feat(psychometric): recover Driver p.16 MANIFESTMEANSstd after positive Θ

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 `MANIFESTMEANSstd`; Table 2, p. 12; footnote 4; Eq. 5, p. 5; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-25T05:04Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised manifest 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 `MANIFESTMEANS` `τ` the `n.manifest × 1` matrix of manifest means. Table 2 names `MANIFESTVAR` `Θ` the residual covariance of the indicators. The relevant variance for that named measurement intercept is residual `MANIFESTVAR` `θ`, not total observed `Var(y) = λ² Var(η) + θ`, matching `MANIFESTVARstd`. The 2017-era `summary.ctsemFit.R` forms unstandardised `MANIFESTMEANS` as `mxEval(MANIFESTMEANS, mxobj, compute=TRUE)`. That source does not form a `MANIFESTMEANSstd` matrix; the scalar map here is the footnote 4 standardisation of that named intercept: `τ / √θ`. Form strictly positive `θ` first, then divide `τ` by `√θ`. A zero mean is exactly zero. Unstandardised `MANIFESTMEANS` is defined for a zero residual; standardised `MANIFESTMEANS` is not. Zero `θ` has no positive SD and fails closed. Manifest means are an event-time measurement quantity, so a non-event clock fails closed. `MANIFESTMEANS` does not require stable `a < 0`. `MANIFESTVARstd` `θ / θ = 1` recovers the same number when `τ = √θ` and remains a distinct named quantity. `τ / √(λ² Var(η) + θ)` uses total observed variance and is not this residual map. The 2017-era source assigns `dimnames(MANIFESTMEANS)` to `list(manifestNames, manifestNames)` on an `n.manifest × 1` matrix; that assignment is a source bug and is not this map. `T0MEANSstd` `μ_0 / √p_0` recovers the same number when `τ = μ_0` and `θ = p_0` and remains a distinct named quantity. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-25T05:04Z: `is_oa: false`, 0 locations; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread (Unpaywall 2026-08-25T05:04Z: `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 `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*).

crates/psychometric_core/src/error.rs

@@ -1099,6 +1099,27 @@ pub enum PsychometricError {
     /// mean using free `T0VAR`, not process-dynamics
     /// `asymDIFFUSION`.
     WithinSubjectScaledInitialLatentMeanIsNotStandardisedInitialLatentMean,
+    /// Driver p. 16 `MANIFESTMEANSstd` was requested with a
+    /// non-positive residual. Footnote 4 standardisation of the
+    /// 2017-era `MANIFESTMEANS` vector requires strictly positive
+    /// `MANIFESTVAR`.
+    StandardisedManifestMeanRequiresPositiveManifestVariance,
+    /// Driver Table 2 unstandardised `MANIFESTMEANS` `τ` was treated
+    /// as `MANIFESTMEANSstd`. Unstandardised measurement intercept
+    /// is defined for a zero residual; standardised `MANIFESTMEANS`
+    /// is not.
+    UnstandardisedManifestMeanIsNotStandardisedManifestMean,
+    /// Driver p. 16 `MANIFESTVARstd` was treated as p. 16
+    /// `MANIFESTMEANSstd`. Equal numbers when `τ = √θ` are still
+    /// distinct named quantities. `MANIFESTVARstd` is the
+    /// correlation form of residual `MANIFESTVAR`;
+    /// `MANIFESTMEANSstd` is the measurement intercept.
+    StandardisedManifestVarianceIsNotStandardisedManifestMean,
+    /// Driver Eq. 5 `τ / √(λ² Var(η) + θ)` was treated as
+    /// `MANIFESTMEANSstd`. Footnote 4 standardises the named
+    /// intercept using residual `MANIFESTVAR`, not total observed
+    /// variance.
+    ObservedScaledManifestMeanIsNotStandardisedManifestMean,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1894,6 +1915,18 @@ impl fmt::Display for PsychometricError {
             Self::WithinSubjectScaledInitialLatentMeanIsNotStandardisedInitialLatentMean => {
                 "within-subject scaled initial latent mean is not standardised initial latent mean"
             }
+            Self::StandardisedManifestMeanRequiresPositiveManifestVariance => {
+                "standardised manifest mean requires strictly positive measurement error"
+            }
+            Self::UnstandardisedManifestMeanIsNotStandardisedManifestMean => {
+                "unstandardised manifest mean is not standardised manifest mean"
+            }
+            Self::StandardisedManifestVarianceIsNotStandardisedManifestMean => {
+                "standardised manifest variance is not standardised manifest mean"
+            }
+            Self::ObservedScaledManifestMeanIsNotStandardisedManifestMean => {
+                "observed scaled manifest mean is not standardised manifest mean"
+            }
         };
         formatter.write_str(message)
     }
@@ -3273,4 +3306,25 @@ mod tests {
             "within-subject scaled initial latent mean is not standardised initial latent mean"
         );
     }
+
+    #[test]
+    fn standardised_manifest_mean_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedManifestMeanRequiresPositiveManifestVariance.to_string(),
+            "standardised manifest mean requires strictly positive measurement error"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedManifestMeanIsNotStandardisedManifestMean.to_string(),
+            "unstandardised manifest mean is not standardised manifest mean"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedManifestVarianceIsNotStandardisedManifestMean
+                .to_string(),
+            "standardised manifest variance is not standardised manifest mean"
+        );
+        assert_eq!(
+            PsychometricError::ObservedScaledManifestMeanIsNotStandardisedManifestMean.to_string(),
+            "observed scaled manifest mean is not standardised manifest mean"
+        );
+    }
 }