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

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 `discreteCINTstd`; Eq. 3, p. 4; footnote 4; Table 2, p. 12; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-24T05:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised discrete continuous intercept. Page 16 prints discrete-time transformations for a chosen event interval and, when appropriate, standardised matrices with the suffix `std`. Footnote 4 standardises using only the relevant variance, not the total. `CINT` is the process intercept of individual, or average individual, dynamics, so that relevant variance is within-subject `asymDIFFUSION` `p = −q / (2 a)`. The 2017-era `summary.ctsemFit.R` forms `discreteCINT` whenever `verbose = TRUE`, as `solve(DRIFT) %*% (discreteDRIFT − I) %*% CINT`. That source does not form a `discreteCINTstd` matrix; the scalar map here is the footnote 4 standardisation of that named discrete intercept: `A^{-1}[e^{A Δt} − I] κ / √p`. Form strictly positive `p` first, then the discrete intercept, then divide by `√p`. A zero intercept is exactly zero. Unstandardised `discreteCINT` is defined for growing `a ≥ 0` and for zero diffusion; standardised `discreteCINT` 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. `κ / √p` does not depend on `Δt` and is not this finite-interval map. `(-κ / a) / √p` is the standardised asymptotic intercept and is not this map. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, not `CINTstd`, 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, 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*).

crates/psychometric_core/src/error.rs

@@ -1042,6 +1042,25 @@ pub enum PsychometricError {
     /// continuous-diffusion ratio, not the correlation of
     /// `asymDIFFUSION`.
     StandardisedContinuousDiffusionIsNotStandardisedAsymptoticDiffusion,
+    /// Driver p. 16 `discreteCINTstd` was requested with a
+    /// non-positive within-subject variance. Footnote 4
+    /// standardisation of the 2017-era `discreteCINT` vector
+    /// requires strictly positive `asymDIFFUSION`.
+    StandardisedDiscreteContinuousInterceptRequiresPositiveWithinSubjectVariance,
+    /// Driver Eq. 3 unstandardised `discreteCINT`
+    /// `A^{-1}[e^{A Δt} − I] κ` was treated as `discreteCINTstd`.
+    /// Unstandardised discrete intercept is defined for growing
+    /// `a ≥ 0` and for zero diffusion; standardised `discreteCINT`
+    /// is not.
+    UnstandardisedDiscreteContinuousInterceptIsNotStandardisedDiscreteContinuousIntercept,
+    /// Driver p. 16 `CINTstd` analog `κ / √p` was treated as
+    /// `discreteCINTstd`. The continuous intercept standardisation
+    /// does not depend on the event interval.
+    StandardisedContinuousInterceptIsNotStandardisedDiscreteContinuousIntercept,
+    /// Driver Table 2 `asymCINT` `/ √p` was treated as
+    /// `discreteCINTstd`. `(-κ / a) / √p` is the standardised
+    /// total intercept change, not the finite-interval map.
+    AsymptoticStandardisedContinuousInterceptIsNotStandardisedDiscreteContinuousIntercept,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1801,6 +1820,18 @@ impl fmt::Display for PsychometricError {
             Self::StandardisedContinuousDiffusionIsNotStandardisedAsymptoticDiffusion => {
                 "standardised continuous DIFFUSION is not standardised asymptotic DIFFUSION"
             }
+            Self::StandardisedDiscreteContinuousInterceptRequiresPositiveWithinSubjectVariance => {
+                "standardised discrete continuous intercept requires strictly positive within-subject variance"
+            }
+            Self::UnstandardisedDiscreteContinuousInterceptIsNotStandardisedDiscreteContinuousIntercept => {
+                "unstandardised discrete continuous intercept is not standardised discrete continuous intercept"
+            }
+            Self::StandardisedContinuousInterceptIsNotStandardisedDiscreteContinuousIntercept => {
+                "standardised continuous intercept is not standardised discrete continuous intercept"
+            }
+            Self::AsymptoticStandardisedContinuousInterceptIsNotStandardisedDiscreteContinuousIntercept => {
+                "asymptotic standardised continuous intercept is not standardised discrete continuous intercept"
+            }
         };
         formatter.write_str(message)
     }
@@ -3108,4 +3139,28 @@ mod tests {
             "standardised continuous DIFFUSION is not standardised asymptotic DIFFUSION"
         );
     }
+
+    #[test]
+    fn standardised_discrete_continuous_intercept_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedDiscreteContinuousInterceptRequiresPositiveWithinSubjectVariance
+                .to_string(),
+            "standardised discrete continuous intercept requires strictly positive within-subject variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedDiscreteContinuousInterceptIsNotStandardisedDiscreteContinuousIntercept
+                .to_string(),
+            "unstandardised discrete continuous intercept is not standardised discrete continuous intercept"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedContinuousInterceptIsNotStandardisedDiscreteContinuousIntercept
+                .to_string(),
+            "standardised continuous intercept is not standardised discrete continuous intercept"
+        );
+        assert_eq!(
+            PsychometricError::AsymptoticStandardisedContinuousInterceptIsNotStandardisedDiscreteContinuousIntercept
+                .to_string(),
+            "asymptotic standardised continuous intercept is not standardised discrete continuous intercept"
+        );
+    }
 }