feat(psychometric): restore Driver p.16 discreteDIFFUSIONstd Q_Δt/p on main

CHANGELOG.md

@@ -37,6 +37,7 @@ 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 `discreteDIFFUSIONstd`; Eq. 3–4, pp. 4–5; footnote 4; §7.1, pp. 18–19; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-28T13:24Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised discrete process noise on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 57–58). Page 16 prints discrete-time transformations for a chosen event interval (`discreteDRIFT`, `discreteDIFFUSION`) and, when appropriate, standardised matrices with the suffix `std`. The printed example on p. 16 is `discreteDRIFTstd`, not `discreteDIFFUSIONstd`. Footnote 4 standardises using only the relevant variance, not the total. Process noise is within-subject stochastic input, so that relevant variance is within-subject `asymDIFFUSION` `p = −q / (2 a)`, the same footnote 4 variance used for `DRIFT`. The 2017-era source forms unstandardised `discreteDIFFUSION` whenever `verbose = TRUE`, as `matrix(solve(DRIFTHATCH) %*% (expm(DRIFTHATCH Δt) − I ⊗ I) %*% rvectorize(DIFFUSION), nrow = n.latent)`. That source forms `asymDIFFUSIONstd` and `discreteDRIFTstd` in the same `verbose` block and does not form a `discreteDIFFUSIONstd` matrix. Form strictly positive `p` first, then `Q_Δt` from Equation 4, then `Q_Δt / p`. In the scalar stationary case that ratio equals `1 − exp(2 a Δt)` and does not depend on `q` once `q > 0`. Unstandardised `Q_Δt` is defined for growing `a ≥ 0` and for zero diffusion; standardised discrete `DIFFUSION` is not. Zero `q` has no positive process SD and fails closed. Lasting `asymDIFFUSION` requires stable `a < 0`. A non-event clock fails closed. A non-positive event interval fails closed. `q / p = −2 a` is `DIFFUSIONstd` and does not depend on `Δt`. `Q_Δt / (trait + p + added)` uses the total, not `asymDIFFUSION`, and is not this map when `TRAITVAR` is nonzero. `TRAITVAR` is not the standardisation variance. Meredith (1993) remains unread (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.
 - `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.
 
 - `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 2026-08-26T17:45Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised trait variance on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 81–82). 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 printed example on p. 16 is `discreteDRIFTstd`, not `TRAITVARstd`. Footnote 4 standardises using only the relevant variance, not the total. The relevant variance for that named between-subject correlation is `TRAITVAR`, not free first-occasion `T0VAR` and not process-dynamics `asymDIFFUSION`. The 2017-era source forms `TRAITVARstd` only when `TRAITVAR != 0`, as `solve(sqrt(diag(TRAITVAR))) %&% TRAITVAR` when `verbose = TRUE`. OpenMx `%&%` is `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. `p_0 / p_0 = 1` is `T0VARstd` and recovers the same number and remains a distinct named quantity. `t0_b² v` is `addedT0TIPREDVAR` and is extra first-occasion TI variance, not this correlation. Meredith (1993) remains unread (Unpaywall 2026-08-26T17:20Z: `is_oa: false`; OpenAlex closed; Springer `content/pdf` is an 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.

crates/psychometric_core/src/error.rs

@@ -710,6 +710,25 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+    /// Driver p. 16 `discreteDIFFUSIONstd` was requested with a
+    /// non-positive within-subject variance. Footnote 4
+    /// standardises `DIFFUSION` using only strictly positive
+    /// `asymDIFFUSION`.
+    StandardisedDiscreteDiffusionRequiresPositiveWithinSubjectVariance,
+    /// Driver p. 16 unstandardised `discreteDIFFUSION` `Q_Δt` was
+    /// treated as `discreteDIFFUSIONstd`. Unstandardised `Q_Δt` is
+    /// defined for growing or zero-diffusion processes;
+    /// standardised discrete `DIFFUSION` is not.
+    UnstandardisedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion,
+    /// Driver p. 16 `DIFFUSIONstd` `q / p = −2 a` was treated as
+    /// `discreteDIFFUSIONstd`. The continuous-diffusion ratio does
+    /// not depend on `Δt`.
+    StandardisedContinuousDiffusionIsNotStandardisedDiscreteDiffusion,
+    /// Driver §7.1 trait-contaminated process-noise ratio
+    /// `Q_Δt / (trait + p + added)` was treated as p. 16
+    /// `discreteDIFFUSIONstd`. Footnote 4 uses only
+    /// `asymDIFFUSION`.
+    TraitContaminatedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1235,6 +1254,18 @@ impl fmt::Display for PsychometricError {
             Self::ObservedVarianceIsNotStandardisedManifestVariance => {
                 "observed-indicator variance is not standardised measurement-error variance"
             }
+            Self::StandardisedDiscreteDiffusionRequiresPositiveWithinSubjectVariance => {
+                "standardised discrete DIFFUSION requires strictly positive within-subject variance"
+            }
+            Self::UnstandardisedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion => {
+                "unstandardised discrete DIFFUSION is not standardised discrete DIFFUSION"
+            }
+            Self::StandardisedContinuousDiffusionIsNotStandardisedDiscreteDiffusion => {
+                "standardised continuous DIFFUSION is not standardised discrete DIFFUSION"
+            }
+            Self::TraitContaminatedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion => {
+                "trait-contaminated discrete DIFFUSION is not standardised discrete DIFFUSION"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2104,28 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn standardised_discrete_diffusion_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedDiscreteDiffusionRequiresPositiveWithinSubjectVariance
+                .to_string(),
+            "standardised discrete DIFFUSION requires strictly positive within-subject variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion
+                .to_string(),
+            "unstandardised discrete DIFFUSION is not standardised discrete DIFFUSION"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedContinuousDiffusionIsNotStandardisedDiscreteDiffusion
+                .to_string(),
+            "standardised continuous DIFFUSION is not standardised discrete DIFFUSION"
+        );
+        assert_eq!(
+            PsychometricError::TraitContaminatedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion
+                .to_string(),
+            "trait-contaminated discrete DIFFUSION is not standardised discrete DIFFUSION"
+        );
+    }
 }