feat(psychometric): recover Driver Table 3 T0TIPREDEFFECTstd after positive T0VAR

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 3, p. 13 `T0TIPREDEFFECTstd`; p. 16; footnote 4; Eq. 3, p. 5; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T17:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised first-occasion time-independent predictor effect. Table 3 names `T0TIPREDEFFECT` the effect of time-independent predictors on latents at `T0`. Page 16 prints standardised matrices with the suffix `std` when appropriate. Footnote 4: standardisations use only the relevant variance, not the total. The affecting variance is predictor variance `TIPREDVAR` `v`. The affected variance is free first-occasion `T0VAR` `p_0`, not within-subject `asymDIFFUSION` `-q / (2 a)`, because Table 3 is the first occasion, not the process dynamics. Form strictly positive `p_0` first, then strictly positive `v`, then `t0_b · √v / √p_0`. Unstandardised `t0_b` is defined for a zero coefficient and for zero predictor variance; standardised `T0TIPREDEFFECT` is not. Zero `p_0` or zero `v` 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`. The continuous standardisation `B · √v / √(-q / (2 a))` uses `asymDIFFUSION` and is not this first-occasion map. The asymptotic standardisation `(-B / a) · √v / √p` is the total change, not this first-occasion coefficient. Section 7.1 warns that omitting trait variance confounds between- and within-person information. `t0_b · √v / √(trait + p_0 + added)` uses the total, not free `T0VAR`, and is not `T0TIPREDEFFECTstd` 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 2026-08-23T17:20Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T17:20Z: `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 +786,35 @@ pub enum PsychometricError {
     /// `TIPREDEFFECTstd`. Footnote 4 uses only `asymDIFFUSION`,
     /// not `TRAITVAR`.
     TraitContaminatedContinuousTimeIndependentEffectIsNotStandardisedContinuousTimeIndependentEffect,
+    /// Driver Table 3 / p. 16 `T0TIPREDEFFECTstd` was requested with
+    /// a non-positive free first-occasion variance. Footnote 4
+    /// standardises the affected first-occasion latent using only
+    /// strictly positive free `T0VAR`.
+    StandardisedInitialTimeIndependentEffectRequiresPositiveInitialLatentVariance,
+    /// Driver Table 3 / p. 16 `T0TIPREDEFFECTstd` was requested with
+    /// a non-positive predictor variance. Footnote 4 standardises the
+    /// affecting predictor using only strictly positive `TIPREDVAR`.
+    StandardisedInitialTimeIndependentEffectRequiresPositivePredictorVariance,
+    /// Driver Table 3 unstandardised `T0TIPREDEFFECT` `t0_b` was
+    /// treated as p. 16 `T0TIPREDEFFECTstd`. Unstandardised `t0_b`
+    /// is defined for a zero coefficient or zero predictor variance;
+    /// standardised `T0TIPREDEFFECT` is not.
+    UnstandardisedInitialTimeIndependentEffectIsNotStandardisedInitialTimeIndependentEffect,
+    /// Driver p. 16 `TIPREDEFFECTstd`
+    /// `B · √v / √(-q / (2 a))` was treated as Table 3 / p. 16
+    /// `T0TIPREDEFFECTstd`. The continuous map uses `asymDIFFUSION`;
+    /// the first-occasion map uses free `T0VAR`.
+    StandardisedContinuousTimeIndependentEffectIsNotStandardisedInitialTimeIndependentEffect,
+    /// Driver p. 16 `asymTIPREDEFFECTstd`
+    /// `(-B / a) · √v / √(-q / (2 a))` was treated as Table 3 /
+    /// p. 16 `T0TIPREDEFFECTstd`. The asymptotic map is the total
+    /// change, not the first-occasion coefficient.
+    StandardisedAsymptoticTimeIndependentEffectIsNotStandardisedInitialTimeIndependentEffect,
+    /// Driver §7.1 trait-contaminated first-occasion TI effect
+    /// `t0_b · √v / √(trait + p_0 + added)` was treated as Table 3 /
+    /// p. 16 `T0TIPREDEFFECTstd`. Footnote 4 uses only free `T0VAR`,
+    /// not `TRAITVAR`.
+    TraitContaminatedInitialTimeIndependentEffectIsNotStandardisedInitialTimeIndependentEffect,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1383,6 +1412,24 @@ impl fmt::Display for PsychometricError {
             Self::TraitContaminatedContinuousTimeIndependentEffectIsNotStandardisedContinuousTimeIndependentEffect => {
                 "trait-contaminated continuous time-independent predictor effect is not standardised continuous time-independent predictor effect"
             }
+            Self::StandardisedInitialTimeIndependentEffectRequiresPositiveInitialLatentVariance => {
+                "standardised initial time-independent predictor effect requires strictly positive initial latent variance"
+            }
+            Self::StandardisedInitialTimeIndependentEffectRequiresPositivePredictorVariance => {
+                "standardised initial time-independent predictor effect requires strictly positive predictor variance"
+            }
+            Self::UnstandardisedInitialTimeIndependentEffectIsNotStandardisedInitialTimeIndependentEffect => {
+                "unstandardised initial time-independent predictor effect is not standardised initial time-independent predictor effect"
+            }
+            Self::StandardisedContinuousTimeIndependentEffectIsNotStandardisedInitialTimeIndependentEffect => {
+                "standardised continuous time-independent predictor effect is not standardised initial time-independent predictor effect"
+            }
+            Self::StandardisedAsymptoticTimeIndependentEffectIsNotStandardisedInitialTimeIndependentEffect => {
+                "standardised asymptotic time-independent predictor effect is not standardised initial time-independent predictor effect"
+            }
+            Self::TraitContaminatedInitialTimeIndependentEffectIsNotStandardisedInitialTimeIndependentEffect => {
+                "trait-contaminated initial time-independent predictor effect is not standardised initial time-independent predictor effect"
+            }
         };
         formatter.write_str(message)
     }
@@ -2377,4 +2424,38 @@ mod tests {
             "trait-contaminated continuous time-independent predictor effect is not standardised continuous time-independent predictor effect"
         );
     }
+
+    #[test]
+    fn standardised_initial_time_independent_effect_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedInitialTimeIndependentEffectRequiresPositiveInitialLatentVariance
+                .to_string(),
+            "standardised initial time-independent predictor effect requires strictly positive initial latent variance"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedInitialTimeIndependentEffectRequiresPositivePredictorVariance
+                .to_string(),
+            "standardised initial time-independent predictor effect requires strictly positive predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedInitialTimeIndependentEffectIsNotStandardisedInitialTimeIndependentEffect
+                .to_string(),
+            "unstandardised initial time-independent predictor effect is not standardised initial time-independent predictor effect"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedContinuousTimeIndependentEffectIsNotStandardisedInitialTimeIndependentEffect
+                .to_string(),
+            "standardised continuous time-independent predictor effect is not standardised initial time-independent predictor effect"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedAsymptoticTimeIndependentEffectIsNotStandardisedInitialTimeIndependentEffect
+                .to_string(),
+            "standardised asymptotic time-independent predictor effect is not standardised initial time-independent predictor effect"
+        );
+        assert_eq!(
+            PsychometricError::TraitContaminatedInitialTimeIndependentEffectIsNotStandardisedInitialTimeIndependentEffect
+                .to_string(),
+            "trait-contaminated initial time-independent predictor effect is not standardised initial time-independent predictor effect"
+        );
+    }
 }