feat(psychometric): recover Driver p.16 asymDIFFUSIONstd after positive asymDIFFUSION

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, p. 16 `asymDIFFUSIONstd`; footnote 4; Eq. 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T23:02Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised asymptotic within-subject variance. Page 16 names `asymDIFFUSION` the total within-subject variance as `Δt → ∞` and prints standardised matrices with the suffix `std` when appropriate. Footnote 4 standardises using only the relevant variance, not the total. The 2017-era `summary.ctsemFit.R` forms `asymDIFFUSIONstd` whenever `verbose = TRUE`, as `solve(sqrt(diag(asymDIFFUSION) + ridging)) %&% asymDIFFUSION`. OpenMx `%&%` is the quadratic form `t(A) %*% B %*% A`. That formation adds `diag(c(ridging), n.latent)`. 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(asymDIFFUSIONstd)` to `latentNames`; that assignment matches the `n.latent × n.latent` matrix and is this map. The scalar correlation is `p / p = 1` after strictly positive Lyapunov `p = −q / (2 a)`. Form strictly positive `p` first, then `1 / √p`, then `(1 / √p) p (1 / √p)`. Unstandardised `asymDIFFUSION` is defined for a zero process; standardised `asymDIFFUSION` is not. Zero `q` makes `solve(sqrt(0))` fail in the 2017-era source and fails closed here. That source does not skip forming `asymDIFFUSIONstd` when `p = 0`. Within-subject variance is an event-time structural quantity, so a non-event clock fails closed. Lasting `asymDIFFUSION` requires stable `a < 0`. Distinct positive `p` recover the same 1. `TIPREDVARstd` `v / v = 1` recovers the same number and remains a distinct named quantity. `DIFFUSIONstd` `q / p = −2 a` is the continuous-diffusion ratio, 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 2026-08-24T08:02Z: `is_oa: false`, 0 locations; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-24T08:02Z: `is_oa: false`, 0 locations; title *Randomization-Based Inference about Latent Variables from Complex Samples*).
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 2, p. 12 `TIPREDVAR`; p. 16 `TIPREDVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T22:53Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised time-independent predictor variance. Table 2 names `TIPREDVAR` the variance/covariance of time-independent predictors. Page 16 prints standardised matrices with the suffix `std` when appropriate. The 2017-era `summary.ctsemFit.R` forms `TIPREDVARstd` whenever `verbose = TRUE` and `n.TIpred > 0`, as `solve(sqrt(diag(TIPREDVAR) + ridging)) %&% TIPREDVAR`. OpenMx `%&%` is the quadratic form `t(A) %*% B %*% A`. Unlike `TRAITVARstd`, that formation adds `diag(c(ridging), n.TIpred)`. 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(TIPREDVARstd)` to `TIpredNames`; that assignment matches the `n.TIpred × n.TIpred` matrix and is this map. The scalar correlation is `v / v = 1` after strictly positive `TIPREDVAR`. Form strictly positive `v` first, then `1 / √v`, then `(1 / √v) v (1 / √v)`. Unstandardised `TIPREDVAR` is defined for a zero predictor; standardised `TIPREDVAR` 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 `TIPREDVARstd` when `v = 0`. Predictor variance is an event-time structural quantity, so a non-event clock fails closed. `TIPREDVAR` does not require stable `a < 0`. Distinct positive `v` recover the same 1. `MANIFESTVARstd` `θ / θ = 1` recovers the same number and remains a distinct named quantity. Section 7.2 `addedTIPREDVAR` `(B / a)² v` is extra process 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 `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*).

crates/psychometric_core/src/error.rs

@@ -1021,6 +1021,27 @@ pub enum PsychometricError {
     /// `TIPREDVARstd`. `(B / a)² v` is extra process variance, not
     /// the correlation form of the predictor covariance.
     AsymptoticTimeIndependentPredictorVarianceIsNotStandardisedTimeIndependentPredictorVariance,
+    /// Driver p. 16 `asymDIFFUSIONstd` was requested with a
+    /// non-positive within-subject variance. The 2017-era
+    /// correlation form requires strictly positive `asymDIFFUSION`.
+    /// Zero `q` makes `solve(sqrt(0))` fail in that source.
+    StandardisedAsymptoticDiffusionRequiresPositiveWithinSubjectVariance,
+    /// Driver p. 16 unstandardised `asymDIFFUSION` `p` was treated
+    /// as `asymDIFFUSIONstd`. Unstandardised within-subject variance
+    /// is defined for a zero process; standardised `asymDIFFUSION`
+    /// is not.
+    UnstandardisedAsymptoticDiffusionIsNotStandardisedAsymptoticDiffusion,
+    /// Driver p. 16 `TIPREDVARstd` was treated as p. 16
+    /// `asymDIFFUSIONstd`. Equal numbers when both correlations
+    /// equal 1 are still distinct named quantities. `TIPREDVAR` is
+    /// predictor covariance; `asymDIFFUSION` is within-subject
+    /// process variance.
+    StandardisedTimeIndependentPredictorVarianceIsNotStandardisedAsymptoticDiffusion,
+    /// Driver p. 16 `DIFFUSIONstd` `q / p = −2 a` was treated as
+    /// `asymDIFFUSIONstd`. Footnote 4 `DIFFUSIONstd` is the
+    /// continuous-diffusion ratio, not the correlation of
+    /// `asymDIFFUSION`.
+    StandardisedContinuousDiffusionIsNotStandardisedAsymptoticDiffusion,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1768,6 +1789,18 @@ impl fmt::Display for PsychometricError {
             Self::AsymptoticTimeIndependentPredictorVarianceIsNotStandardisedTimeIndependentPredictorVariance => {
                 "asymptotic time-independent predictor variance is not standardised time-independent predictor variance"
             }
+            Self::StandardisedAsymptoticDiffusionRequiresPositiveWithinSubjectVariance => {
+                "standardised asymptotic DIFFUSION requires strictly positive within-subject variance"
+            }
+            Self::UnstandardisedAsymptoticDiffusionIsNotStandardisedAsymptoticDiffusion => {
+                "unstandardised asymptotic DIFFUSION is not standardised asymptotic DIFFUSION"
+            }
+            Self::StandardisedTimeIndependentPredictorVarianceIsNotStandardisedAsymptoticDiffusion => {
+                "standardised time-independent predictor variance is not standardised asymptotic DIFFUSION"
+            }
+            Self::StandardisedContinuousDiffusionIsNotStandardisedAsymptoticDiffusion => {
+                "standardised continuous DIFFUSION is not standardised asymptotic DIFFUSION"
+            }
         };
         formatter.write_str(message)
     }
@@ -3051,4 +3084,28 @@ mod tests {
             "asymptotic time-independent predictor variance is not standardised time-independent predictor variance"
         );
     }
+
+    #[test]
+    fn standardised_asymptotic_diffusion_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedAsymptoticDiffusionRequiresPositiveWithinSubjectVariance
+                .to_string(),
+            "standardised asymptotic DIFFUSION requires strictly positive within-subject variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedAsymptoticDiffusionIsNotStandardisedAsymptoticDiffusion
+                .to_string(),
+            "unstandardised asymptotic DIFFUSION is not standardised asymptotic DIFFUSION"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedTimeIndependentPredictorVarianceIsNotStandardisedAsymptoticDiffusion
+                .to_string(),
+            "standardised time-independent predictor variance is not standardised asymptotic DIFFUSION"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedContinuousDiffusionIsNotStandardisedAsymptoticDiffusion
+                .to_string(),
+            "standardised continuous DIFFUSION is not standardised asymptotic DIFFUSION"
+        );
+    }
 }