feat(psychometric): recover 2017-era commented asymTOTALVAR after addedTIPREDVAR on main

CHANGELOG.md

@@ -38,6 +38,7 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 
 ## [Unreleased]
 
+- `psychometric_core` recovers the 2017-era commented-out `asymTOTALVAR` after `addedTIPREDVAR` as `-q / (2 a) + trait / a² + (B / a)² v` on current main. 2017-era ctsem `summary.ctsemFit.R` (cran/ctsem 2.5.0) comments `asymTOTALVAR <- asymDIFFUSION + asymTRAITVAR` with `asymTRAITVAR <- solve(DRIFT) %*% TRAITVAR %*% t(solve(DRIFT))`, then later comments `asymTOTALVAR <- asymTOTALVAR + addedTIPREDVAR` immediately after forming `addedTIPREDVAR`. Driver, Oud, and Voelkle (2017, Eq. 1, p. 4; Eq. 4, p. 5; Table 2, p. 12; §4.3, p. 9; §7.2, pp. 20–21; JSS PDF re-opened 2026-08-31T04:40Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) write `dη = (Aη + ξ + Bz + Mx) dt + G dW`. Form the two-term total first (`1 / a`, then square, then multiply by `trait`, then add `asymDIFFUSION`). Then include `addedTIPREDVAR` (unit asymptotic effect, then square, then multiply by `v`). Then add. This crate does not currently export `recover_asymptotic_total_variance` or `recover_asymptotic_trait_variance`; form those terms inline. Table 2/3 do not name `asymTOTALVAR`. A zero trait, a zero diffusion, and a zero TI extra is exactly zero even if `a ≥ 0`. `a ≥ 0` with a nonzero contribution fails closed. A zero TI extra keeps the two-term total. A zero trait and a zero diffusion keep `addedTIPREDVAR`. `p + trait / a²` is the two-term commented total and is not this map when `addedTIPREDVAR ≠ 0`. Stationary `T0VAR` `trait + p + (B / a)² v` keeps `TRAITVAR` in process units and is not this map. `(B / a)² v` is `addedTIPREDVAR` and equals this total when `q = 0` and `trait = 0` and remains a distinct named quantity. This slice does not duplicate queued `#340` two-term `asymTOTALVAR`. Meredith (1993) remains unread (web search 2026-08-31T04:40Z: Springer/Cambridge Core paywalled; Unpaywall historically `is_oa: false`; Springer `content/pdf` is an HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.
 - `event_core` adds bounded Allen interval-consistency classification, atomic path-consistency closure, contradiction/resource refusals, and an explicit dependency-error fallback without claiming unrestricted global satisfiability.
 
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 2, p. 12 `MANIFESTTRAITVAR`; §7.1, p. 19; p. 16 `MANIFESTTRAITVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-27T14:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised manifest-trait variance on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 83–84). Table 2 names `MANIFESTTRAITVAR` `Ψ_τ` the additional time-invariant variance-covariance on the measurement level and sets it `NULL` when there is no manifest trait. Equation 5 writes `Γ ~ N(τ, Ψ)` and names that covariance the manifest traits. Section 7.1 names manifest traits stable individual differences in indicator levels, distinct from process-level `TRAITVAR` `φ_ξ`. Page 16 prints standardised matrices with the suffix `std` when appropriate. The printed example on p. 16 is `discreteDRIFTstd`, not `MANIFESTTRAITVARstd`. Footnote 4 standardises using only the relevant variance, not the total. The relevant variance for that named indicator-level correlation is `MANIFESTTRAITVAR`, not process-level `TRAITVAR` and not residual `MANIFESTVAR` `θ`. The 2017-era source forms `MANIFESTTRAITVARstd` only when `MANIFESTTRAITVAR != 0`, as `solve(sqrt(diag(MANIFESTTRAITVAR) + ridging)) %&% MANIFESTTRAITVAR` when `verbose = TRUE`. OpenMx `%&%` is `t(A) %*% B %*% A`. Unlike `TRAITVARstd`, that formation adds `diag(c(ridging), n.manifest)`. 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 `ψ / ψ = 1` after strictly positive `MANIFESTTRAITVAR`. Form strictly positive `ψ` first, then `1 / √ψ`, then `(1 / √ψ) ψ (1 / √ψ)`. Unstandardised `MANIFESTTRAITVAR` is defined for a zero trait; standardised `MANIFESTTRAITVAR` is not. Zero `MANIFESTTRAITVAR` skips forming `MANIFESTTRAITVARstd` in the 2017-era source and fails closed here. Indicator-level trait variance is an event-time structural quantity, so a non-event clock fails closed. `MANIFESTTRAITVAR` does not require stable `a < 0`. Distinct positive `ψ` recover the same 1. `trait / trait = 1` is `TRAITVARstd` and recovers the same number and remains a distinct named quantity. `θ` is `MANIFESTVAR` and is measurement error, not this correlation. Meredith (1993) remains unread (web search 2026-08-27T14:20Z: Springer/Cambridge Core paywalled; Unpaywall historically `is_oa: false`; Springer `content/pdf` is an HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.

crates/psychometric_core/src/error.rs

@@ -710,6 +710,26 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+    /// 2017-era commented-out `asymTOTALVAR` after `addedTIPREDVAR`
+    /// was requested for a non-stable drift. The three-term map
+    /// `-q / (2 a) + trait / a² + (B / a)² v` requires `a < 0`
+    /// whenever a contribution is nonzero.
+    AsymptoticTotalVarianceAfterAddedPredictorRequiresStableDrift,
+    /// 2017-era two-term `asymTOTALVAR` was treated as the later
+    /// commented three-term total. `p + trait / a²` omits
+    /// `addedTIPREDVAR`. Equal numbers when `B = 0` or `v = 0`
+    /// remain distinct named quantities.
+    TwoTermAsymptoticTotalVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor,
+    /// Driver §4.3 / p. 16 stationary `T0VAR` was treated as 2017-era
+    /// `asymTOTALVAR` after `addedTIPREDVAR`. `trait + p + (B / a)² v`
+    /// keeps `TRAITVAR` in process units; the commented total uses
+    /// `solve(DRIFT)` and is `p + trait / a² + (B / a)² v`.
+    StationaryInitialLatentVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor,
+    /// Driver §7.2 `addedTIPREDVAR` was treated as 2017-era
+    /// `asymTOTALVAR` after `addedTIPREDVAR`. `(B / a)² v` is the
+    /// later addend, not the three-term total that also includes
+    /// `asymDIFFUSION` and `asymTRAITVAR`.
+    AsymptoticTimeIndependentVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1235,6 +1255,18 @@ impl fmt::Display for PsychometricError {
             Self::ObservedVarianceIsNotStandardisedManifestVariance => {
                 "observed-indicator variance is not standardised measurement-error variance"
             }
+            Self::AsymptoticTotalVarianceAfterAddedPredictorRequiresStableDrift => {
+                "asymptotic total variance after added time-independent predictor requires a stable negative drift"
+            }
+            Self::TwoTermAsymptoticTotalVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor => {
+                "two-term asymptotic total variance is not asymptotic total variance after added time-independent predictor"
+            }
+            Self::StationaryInitialLatentVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor => {
+                "stationary initial latent variance is not asymptotic total variance after added time-independent predictor"
+            }
+            Self::AsymptoticTimeIndependentVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor => {
+                "asymptotic time-independent predictor variance is not asymptotic total variance after added time-independent predictor"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2105,28 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn asymptotic_total_variance_after_added_predictor_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::AsymptoticTotalVarianceAfterAddedPredictorRequiresStableDrift
+                .to_string(),
+            "asymptotic total variance after added time-independent predictor requires a stable negative drift"
+        );
+        assert_eq!(
+            PsychometricError::TwoTermAsymptoticTotalVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor
+                .to_string(),
+            "two-term asymptotic total variance is not asymptotic total variance after added time-independent predictor"
+        );
+        assert_eq!(
+            PsychometricError::StationaryInitialLatentVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor
+                .to_string(),
+            "stationary initial latent variance is not asymptotic total variance after added time-independent predictor"
+        );
+        assert_eq!(
+            PsychometricError::AsymptoticTimeIndependentVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor
+                .to_string(),
+            "asymptotic time-independent predictor variance is not asymptotic total variance after added time-independent predictor"
+        );
+    }
 }

crates/psychometric_core/src/event_time.rs

@@ -190,7 +190,11 @@
 //! mean when `u ≠ t0`; `e^{a(t−u)} m x` is a Dirac on the original
 //! process, not this `DRIFT` drive). The JSS article
 //! has no numbered §2.2 (2.1 is Continuous time and SEM; §3 follows).
-//! The difference quotient `(x(t+Δt) − x(t)) / Δt` (their
+//! The 2017-era commented `asymTOTALVAR` after `addedTIPREDVAR` is
+//! `-q / (2 a) + trait / a² + (B / a)² v` (cran/ctsem 2.5.0
+//! `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-31T04:40Z). The
+//! two-term total omits the later addend. Stationary `T0VAR` keeps
+//! `TRAITVAR` in process units. The difference quotient `(x(t+Δt) − x(t)) / Δt` (their
 //! Eqs. 3–4) is refused. This is not DSEM and not a matrix `expm`.
 
 use std::collections::BTreeMap;
@@ -4160,6 +4164,186 @@ pub fn refuse_asymptotic_time_independent_variance_as_asymptotic_effect(
     Err(PsychometricError::AsymptoticTimeIndependentVarianceIsNotAsymptoticEffect)
 }
 
+/// Exact scalar 2017-era commented-out `asymTOTALVAR` after
+/// `addedTIPREDVAR`.
+///
+/// 2017-era ctsem `summary.ctsemFit.R` (cran/ctsem 2.5.0; JSS PDF
+/// re-opened 2026-08-31T04:40Z from
+/// <https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104>)
+/// comments `asymTOTALVAR <- asymDIFFUSION + asymTRAITVAR` with
+/// `asymTRAITVAR <- solve(DRIFT) %*% TRAITVAR %*% t(solve(DRIFT))`,
+/// then later comments
+/// `asymTOTALVAR <- asymTOTALVAR + addedTIPREDVAR` immediately
+/// after forming `addedTIPREDVAR <- asymTIPREDEFFECT %*% TIPREDVAR
+/// %*% t(asymTIPREDEFFECT)`. Driver, Oud, and Voelkle (2017, Eq. 1,
+/// p. 4; Eq. 4, p. 5; Table 2, p. 12; §4.3, p. 9; §7.2, pp. 20–21)
+/// write `dη = (Aη + ξ + Bz + Mx) dt + G dW`. The Lyapunov
+/// within-subject variance is `asymDIFFUSION` `-q / (2 a)`. At a
+/// stable equilibrium a random intercept in `CINT` units has
+/// process-mean variance `trait / a²`. Section 7.2 names
+/// `addedTIPREDVAR` the stable between-subject variance accounted
+/// for by a time-independent predictor, `(B / a)² v`. The scalar
+/// three-term map is `-q / (2 a) + trait / a² + (B / a)² v`. Form
+/// the two-term total first (`1 / a`, then square, then multiply
+/// by `trait`, then add `asymDIFFUSION`). Then include
+/// `addedTIPREDVAR` (unit asymptotic effect, then square, then
+/// multiply by `v`). Then add. This crate does not currently
+/// export `recover_asymptotic_total_variance` or
+/// `recover_asymptotic_trait_variance`; form those terms inline.
+/// Table 2/3 do not name `asymTOTALVAR`. A zero trait, a zero
+/// diffusion, and a zero TI extra is exactly zero even if
+/// `a ≥ 0`. `a ≥ 0` with a nonzero contribution fails closed. A
+/// zero trait and a zero diffusion keep `addedTIPREDVAR`. A zero
+/// TI extra keeps the two-term total. `p + trait / a²` is the
+/// two-term commented total and is not this map when
+/// `addedTIPREDVAR ≠ 0`. Stationary `T0VAR`
+/// `trait + p + (B / a)² v` keeps `TRAITVAR` in process units and
+/// is not this map. `(B / a)² v` is `addedTIPREDVAR` and equals
+/// this total when `q = 0` and `trait = 0` and remains a distinct
+/// named quantity. This is not a Kalman filter, not a matrix
+/// `expm`, and not ctsem estimation.
+///
+/// # Errors
+///
+/// Returns [`PsychometricError::EventTimeRequired`] for a non-event
+/// clock,
+/// [`PsychometricError::AsymptoticTotalVarianceAfterAddedPredictorRequiresStableDrift`]
+/// when the drift is not strictly negative and a contribution is
+/// nonzero, and [`PsychometricError::InvalidNumericInput`] when an
+/// input is non-finite, a variance is negative, or a product or
+/// sum overflows.
+pub fn recover_asymptotic_total_variance_after_added_time_independent_predictor(
+    trait_variance: f64,
+    continuous_diffusion: f64,
+    time_independent_effect: f64,
+    predictor_variance: f64,
+    log_rate: f64,
+    clock: LagClock,
+) -> Result<f64, PsychometricError> {
+    if !clock.admits_structural_lag() {
+        return Err(PsychometricError::EventTimeRequired);
+    }
+    if !trait_variance.is_finite() || trait_variance < 0.0 {
+        return Err(PsychometricError::InvalidNumericInput);
+    }
+    if !continuous_diffusion.is_finite() || continuous_diffusion < 0.0 {
+        return Err(PsychometricError::InvalidNumericInput);
+    }
+    if !time_independent_effect.is_finite() {
+        return Err(PsychometricError::InvalidNumericInput);
+    }
+    if !predictor_variance.is_finite() || predictor_variance < 0.0 {
+        return Err(PsychometricError::InvalidNumericInput);
+    }
+    if !log_rate.is_finite() {
+        return Err(PsychometricError::InvalidNumericInput);
+    }
+    let ti_extra_is_zero = time_independent_effect == 0.0 || predictor_variance == 0.0;
+    if trait_variance == 0.0 && continuous_diffusion == 0.0 && ti_extra_is_zero {
+        return Ok(0.0);
+    }
+    if log_rate >= 0.0 {
+        return Err(
+            PsychometricError::AsymptoticTotalVarianceAfterAddedPredictorRequiresStableDrift,
+        );
+    }
+    let stationary = if continuous_diffusion == 0.0 {
+        0.0
+    } else {
+        recover_stationary_latent_variance(continuous_diffusion, log_rate, clock)?
+    };
+    let asymptotic_trait = if trait_variance == 0.0 {
+        0.0
+    } else {
+        let inverse_rate = require_finite(1.0 / log_rate)?;
+        let inverse_rate_squared = require_finite(inverse_rate * inverse_rate)?;
+        require_finite(inverse_rate_squared * trait_variance)?
+    };
+    let two_term = if stationary == 0.0 {
+        asymptotic_trait
+    } else if asymptotic_trait == 0.0 {
+        stationary
+    } else {
+        require_finite(stationary + asymptotic_trait)?
+    };
+    let added = recover_asymptotic_time_independent_predictor_variance(
+        time_independent_effect,
+        predictor_variance,
+        log_rate,
+        clock,
+    )?;
+    if added == 0.0 {
+        return Ok(two_term);
+    }
+    if two_term == 0.0 {
+        return Ok(added);
+    }
+    require_finite(two_term + added)
+}
+
+/// Refuse treating the two-term commented `asymTOTALVAR` as the
+/// later three-term total.
+///
+/// `p + trait / a²` omits `addedTIPREDVAR`. Equal numbers when the
+/// TI extra is zero remain distinct named quantities.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::TwoTermAsymptoticTotalVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor`].
+pub fn refuse_two_term_asymptotic_total_variance_as_asymptotic_total_variance_after_added_predictor(
+    two_term_total: f64,
+    three_term_total: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (two_term_total, three_term_total);
+    Err(
+        PsychometricError::TwoTermAsymptoticTotalVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor,
+    )
+}
+
+/// Refuse treating §4.3 stationary `T0VAR` as 2017-era
+/// `asymTOTALVAR` after `addedTIPREDVAR`.
+///
+/// `trait + p + (B / a)² v` keeps `TRAITVAR` in process units. The
+/// commented three-term total uses `solve(DRIFT)` and is
+/// `p + trait / a² + (B / a)² v`.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::StationaryInitialLatentVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor`].
+pub fn refuse_stationary_initial_latent_variance_as_asymptotic_total_variance_after_added_predictor(
+    stationary_initial: f64,
+    three_term_total: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (stationary_initial, three_term_total);
+    Err(
+        PsychometricError::StationaryInitialLatentVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor,
+    )
+}
+
+/// Refuse treating §7.2 `addedTIPREDVAR` as 2017-era
+/// `asymTOTALVAR` after `addedTIPREDVAR`.
+///
+/// `(B / a)² v` is the later addend. The commented three-term
+/// total also includes `asymDIFFUSION` and `asymTRAITVAR`. Equal
+/// numbers when `q = 0` and `trait = 0` remain distinct named
+/// quantities.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::AsymptoticTimeIndependentVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor`].
+pub fn refuse_asymptotic_time_independent_variance_as_asymptotic_total_variance_after_added_predictor(
+    added_predictor_variance: f64,
+    three_term_total: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (added_predictor_variance, three_term_total);
+    Err(
+        PsychometricError::AsymptoticTimeIndependentVarianceIsNotAsymptoticTotalVarianceAfterAddedPredictor,
+    )
+}
+
 /// Exact scalar Table 2 `asymCINT`.
 ///
 /// Driver, Oud, and Voelkle (2017, Table 2, p. 12; Eq. 3, p. 5;