError {
     /// `MANIFESTTRAITVARstd`. Measurement error is not the
     /// correlation form of indicator-level trait variance.
     MeasurementErrorIsNotStandardisedManifestTraitVariance,
+    /// Driver p. 16 `MANIFESTVARstd` was requested with a
+    /// non-positive measurement-error variance. The 2017-era
+    /// correlation form requires strictly positive `MANIFESTVAR`.
+    /// Zero `θ` makes `solve(sqrt(0))` fail in that source.
+    StandardisedManifestVarianceRequiresPositiveManifestVariance,
+    /// Driver Table 2 unstandardised `MANIFESTVAR` `Θ` was treated
+    /// as p. 16 `MANIFESTVARstd`. Unstandardised measurement error
+    /// is defined for a zero residual; standardised `MANIFESTVAR`
+    /// is not.
+    UnstandardisedManifestVarianceIsNotStandardisedManifestVariance,
+    /// Driver p. 16 `MANIFESTTRAITVARstd` was treated as p. 16
+    /// `MANIFESTVARstd`. Equal numbers when both correlations equal
+    /// 1 are still distinct named quantities. `MANIFESTTRAITVAR` is
+    /// indicator-level trait variance; `MANIFESTVAR` is
+    /// contemporaneous measurement error.
+    StandardisedManifestTraitVarianceIsNotStandardisedManifestVariance,
+    /// Driver Eq. 5 observed-indicator variance was treated as p. 16
+    /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
+    /// correlation form of `Θ`.
+    ObservedVarianceIsNotStandardisedManifestVariance,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1705,6 +1725,18 @@ impl fmt::Display for PsychometricError {
             Self::MeasurementErrorIsNotStandardisedManifestTraitVariance => {
                 "measurement error is not standardised manifest-trait variance"
             }
+            Self::StandardisedManifestVarianceRequiresPositiveManifestVariance => {
+                "standardised measurement-error variance requires strictly positive measurement-error variance"
+            }
+            Self::UnstandardisedManifestVarianceIsNotStandardisedManifestVariance => {
+                "unstandardised measurement-error variance is not standardised measurement-error variance"
+            }
+            Self::StandardisedManifestTraitVarianceIsNotStandardisedManifestVariance => {
+                "standardised manifest-trait variance is not standardised measurement-error variance"
+            }
+            Self::ObservedVarianceIsNotStandardisedManifestVariance => {
+                "observed-indicator variance is not standardised measurement-error variance"
+            }
         };
         formatter.write_str(message)
     }
@@ -2941,4 +2973,27 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn standardised_manifest_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedManifestVarianceRequiresPositiveManifestVariance
+                .to_string(),
+            "standardised measurement-error variance requires strictly positive measurement-error variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedManifestVarianceIsNotStandardisedManifestVariance
+                .to_string(),
+            "unstandardised measurement-error variance is not standardised measurement-error variance"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedManifestTraitVarianceIsNotStandardisedManifestVariance
+                .to_string(),
+            "standardised manifest-trait variance is not standardised measurement-error variance"
+        );
+        assert_eq!(
+            PsychometricError::ObservedVarianceIsNotStandardisedManifestVariance.to_string(),
+            "observed-indicator variance is not standardised measurement-error variance"
+        );
+    }
 }