feat(psychometric): recover Driver p.16 T0MEANSstd 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, p. 16 `T0MEANSstd`; Table 2, p. 12; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-24T22:30Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised initial latent mean. Page 16 prints standardised matrices with the suffix `std` when appropriate. Footnote 4 standardises using only the relevant variance, not the total. Table 2 names `T0MEANS` the latent process means at the first time point `T0`. The first-occasion relevant variance is free `T0VAR` `p_0`, not process-dynamics `asymDIFFUSION` `-q / (2 a)`, matching Table 3 `T0TIPREDEFFECTstd`. The 2017-era `summary.ctsemFit.R` forms unstandardised `T0MEANS` as `OpenMx::mxEval(T0MEANS, mxobj, compute=TRUE)`. That source does not form a `T0MEANSstd` matrix; the scalar map here is the footnote 4 standardisation of that named first-occasion mean: `μ_0 / √p_0`. Form strictly positive `p_0` first, then divide `μ_0` by `√p_0`. A zero mean is exactly zero. Unstandardised `T0MEANS` is defined for a zero first-occasion variance; standardised `T0MEANS` is not. Zero `p_0` has no positive SD and fails closed. `T0` is an event-time occasion, so a non-event clock fails closed. Free `T0MEANS` does not require stable `a < 0`. `T0VARstd` `p_0 / p_0 = 1` recovers the same number when `μ_0 = √p_0` and remains a distinct named quantity. `μ_0 / √asymDIFFUSION` uses process-dynamics variance and is not this first-occasion map. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-24T08:02Z: `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 `asymCINTstd`; Eq. 3, p. 4; footnote 4; Table 2, p. 12; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-24T09:05Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised asymptotic continuous intercept. Page 16 prints standardised matrices with the suffix `std` when appropriate. 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 `asymCINT` whenever `verbose = TRUE`, as `-solve(DRIFT) %*% CINT`. That source does not form an `asymCINTstd` matrix; the scalar map here is the footnote 4 standardisation of that named asymptotic intercept: `(-κ / a) / √p`. Form strictly positive `p` first, then the asymptotic intercept, then divide by `√p`. A zero intercept is exactly zero. Unstandardised `asymCINT` is defined for a zero process; standardised `asymCINT` is not. Zero `q` has no positive process SD and fails closed. Lasting `asymDIFFUSION` requires stable `a < 0`. A non-event clock fails closed. `κ / √p` is the continuous intercept standardisation and is not this total-change map. `A^{-1}[e^{A Δt} − I] κ / √p` depends on the event interval and is not this `Δt → ∞` map. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, not `CINTstd`, not `discreteCINTstd`, 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 `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*).

crates/psychometric_core/src/error.rs

@@ -1079,6 +1079,26 @@ pub enum PsychometricError {
     /// `asymCINTstd`. A finite event interval is not the
     /// `Δt → ∞` intercept change.
     StandardisedDiscreteContinuousInterceptIsNotStandardisedAsymptoticContinuousIntercept,
+    /// Driver p. 16 `T0MEANSstd` was requested with a
+    /// non-positive first-occasion variance. Footnote 4
+    /// standardisation of the 2017-era `T0MEANS` vector
+    /// requires strictly positive free `T0VAR`.
+    StandardisedInitialLatentMeanRequiresPositiveInitialLatentVariance,
+    /// Driver Table 2 unstandardised `T0MEANS` `μ_0` was treated
+    /// as `T0MEANSstd`. Unstandardised first-occasion mean is
+    /// defined for a zero first-occasion variance; standardised
+    /// `T0MEANS` is not.
+    UnstandardisedInitialLatentMeanIsNotStandardisedInitialLatentMean,
+    /// Driver p. 16 `T0VARstd` was treated as p. 16 `T0MEANSstd`.
+    /// Equal numbers when `μ_0 = √p_0` are still distinct named
+    /// quantities. `T0VARstd` is the correlation form of free
+    /// `T0VAR`; `T0MEANSstd` is the first-occasion mean.
+    StandardisedInitialLatentVarianceIsNotStandardisedInitialLatentMean,
+    /// Driver p. 16 `T0MEANS` `/ √asymDIFFUSION` was treated as
+    /// `T0MEANSstd`. Footnote 4 standardises the first-occasion
+    /// mean using free `T0VAR`, not process-dynamics
+    /// `asymDIFFUSION`.
+    WithinSubjectScaledInitialLatentMeanIsNotStandardisedInitialLatentMean,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1862,6 +1882,18 @@ impl fmt::Display for PsychometricError {
             Self::StandardisedDiscreteContinuousInterceptIsNotStandardisedAsymptoticContinuousIntercept => {
                 "standardised discrete continuous intercept is not standardised asymptotic continuous intercept"
             }
+            Self::StandardisedInitialLatentMeanRequiresPositiveInitialLatentVariance => {
+                "standardised initial latent mean requires strictly positive initial latent variance"
+            }
+            Self::UnstandardisedInitialLatentMeanIsNotStandardisedInitialLatentMean => {
+                "unstandardised initial latent mean is not standardised initial latent mean"
+            }
+            Self::StandardisedInitialLatentVarianceIsNotStandardisedInitialLatentMean => {
+                "standardised initial latent variance is not standardised initial latent mean"
+            }
+            Self::WithinSubjectScaledInitialLatentMeanIsNotStandardisedInitialLatentMean => {
+                "within-subject scaled initial latent mean is not standardised initial latent mean"
+            }
         };
         formatter.write_str(message)
     }
@@ -3217,4 +3249,28 @@ mod tests {
             "standardised discrete continuous intercept is not standardised asymptotic continuous intercept"
         );
     }
+
+    #[test]
+    fn standardised_initial_latent_mean_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedInitialLatentMeanRequiresPositiveInitialLatentVariance
+                .to_string(),
+            "standardised initial latent mean requires strictly positive initial latent variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedInitialLatentMeanIsNotStandardisedInitialLatentMean
+                .to_string(),
+            "unstandardised initial latent mean is not standardised initial latent mean"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedInitialLatentVarianceIsNotStandardisedInitialLatentMean
+                .to_string(),
+            "standardised initial latent variance is not standardised initial latent mean"
+        );
+        assert_eq!(
+            PsychometricError::WithinSubjectScaledInitialLatentMeanIsNotStandardisedInitialLatentMean
+                .to_string(),
+            "within-subject scaled initial latent mean is not standardised initial latent mean"
+        );
+    }
 }