feat(psychometric): recover Driver 2017-era addedTIPREDVARstd after addedTIPREDVAR

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; §7.2, pp. 20–21; Table 2, p. 12; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T21:22Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised extra time-independent predictor variance `addedTIPREDVARstd`. Page 16 prints standardised matrices with the suffix `std` when appropriate. After `addedTIPREDVAR` as `asymTIPREDEFFECT %*% TIPREDVAR %*% t(asymTIPREDEFFECT)`, the 2017-era `summary.ctsemFit.R` forms `addedTIPREDVARstd = solve(sqrt(diag(addedTIPREDVAR))) %&% addedTIPREDVAR`. OpenMx `%&%` is the quadratic form `t(A) %*% B %*% A`. 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 `extra / extra = 1` after strictly positive extra. Form `addedTIPREDVAR` first, then the ratio. A zero extra has no positive extra SD and fails closed. Unstandardised `(B / a)² v` is defined for a zero coefficient and for zero predictor variance; standardised `addedTIPREDVAR` is not. `λ² (B / a)² v` is Eq. 5 of the extra, not this correlation. `t0_b² v` is `addedT0TIPREDVAR`, not this asymptotic extra correlation. `TRAITVAR` is not the standardisation variance. The printed 2-latent `addedTIPREDVAR` 2.838 is not this scalar 1. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T21:22Z: `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-23T21:22Z: `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 +865,22 @@ pub enum PsychometricError {
     /// treated as `MANIFESTVAR` `θ`. Measurement error is not extra
     /// observed TI variance.
     AsymptoticTimeIndependentObservedVarianceIsNotMeasurementError,
+    /// Driver 2017-era `addedTIPREDVARstd` was requested with a
+    /// non-positive extra TI variance. The scalar correlation form
+    /// `extra / extra` requires strictly positive `addedTIPREDVAR`.
+    StandardisedAsymptoticTimeIndependentVarianceRequiresPositiveExtraVariance,
+    /// Driver 2017-era unstandardised `addedTIPREDVAR` `(B / a)² v`
+    /// was treated as `addedTIPREDVARstd`. Those remain distinct
+    /// named quantities even when a 1-latent correlation is 1.
+    UnstandardisedAsymptoticTimeIndependentVarianceIsNotStandardisedAsymptoticTimeIndependentVariance,
+    /// Driver Eq. 5 of §7.2 `addedTIPREDVAR` `λ² (B / a)² v` was
+    /// treated as 2017-era `addedTIPREDVARstd`. Observed extra is
+    /// not the latent extra correlation.
+    AsymptoticTimeIndependentObservedVarianceIsNotStandardisedAsymptoticTimeIndependentVariance,
+    /// Driver 2017-era `addedT0TIPREDVAR` `t0_b² v` was treated as
+    /// `addedTIPREDVARstd`. First-occasion extra is not the
+    /// asymptotic extra correlation.
+    InitialTimeIndependentVarianceIsNotStandardisedAsymptoticTimeIndependentVariance,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1516,6 +1532,18 @@ impl fmt::Display for PsychometricError {
             Self::AsymptoticTimeIndependentObservedVarianceIsNotMeasurementError => {
                 "asymptotic time-independent observed variance is not measurement-error variance"
             }
+            Self::StandardisedAsymptoticTimeIndependentVarianceRequiresPositiveExtraVariance => {
+                "standardised asymptotic time-independent predictor variance requires positive extra variance"
+            }
+            Self::UnstandardisedAsymptoticTimeIndependentVarianceIsNotStandardisedAsymptoticTimeIndependentVariance => {
+                "unstandardised asymptotic time-independent predictor variance is not standardised asymptotic time-independent predictor variance"
+            }
+            Self::AsymptoticTimeIndependentObservedVarianceIsNotStandardisedAsymptoticTimeIndependentVariance => {
+                "asymptotic time-independent observed variance is not standardised asymptotic time-independent predictor variance"
+            }
+            Self::InitialTimeIndependentVarianceIsNotStandardisedAsymptoticTimeIndependentVariance => {
+                "initial time-independent predictor variance is not standardised asymptotic time-independent predictor variance"
+            }
         };
         formatter.write_str(message)
     }
@@ -2614,4 +2642,28 @@ mod tests {
             "asymptotic time-independent observed variance is not measurement-error variance"
         );
     }
+
+    #[test]
+    fn standardised_asymptotic_time_independent_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedAsymptoticTimeIndependentVarianceRequiresPositiveExtraVariance
+                .to_string(),
+            "standardised asymptotic time-independent predictor variance requires positive extra variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedAsymptoticTimeIndependentVarianceIsNotStandardisedAsymptoticTimeIndependentVariance
+                .to_string(),
+            "unstandardised asymptotic time-independent predictor variance is not standardised asymptotic time-independent predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::AsymptoticTimeIndependentObservedVarianceIsNotStandardisedAsymptoticTimeIndependentVariance
+                .to_string(),
+            "asymptotic time-independent observed variance is not standardised asymptotic time-independent predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTimeIndependentVarianceIsNotStandardisedAsymptoticTimeIndependentVariance
+                .to_string(),
+            "initial time-independent predictor variance is not standardised asymptotic time-independent predictor variance"
+        );
+    }
 }