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

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 `TDPREDEFFECTstd`; Table 2, p. 12; Eq. 3, p. 5; footnote 4; §7.1, pp. 18–19; JSS PDF re-opened 2026-08-23T21:10Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised continuous time-dependent predictor effect. Page 16 prints continuous-time parameters and, when appropriate, standardised matrices with the suffix `std`. Table 2 names `M` `TDPREDEFFECT`. Footnote 4: standardisations use only the relevant variance, not the total. The affecting variance is time-dependent predictor variance `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 `m · √v / √(-q / (2 a))`. Unstandardised `M` is defined for a zero coefficient and for zero predictor variance; standardised `TDPREDEFFECT` is not. Zero `asymDIFFUSION` or zero `v` has no positive SD and fails closed. `TIPREDEFFECTstd` `B · √v / √p` is a different named matrix even when `M = B` and the predictor variances match. The finite-interval intercept-style standardisation `A^{-1}[e^{A Δt} − I] M · √v / √p` depends on the event interval and is not this continuous Dirac coefficient. Section 7.1 warns that omitting trait variance confounds between- and within-person information. `m · √v / √(trait + p + added)` uses the total, not `asymDIFFUSION`, and is not `TDPREDEFFECTstd` when `TRAITVAR` is nonzero. `TRAITVAR` is not the standardisation variance. Predecessor `event_time.rs` asymptotic-std `process_sd == 0` / `predictor_sd == 0` gates after already-checked `within == 0` and `v == 0` were unreachable; this slice drops them so stacked line/branch coverage can close. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T21:10Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T21:10Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*).
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Eq. 5, p. 5; Table 2, p. 12; §7.2, pp. 20–21; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T19:23Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar extra observed-indicator time-independent predictor variance of §7.2 `addedTIPREDVAR`. Equation 5 writes `y_i(t) = Γ + Λ η_i(t) + ζ_i(t)` with `ζ ~ N(0, Θ)` and `Γ ~ N(τ, Ψ)`. The 2017-era `summary.ctsemFit.R` forms the latent extra `addedTIPREDVAR` as `asymTIPREDEFFECT %*% TIPREDVAR %*% t(asymTIPREDEFFECT)`. The scalar latent extra is `(B / a)² v`. Equation 5 of that extra, with `θ = 0` and `ψ = 0`, is `λ² (B / a)² v`. Form `addedTIPREDVAR` first, then `(λ extra) λ`. Do not form `λ²` first. A zero loading or zero extra is exactly zero. `v < 0` fails closed. A non-event clock fails closed. `a ≥ 0` cannot hold a finite process-mean change when the extra is nonzero and fails closed. `(B / a)² v` is the latent extra, not this observed extra. `λ² t0_b² v` is Eq. 5 of `addedT0TIPREDVAR`, not this asymptotic observed extra. `λ² p + θ` is stationary observed variance, not this extra. `MANIFESTVAR` `θ` is measurement error, not this extra. `Ψ` is intercept variance and is not extra TI. The printed 2-latent `addedTIPREDVAR` 2.838 is not this scalar map. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T19:10Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T19:10Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*).
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Eq. 5, p. 5; Table 3, p. 13 `T0TIPREDEFFECT`; Table 2, p. 12; p. 16; §7.2, pp. 20–21; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T19:10Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar extra observed-indicator time-independent predictor variance of 2017-era `addedT0TIPREDVAR`. Equation 5 writes `y_i(t) = Γ + Λ η_i(t) + ζ_i(t)` with `ζ ~ N(0, Θ)` and `Γ ~ N(τ, Ψ)`. The 2017-era `summary.ctsemFit.R` forms the latent extra `addedT0TIPREDVAR` as `T0TIPREDEFFECT %*% TIPREDVAR %*% t(T0TIPREDEFFECT)` immediately after `T0TIPREDEFFECTstd`. The scalar latent extra is `t0_b² v`. Equation 5 of that extra, with `θ = 0` and `ψ = 0`, is `λ² t0_b² v`. Form `addedT0TIPREDVAR` first, then `(λ extra) λ`. Do not form `λ²` first. A zero loading or zero extra is exactly zero. `v < 0` fails closed. `T0` is an event-time occasion, so a non-event clock fails closed. Free `T0TIPREDEFFECT` does not require stable `a < 0`. `t0_b² v` is the latent extra, not this observed extra. `λ² p_0 + θ` is first-occasion observed variance, not this extra. `λ² (B / a)² v` is Eq. 5 of `addedTIPREDVAR`, not this first-occasion observed extra. `MANIFESTVAR` `θ` is measurement error, not this extra. `Ψ` is intercept variance and is not extra TI. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T19:10Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T19:10Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*).
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 3, p. 13 `T0TIPREDEFFECT`; p. 16; §7.2, pp. 20–21; Eq. 3, p. 5; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T18:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar first-occasion extra time-independent predictor variance `addedT0TIPREDVAR`. Table 3 names `T0TIPREDEFFECT` the effect of time-independent predictors on latents at `T0`. Page 16 prints extra summary matrices when `verbose = TRUE`. The 2017-era `summary.ctsemFit.R` forms `addedT0TIPREDVAR` as `T0TIPREDEFFECT %*% TIPREDVAR %*% t(T0TIPREDEFFECT)` immediately after `T0TIPREDEFFECTstd`. Section 7.2 names `addedTIPREDVAR` the stable between-subject variance accounted for by time-independent predictors at the process asymptote, `(B / a)² v`. The first-occasion analogue uses free `T0TIPREDEFFECT`, not `-B / a`. The scalar map is `t0_b² v`. Form `t0_b` first, then square, then multiply by `v`. A zero coefficient or zero predictor variance is exactly zero. `v < 0` fails closed. `T0` is an event-time occasion, so a non-event clock fails closed. Free `T0TIPREDEFFECT` does not require stable `a < 0`. `(B / a)² v` is `addedTIPREDVAR` and is not this first-occasion map. `t0_b · √v / √p_0` is `T0TIPREDEFFECTstd` and is not this variance. Free `T0VAR` `p_0` is the first-occasion state, not the extra TI variance. `TRAITVAR` is a zero-drift latent process, not `t0_b² v`. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T18:20Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T18:20Z: `is_oa: false`; title *Randomization-Based Inference about Latent Variables from Complex Samples*).

crates/psychometric_core/src/error.rs

@@ -865,6 +865,38 @@ pub enum PsychometricError {
     /// treated as `MANIFESTVAR` `θ`. Measurement error is not extra
     /// observed TI variance.
     AsymptoticTimeIndependentObservedVarianceIsNotMeasurementError,
+    /// Driver p. 16 `TDPREDEFFECTstd` was requested with a
+    /// non-positive within-subject variance. Footnote 4 standardises
+    /// the affected process using only strictly positive
+    /// `asymDIFFUSION`.
+    StandardisedContinuousTimeDependentEffectRequiresPositiveWithinSubjectVariance,
+    /// Driver p. 16 `TDPREDEFFECTstd` was requested with a
+    /// non-positive predictor variance. Footnote 4 standardises the
+    /// affecting predictor using only strictly positive TD predictor
+    /// variance.
+    StandardisedContinuousTimeDependentEffectRequiresPositivePredictorVariance,
+    /// Driver Table 2 unstandardised `TDPREDEFFECT` `M` was treated
+    /// as p. 16 `TDPREDEFFECTstd`. Unstandardised `M` is defined for
+    /// a zero coefficient or zero predictor variance; standardised
+    /// `TDPREDEFFECT` is not.
+    UnstandardisedContinuousTimeDependentEffectIsNotStandardisedContinuousTimeDependentEffect,
+    /// Driver p. 16 `TIPREDEFFECTstd` `B · √v / √(-q / (2 a))` was
+    /// treated as p. 16 `TDPREDEFFECTstd`. Table 2 names `M`
+    /// `TDPREDEFFECT` and `B` `TIPREDEFFECT`. Equal numbers when
+    /// `M = B` and the predictor variances match are still distinct
+    /// named quantities.
+    StandardisedContinuousTimeIndependentEffectIsNotStandardisedContinuousTimeDependentEffect,
+    /// Driver finite-interval standardised `TDPREDEFFECT`
+    /// `A^{-1}[e^{A Δt} − I] M · √v / √p` was treated as p. 16
+    /// `TDPREDEFFECTstd`. That intercept-style discrete map depends
+    /// on the event interval; the continuous Dirac coefficient does
+    /// not.
+    StandardisedDiscreteTimeDependentEffectIsNotStandardisedContinuousTimeDependentEffect,
+    /// Driver §7.1 trait-contaminated continuous TD effect
+    /// `m · √v / √(trait + p + added)` was treated as p. 16
+    /// `TDPREDEFFECTstd`. Footnote 4 uses only `asymDIFFUSION`,
+    /// not `TRAITVAR`.
+    TraitContaminatedContinuousTimeDependentEffectIsNotStandardisedContinuousTimeDependentEffect,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1516,6 +1548,24 @@ impl fmt::Display for PsychometricError {
             Self::AsymptoticTimeIndependentObservedVarianceIsNotMeasurementError => {
                 "asymptotic time-independent observed variance is not measurement-error variance"
             }
+            Self::StandardisedContinuousTimeDependentEffectRequiresPositiveWithinSubjectVariance => {
+                "standardised continuous time-dependent predictor effect requires strictly positive within-subject variance"
+            }
+            Self::StandardisedContinuousTimeDependentEffectRequiresPositivePredictorVariance => {
+                "standardised continuous time-dependent predictor effect requires strictly positive predictor variance"
+            }
+            Self::UnstandardisedContinuousTimeDependentEffectIsNotStandardisedContinuousTimeDependentEffect => {
+                "unstandardised continuous time-dependent predictor effect is not standardised continuous time-dependent predictor effect"
+            }
+            Self::StandardisedContinuousTimeIndependentEffectIsNotStandardisedContinuousTimeDependentEffect => {
+                "standardised continuous time-independent predictor effect is not standardised continuous time-dependent predictor effect"
+            }
+            Self::StandardisedDiscreteTimeDependentEffectIsNotStandardisedContinuousTimeDependentEffect => {
+                "standardised discrete time-dependent predictor effect is not standardised continuous time-dependent predictor effect"
+            }
+            Self::TraitContaminatedContinuousTimeDependentEffectIsNotStandardisedContinuousTimeDependentEffect => {
+                "trait-contaminated continuous time-dependent predictor effect is not standardised continuous time-dependent predictor effect"
+            }
         };
         formatter.write_str(message)
     }
@@ -2614,4 +2664,38 @@ mod tests {
             "asymptotic time-independent observed variance is not measurement-error variance"
         );
     }
+
+    #[test]
+    fn standardised_continuous_time_dependent_effect_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedContinuousTimeDependentEffectRequiresPositiveWithinSubjectVariance
+                .to_string(),
+            "standardised continuous time-dependent predictor effect requires strictly positive within-subject variance"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedContinuousTimeDependentEffectRequiresPositivePredictorVariance
+                .to_string(),
+            "standardised continuous time-dependent predictor effect requires strictly positive predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedContinuousTimeDependentEffectIsNotStandardisedContinuousTimeDependentEffect
+                .to_string(),
+            "unstandardised continuous time-dependent predictor effect is not standardised continuous time-dependent predictor effect"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedContinuousTimeIndependentEffectIsNotStandardisedContinuousTimeDependentEffect
+                .to_string(),
+            "standardised continuous time-independent predictor effect is not standardised continuous time-dependent predictor effect"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedDiscreteTimeDependentEffectIsNotStandardisedContinuousTimeDependentEffect
+                .to_string(),
+            "standardised discrete time-dependent predictor effect is not standardised continuous time-dependent predictor effect"
+        );
+        assert_eq!(
+            PsychometricError::TraitContaminatedContinuousTimeDependentEffectIsNotStandardisedContinuousTimeDependentEffect
+                .to_string(),
+            "trait-contaminated continuous time-dependent predictor effect is not standardised continuous time-dependent predictor effect"
+        );
+    }
 }