feat(psychometric): recover Driver p.16 CINTstd 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 `CINTstd`; Eq. 1, p. 4; Table 2, p. 12; footnote 4; §7.1, pp. 18–19; JSS PDF re-opened 2026-08-23T17:10Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised continuous intercept. Page 16 prints continuous-time parameters and, when appropriate, standardised matrices with the suffix `std`. Table 2 names `κ` `CINT`. Footnote 4: standardisations use 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` `-q / (2 a)`. Form strictly positive `asymDIFFUSION` first, then `κ / √(-q / (2 a))`. Unstandardised `κ` is defined for growing `a ≥ 0` and for zero diffusion; standardised `CINT` is not. Zero `asymDIFFUSION` has no positive SD and fails closed. The asymptotic standardisation `(-κ / a) / √p` is the total change, not this continuous intercept. The finite-interval standardisation `A^{-1}[e^{A Δt} − I] κ / √p` depends on the event interval and is not this continuous map. Section 7.1 warns that omitting trait variance confounds between- and within-person information. `κ / √(trait + p + added)` uses the total, not `asymDIFFUSION`, and is not `CINTstd` when `TRAITVAR` is nonzero. `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 2026-08-23T13:19Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T13:19Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*).
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, p. 16 `TIPREDEFFECTstd`; §7.2, pp. 20–21; Eq. 3, p. 5; Table 2, p. 12; footnote 4; JSS PDF re-opened 2026-08-23T16:21Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised continuous time-independent predictor effect. Page 16 prints continuous-time parameters and, when appropriate, standardised matrices with the suffix `std`. Table 2 names `B` `TIPREDEFFECT`. Footnote 4: standardisations use only the relevant variance, not the total. The affecting variance is predictor variance `TIPREDVAR` `v`. The affected variance is within-subject `asymDIFFUSION` `-q / (2 a)`, because the process dynamics are individual, or average individual, temporal dynamics. Form strictly positive `asymDIFFUSION` first, then strictly positive `v`, then `B · √v / √(-q / (2 a))`. Unstandardised `B` is defined for a zero coefficient and for zero predictor variance; standardised `TIPREDEFFECT` is not. Zero `asymDIFFUSION` or zero `v` has no positive SD and fails closed. The asymptotic standardisation `(-B / a) · √v / √p` is the total change, not this continuous coefficient. The finite-interval standardisation `A^{-1}[e^{A Δt} − I] B · √v / √p` depends on the event interval and is not this continuous map. Section 7.1 warns that omitting trait variance confounds between- and within-person information. `B · √v / √(trait + p + added)` uses the total, not `asymDIFFUSION`, and is not `TIPREDEFFECTstd` when `TRAITVAR` is nonzero. `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 2026-08-23T13:19Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T13:19Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*).
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, p. 16 `asymTIPREDEFFECTstd`; §7.2, pp. 20–21; Eq. 3, p. 5; Table 2, p. 12; footnote 4; JSS PDF re-opened 2026-08-23T14:25Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised asymptotic time-independent predictor effect. Page 16 prints continuous-time parameters and, when appropriate, standardised matrices with the suffix `std`. Section 7.2 names `asymTIPREDEFFECT` the expected total change in process means given a unit increase on a time-independent predictor. The scalar map is `-B / a` for stable `a < 0`. Footnote 4: standardisations use only the relevant variance, not the total. The affecting variance is predictor variance `TIPREDVAR` `v`. The affected variance is within-subject `asymDIFFUSION` `-q / (2 a)`, because the process dynamics are individual, or average individual, temporal dynamics. Form strictly positive `asymDIFFUSION` first, then strictly positive `v`, then the unit asymptotic effect, then `(-B / a) · √v / √(-q / (2 a))`. Unstandardised `-B / a` is defined for a zero coefficient and for zero predictor variance; standardised `asymTIPREDEFFECT` is not. Zero `asymDIFFUSION` or zero `v` has no positive SD and fails closed. The finite-interval standardisation `A^{-1}[e^{A Δt} − I] B · √v / √p` depends on the event interval and is not this `Δt → ∞` map. Section 7.1 warns that omitting trait variance confounds between- and within-person information. `(-B / a) · √v / √(trait + p + added)` uses the total, not `asymDIFFUSION`, and is not `asymTIPREDEFFECTstd` when `TRAITVAR` is nonzero. `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 2026-08-23T13:19Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T13:19Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*).
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, p. 16 `DRIFTstd`; Eq. 1, p. 4; footnote 4; §7.1, pp. 18–19; JSS PDF re-opened 2026-08-23T13:28Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised continuous `DRIFT`. Page 16 prints continuous-time parameters (e.g., `DRIFT`) and, when appropriate, standardised matrices with the suffix `std`. Footnote 4: standardisations use only the relevant variance, not the total. For `DRIFT` that relevant variance is within-subject `asymDIFFUSION` `-q / (2 a)`, because `DRIFT` is intended to represent individual, or average individual, temporal dynamics. Form strictly positive `asymDIFFUSION` first. In the scalar stationary case the within-subject SD ratio is 1, so the standardised auto-effect equals the unstandardised log-rate numerically; those remain distinct named quantities. Unstandardised `a` is defined for growing `a ≥ 0` and for zero diffusion; standardised `DRIFT` is not. Zero `asymDIFFUSION` has no positive SD and fails closed. The discrete standardisation `e^{a Δt}` depends on the event interval and is not the continuous map. Section 7.1 warns that omitting trait variance confounds between- and within-person information. `a p / (trait + p + added)` uses the total, not `asymDIFFUSION`, and is not `DRIFTstd` when `TRAITVAR` is nonzero. `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 2026-08-23T13:19Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T13:19Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*).

crates/psychometric_core/src/error.rs

@@ -786,6 +786,27 @@ pub enum PsychometricError {
     /// `TIPREDEFFECTstd`. Footnote 4 uses only `asymDIFFUSION`,
     /// not `TRAITVAR`.
     TraitContaminatedContinuousTimeIndependentEffectIsNotStandardisedContinuousTimeIndependentEffect,
+    /// Driver p. 16 `CINTstd` was requested with a non-positive
+    /// within-subject variance. Footnote 4 standardises the process
+    /// intercept using only strictly positive `asymDIFFUSION`.
+    StandardisedContinuousInterceptRequiresPositiveWithinSubjectVariance,
+    /// Driver Table 2 unstandardised `CINT` `κ` was treated as p. 16
+    /// `CINTstd`. Unstandardised `κ` is defined for growing or
+    /// zero-diffusion processes; standardised `CINT` is not.
+    UnstandardisedContinuousInterceptIsNotStandardisedContinuousIntercept,
+    /// Driver Table 2 `asymCINTstd` `(-κ / a) / √(-q / (2 a))` was
+    /// treated as p. 16 `CINTstd`. The asymptotic map is the total
+    /// change, not the continuous intercept.
+    StandardisedAsymptoticContinuousInterceptIsNotStandardisedContinuousIntercept,
+    /// Driver finite-interval standardised `CINT`
+    /// `A^{-1}[e^{A Δt} − I] κ / √p` was treated as p. 16 `CINTstd`.
+    /// The discrete increment depends on the event interval; the
+    /// continuous intercept does not.
+    StandardisedDiscreteContinuousInterceptIsNotStandardisedContinuousIntercept,
+    /// Driver §7.1 trait-contaminated continuous intercept
+    /// `κ / √(trait + p + added)` was treated as p. 16 `CINTstd`.
+    /// Footnote 4 uses only `asymDIFFUSION`, not `TRAITVAR`.
+    TraitContaminatedContinuousInterceptIsNotStandardisedContinuousIntercept,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1383,6 +1404,21 @@ impl fmt::Display for PsychometricError {
             Self::TraitContaminatedContinuousTimeIndependentEffectIsNotStandardisedContinuousTimeIndependentEffect => {
                 "trait-contaminated continuous time-independent predictor effect is not standardised continuous time-independent predictor effect"
             }
+            Self::StandardisedContinuousInterceptRequiresPositiveWithinSubjectVariance => {
+                "standardised continuous intercept requires strictly positive within-subject variance"
+            }
+            Self::UnstandardisedContinuousInterceptIsNotStandardisedContinuousIntercept => {
+                "unstandardised continuous intercept is not standardised continuous intercept"
+            }
+            Self::StandardisedAsymptoticContinuousInterceptIsNotStandardisedContinuousIntercept => {
+                "standardised asymptotic continuous intercept is not standardised continuous intercept"
+            }
+            Self::StandardisedDiscreteContinuousInterceptIsNotStandardisedContinuousIntercept => {
+                "standardised discrete continuous intercept is not standardised continuous intercept"
+            }
+            Self::TraitContaminatedContinuousInterceptIsNotStandardisedContinuousIntercept => {
+                "trait-contaminated continuous intercept is not standardised continuous intercept"
+            }
         };
         formatter.write_str(message)
     }
@@ -2377,4 +2413,33 @@ mod tests {
             "trait-contaminated continuous time-independent predictor effect is not standardised continuous time-independent predictor effect"
         );
     }
+
+    #[test]
+    fn standardised_continuous_intercept_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedContinuousInterceptRequiresPositiveWithinSubjectVariance
+                .to_string(),
+            "standardised continuous intercept requires strictly positive within-subject variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedContinuousInterceptIsNotStandardisedContinuousIntercept
+                .to_string(),
+            "unstandardised continuous intercept is not standardised continuous intercept"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedAsymptoticContinuousInterceptIsNotStandardisedContinuousIntercept
+                .to_string(),
+            "standardised asymptotic continuous intercept is not standardised continuous intercept"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedDiscreteContinuousInterceptIsNotStandardisedContinuousIntercept
+                .to_string(),
+            "standardised discrete continuous intercept is not standardised continuous intercept"
+        );
+        assert_eq!(
+            PsychometricError::TraitContaminatedContinuousInterceptIsNotStandardisedContinuousIntercept
+                .to_string(),
+            "trait-contaminated continuous intercept is not standardised continuous intercept"
+        );
+    }
 }