feat(psychometric): restore Driver 2017-era T0TOTALVAR extra+p_0 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 Driver, Oud, and Voelkle (2017, Table 2, p. 12 `TRAITVAR` / `T0VAR`; §7.1, pp. 18–19; p. 16; 2017-era ctsem `summary.ctsemFit.R` lines 322–339; JSS PDF re-opened 2026-08-30T18:50Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar 2017-era `T0TOTALVAR` on current main (register items 110–111). Independent of open `#321` unstandardised `T0TRAITVAR` and `#322` `T0TRAITVARstd`. This crate does not currently export `recover_initial_trait_variance`; form the quadratic `t0_trait² · trait` directly, then add free first-occasion `T0VAR` `p_0`. Table 2 names `TRAITVAR` `φ_ξ` the latent trait variance/covariance and `T0VAR` the latent process initial variance/covariance. Section 7.1 names traits the stable between-subject differences (unit-level unobserved heterogeneity). `T0TRAITEFFECT` is not in Table 2 or Table 3. The 2017-era `summary.ctsemFit.R` (ctsem 2.5.0, lines 322–339) comments `T0TRAITVAR <- T0TRAITEFFECT %*% TRAITVAR %*% t(T0TRAITEFFECT)` with `#is this valid?`, then `T0TOTALVAR <- T0TRAITVAR + T0VAR`. The scalar analog extra is `t0_trait² · trait`. The scalar total is `extra + p_0`. Form the extra first, then add free `p_0`. A zero extra or zero `p_0` is kept. A zero extra and a zero `p_0` is exactly zero. `trait < 0` or `p_0 < 0` fails closed. `T0` is an event-time occasion, so a non-event clock fails closed. Free `T0TRAITEFFECT` and free `T0VAR` do not require stable `a < 0`. `t0_trait² · trait` is `T0TRAITVAR` and equals this total when `p_0 = 0` and remains a distinct named quantity. Free `p_0` is `T0VAR` and equals this total when the extra is 0 and remains a distinct named quantity. `TRAITVAR` equals this total when `T0TRAITEFFECT = I` and `p_0 = 0` and remains a distinct named quantity. `t0_b² v` is `addedT0TIPREDVAR` and is extra first-occasion TI variance, not this total. Meredith (1993) remains unread (Unpaywall 2026-08-30T18:40Z: `is_oa: false`; OpenAlex closed; Springer `content/pdf` is an HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`; Unpaywall `is_oa: false`). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.
 - Removed the repository-local hourly PR-maintenance caller now covered by the central required scheduler, retired stale workflow registrations, narrowed documentation triggers, keyed PR concurrency by fixed workflow name, repository, and pull-request number without cancelling non-PR runs, and combined line/branch coverage on one sequential runner while preserving both 100% gates and diagnostics.
 
 - `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.

crates/psychometric_core/src/error.rs

@@ -710,6 +710,23 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+    /// Driver 2017-era `T0TOTALVAR` `t0_trait² · trait + p_0` was
+    /// treated as unstandardised `T0TRAITVAR` `t0_trait² · trait`.
+    /// Equal numbers when `p_0 = 0` are still distinct named
+    /// quantities.
+    InitialTotalVarianceIsNotInitialTraitVariance,
+    /// Driver 2017-era `T0TOTALVAR` was treated as free first-occasion
+    /// `T0VAR` `p_0`. Equal numbers when the trait extra is 0 are
+    /// still distinct named quantities.
+    InitialTotalVarianceIsNotInitialLatentVariance,
+    /// Driver 2017-era `T0TOTALVAR` was treated as Table 2 `TRAITVAR`.
+    /// Equal numbers when `T0TRAITEFFECT = I` and `p_0 = 0` are still
+    /// distinct named quantities.
+    InitialTotalVarianceIsNotTraitVariance,
+    /// Driver 2017-era `T0TOTALVAR` was treated as 2017-era
+    /// `addedT0TIPREDVAR` `t0_b² v`. Extra first-occasion TI variance
+    /// is not the first-occasion trait-plus-state total.
+    InitialTotalVarianceIsNotInitialTimeIndependentVariance,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1235,6 +1252,18 @@ impl fmt::Display for PsychometricError {
             Self::ObservedVarianceIsNotStandardisedManifestVariance => {
                 "observed-indicator variance is not standardised measurement-error variance"
             }
+            Self::InitialTotalVarianceIsNotInitialTraitVariance => {
+                "initial total variance is not initial trait variance"
+            }
+            Self::InitialTotalVarianceIsNotInitialLatentVariance => {
+                "initial total variance is not initial latent variance"
+            }
+            Self::InitialTotalVarianceIsNotTraitVariance => {
+                "initial total variance is not trait variance"
+            }
+            Self::InitialTotalVarianceIsNotInitialTimeIndependentVariance => {
+                "initial total variance is not initial time-independent predictor variance"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2102,24 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn initial_total_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::InitialTotalVarianceIsNotInitialTraitVariance.to_string(),
+            "initial total variance is not initial trait variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTotalVarianceIsNotInitialLatentVariance.to_string(),
+            "initial total variance is not initial latent variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTotalVarianceIsNotTraitVariance.to_string(),
+            "initial total variance is not trait variance"
+        );
+        assert_eq!(
+            PsychometricError::InitialTotalVarianceIsNotInitialTimeIndependentVariance.to_string(),
+            "initial total variance is not initial time-independent predictor variance"
+        );
+    }
 }

crates/psychometric_core/src/event_time.rs

@@ -6795,6 +6795,135 @@ pub fn recover_irregular_centered_residual_log_rate(
     require_finite(sum / count)
 }
 
+/// Exact scalar 2017-era `T0TOTALVAR`.
+///
+/// Driver, Oud, and Voelkle (2017, Table 2, p. 12 `TRAITVAR` /
+/// `T0VAR`; §7.1, pp. 18–19; p. 16; 2017-era ctsem
+/// `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-30T18:50Z from
+/// <https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104>)
+/// print first-occasion matrices. The 2017-era `summary.ctsemFit.R`
+/// (ctsem 2.5.0, lines 322–339) comments
+/// `T0TRAITVAR <- T0TRAITEFFECT %*% TRAITVAR %*% t(T0TRAITEFFECT)`
+/// with `#is this valid?`, then
+/// `T0TOTALVAR <- T0TRAITVAR + T0VAR`. The scalar analog extra is
+/// `t0_trait² · trait`. The scalar total is `extra + p_0`. Form the
+/// extra first, then add free first-occasion `T0VAR`. This crate
+/// does not currently export `recover_initial_trait_variance`; form
+/// the quadratic directly. A zero extra or zero `p_0` is kept. A
+/// zero extra and a zero `p_0` is exactly zero. `trait < 0` or
+/// `p_0 < 0` fails closed. `T0` is an event-time occasion, so a
+/// non-event clock fails closed. Free `T0TRAITEFFECT` and free
+/// `T0VAR` do not require stable `a < 0`. `t0_trait² · trait` is
+/// `T0TRAITVAR` and equals this total when `p_0 = 0` and remains a
+/// distinct named quantity. Free `p_0` is `T0VAR` and equals this
+/// total when the extra is 0 and remains a distinct named quantity.
+/// `TRAITVAR` equals this total when `T0TRAITEFFECT = I` and
+/// `p_0 = 0` and remains a distinct named quantity. `t0_b² v` is
+/// `addedT0TIPREDVAR` and is not this total. This is not a Kalman
+/// filter, not a matrix `expm`, not DSEM, and not ctsem estimation.
+///
+/// # Errors
+///
+/// Returns [`PsychometricError::EventTimeRequired`] for any
+/// non-event clock and [`PsychometricError::InvalidNumericInput`]
+/// when an input is non-finite, the trait variance is negative, the
+/// first-occasion variance is negative, or a product or sum
+/// overflows.
+pub fn recover_initial_total_variance(
+    initial_trait_effect: f64,
+    trait_variance: f64,
+    initial_variance: f64,
+    clock: LagClock,
+) -> Result<f64, PsychometricError> {
+    if !clock.admits_structural_lag() {
+        return Err(PsychometricError::EventTimeRequired);
+    }
+    if !initial_trait_effect.is_finite()
+        || !trait_variance.is_finite()
+        || !initial_variance.is_finite()
+        || trait_variance < 0.0
+        || initial_variance < 0.0
+    {
+        return Err(PsychometricError::InvalidNumericInput);
+    }
+    let squared = require_finite(initial_trait_effect * initial_trait_effect)?;
+    let extra = require_finite(squared * trait_variance)?;
+    require_finite(extra + initial_variance)
+}
+
+/// Refuse treating 2017-era `T0TOTALVAR` as 2017-era `T0TRAITVAR`.
+///
+/// `t0_trait² · trait + p_0` includes free first-occasion `T0VAR`.
+/// `T0TRAITVAR` is the trait extra alone. Equal numbers when
+/// `p_0 = 0` are still distinct named quantities.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::InitialTotalVarianceIsNotInitialTraitVariance`].
+pub fn refuse_initial_total_variance_as_initial_trait_variance(
+    initial_total_variance: f64,
+    initial_trait_variance: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (initial_total_variance, initial_trait_variance);
+    Err(PsychometricError::InitialTotalVarianceIsNotInitialTraitVariance)
+}
+
+/// Refuse treating 2017-era `T0TOTALVAR` as free first-occasion `T0VAR`.
+///
+/// `t0_trait² · trait + p_0` includes first-occasion trait extra.
+/// Free `T0VAR` is `p_0` alone. Equal numbers when the extra is 0
+/// are still distinct named quantities.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::InitialTotalVarianceIsNotInitialLatentVariance`].
+pub fn refuse_initial_total_variance_as_initial_latent_variance(
+    initial_total_variance: f64,
+    initial_latent_variance: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (initial_total_variance, initial_latent_variance);
+    Err(PsychometricError::InitialTotalVarianceIsNotInitialLatentVariance)
+}
+
+/// Refuse treating 2017-era `T0TOTALVAR` as Table 2 `TRAITVAR`.
+///
+/// Stationary `T0TRAITEFFECT = I` with `p_0 = 0` makes the total
+/// equal `TRAITVAR` numerically. Those remain distinct named
+/// quantities.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::InitialTotalVarianceIsNotTraitVariance`].
+pub fn refuse_initial_total_variance_as_trait_variance(
+    initial_total_variance: f64,
+    trait_variance: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (initial_total_variance, trait_variance);
+    Err(PsychometricError::InitialTotalVarianceIsNotTraitVariance)
+}
+
+/// Refuse treating 2017-era `T0TOTALVAR` as 2017-era `addedT0TIPREDVAR`.
+///
+/// `t0_b² v` is extra first-occasion TI variance. `T0TOTALVAR` is
+/// first-occasion trait extra plus free `T0VAR`. This crate does
+/// not currently export `addedT0TIPREDVAR`; the refuse still names
+/// that quantity.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::InitialTotalVarianceIsNotInitialTimeIndependentVariance`].
+pub fn refuse_initial_total_variance_as_initial_time_independent_variance(
+    initial_total_variance: f64,
+    initial_predictor_variance: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (initial_total_variance, initial_predictor_variance);
+    Err(PsychometricError::InitialTotalVarianceIsNotInitialTimeIndependentVariance)
+}
+
 /// Least-squares scalar log-rate for already-formed residual pairs.
 ///
 /// Pair-wise logs initialize Newton. This helper is crate-visible so overflow
@@ -6880,7 +7009,7 @@ mod tests {
         recover_initial_time_dependent_predictor_carry,
         recover_initial_time_dependent_predictor_effect,
         recover_initial_time_independent_predictor_carry,
-        recover_initial_time_independent_predictor_effect,
+        recover_initial_time_independent_predictor_effect, recover_initial_total_variance,
         recover_irregular_centered_residual_log_rate, recover_level_change_continuous_intercept,
         recover_level_change_discrete_increment, recover_level_change_extra_process_contribution,
         recover_level_change_extra_process_contribution_after, recover_local_log_rate,
@@ -6960,6 +7089,10 @@ mod tests {
         refuse_initial_time_independent_effect_as_time_dependent_impulse,
         refuse_initial_time_independent_observed_mean_as_initial_time_dependent_observed_mean,
         refuse_initial_time_independent_variance_as_standardised_trait_variance,
+        refuse_initial_total_variance_as_initial_latent_variance,
+        refuse_initial_total_variance_as_initial_time_independent_variance,
+        refuse_initial_total_variance_as_initial_trait_variance,
+        refuse_initial_total_variance_as_trait_variance,
         refuse_latent_lagged_covariance_as_observed_covariance,
         refuse_latent_mean_as_observed_mean, refuse_latent_variance_as_observed_variance,
         refuse_level_change_extra_process_as_impulse,
@@ -16353,4 +16486,108 @@ mod tests {
             Err(PsychometricError::InvalidNumericInput)
         );
     }
+
+    #[test]
+    fn initial_total_variance_recovers_driver_2017_era_t0_total_var() {
+        // Driver et al. (2017, Table 2 TRAITVAR / T0VAR; §7.1;
+        // 2017-era summary.ctsemFit.R 322–339; JSS PDF re-opened
+        // 2026-08-30T18:50Z): form extra = t0_trait² · trait, then
+        // extra + p_0. This crate does not currently export
+        // recover_initial_trait_variance; form the quadratic
+        // directly. A zero extra or zero p_0 is kept.
+        let effect = 0.5_f64;
+        let trait_variance = 0.8_f64;
+        let initial_variance = 1.6_f64;
+        let recovered = recover_initial_total_variance(
+            effect,
+            trait_variance,
+            initial_variance,
+            LagClock::EventTime,
+        )
+        .expect("T0TOTALVAR");
+        let extra = effect * effect * trait_variance;
+        let expected = extra + initial_variance;
+        assert!((recovered - expected).abs() < 1e-15);
+        let doubled =
+            recover_initial_total_variance(effect, 1.6, initial_variance, LagClock::EventTime)
+                .expect("doubled-trait");
+        assert!((doubled - (2.0 * extra + initial_variance)).abs() < 1e-15);
+        let signed = recover_initial_total_variance(
+            -effect,
+            trait_variance,
+            initial_variance,
+            LagClock::EventTime,
+        )
+        .expect("signed");
+        assert!((signed - expected).abs() < 1e-15);
+        let zero_extra = recover_initial_total_variance(
+            0.0,
+            trait_variance,
+            initial_variance,
+            LagClock::EventTime,
+        )
+        .expect("zero extra");
+        assert!((zero_extra - initial_variance).abs() < 1e-15);
+        let zero_p0 =
+            recover_initial_total_variance(effect, trait_variance, 0.0, LagClock::EventTime)
+                .expect("zero p0");
+        assert!((zero_p0 - extra).abs() < 1e-15);
+        let both_zero =
+            recover_initial_total_variance(0.0, 0.0, 0.0, LagClock::EventTime).expect("0+0");
+        assert_eq!(both_zero.to_bits(), 0.0_f64.to_bits());
+        let stationary_zero_p0 =
+            recover_initial_total_variance(1.0, trait_variance, 0.0, LagClock::EventTime)
+                .expect("I, p0=0");
+        assert!((stationary_zero_p0 - trait_variance).abs() < 1e-15);
+        let added_t0 = 0.3_f64 * 0.3_f64 * 4.0_f64;
+        assert_eq!(
+            refuse_initial_total_variance_as_initial_trait_variance(zero_p0, extra),
+            Err(PsychometricError::InitialTotalVarianceIsNotInitialTraitVariance)
+        );
+        assert_eq!(
+            refuse_initial_total_variance_as_initial_latent_variance(zero_extra, initial_variance),
+            Err(PsychometricError::InitialTotalVarianceIsNotInitialLatentVariance)
+        );
+        assert_eq!(
+            refuse_initial_total_variance_as_trait_variance(stationary_zero_p0, trait_variance),
+            Err(PsychometricError::InitialTotalVarianceIsNotTraitVariance)
+        );
+        assert_eq!(
+            refuse_initial_total_variance_as_initial_time_independent_variance(recovered, added_t0),
+            Err(PsychometricError::InitialTotalVarianceIsNotInitialTimeIndependentVariance)
+        );
+    }
+
+    #[test]
+    fn initial_total_variance_fails_closed_when_operands_are_defined() {
+        let effect = 0.5_f64;
+        assert_eq!(
+            recover_initial_total_variance(effect, 0.8, 1.6, LagClock::SystemTime),
+            Err(PsychometricError::EventTimeRequired)
+        );
+        assert_eq!(
+            recover_initial_total_variance(effect, -1.0, 1.6, LagClock::EventTime),
+            Err(PsychometricError::InvalidNumericInput)
+        );
+        assert_eq!(
+            recover_initial_total_variance(effect, 0.8, -1.6, LagClock::EventTime),
+            Err(PsychometricError::InvalidNumericInput)
+        );
+        assert_eq!(
+            recover_initial_total_variance(1e200, 1.0, 1.0, LagClock::EventTime),
+            Err(PsychometricError::InvalidNumericInput)
+        );
+        assert_eq!(
+            recover_initial_total_variance(f64::NAN, 0.8, 1.6, LagClock::EventTime),
+            Err(PsychometricError::InvalidNumericInput)
+        );
+        assert_eq!(
+            recover_initial_total_variance(effect, f64::INFINITY, 1.6, LagClock::EventTime),
+            Err(PsychometricError::InvalidNumericInput)
+        );
+        assert_eq!(
+            recover_initial_total_variance(effect, 0.8, f64::INFINITY, LagClock::EventTime),
+            Err(PsychometricError::InvalidNumericInput)
+        );
+    }
 }

crates/psychometric_core/src/lib.rs

@@ -379,6 +379,8 @@ pub use event_time::recover_initial_time_dependent_predictor_effect;
 pub use event_time::recover_initial_time_independent_predictor_carry;
 /// Exact scalar first-occasion `T0TIPREDEFFECT` shift `t0_b z`.
 pub use event_time::recover_initial_time_independent_predictor_effect;
+/// Exact scalar 2017-era `T0TOTALVAR` `t0_trait² · trait + p_0`.
+pub use event_time::recover_initial_total_variance;
 /// Mean exact log-rate on already-centered irregular residuals.
 pub use event_time::recover_irregular_centered_residual_log_rate;
 /// Exact scalar §7.2 level-change `CINT` `κ = −a m x`.
@@ -572,6 +574,14 @@ pub use event_time::refuse_initial_time_independent_effect_as_time_dependent_imp
 pub use event_time::refuse_initial_time_independent_observed_mean_as_initial_time_dependent_observed_mean;
 /// Refuse treating 2017-era `addedT0TIPREDVAR` as p. 16 `TRAITVARstd`.
 pub use event_time::refuse_initial_time_independent_variance_as_standardised_trait_variance;
+/// Refuse treating 2017-era `T0TOTALVAR` as free first-occasion `T0VAR`.
+pub use event_time::refuse_initial_total_variance_as_initial_latent_variance;
+/// Refuse treating 2017-era `T0TOTALVAR` as 2017-era `addedT0TIPREDVAR`.
+pub use event_time::refuse_initial_total_variance_as_initial_time_independent_variance;
+/// Refuse treating 2017-era `T0TOTALVAR` as 2017-era `T0TRAITVAR`.
+pub use event_time::refuse_initial_total_variance_as_initial_trait_variance;
+/// Refuse treating 2017-era `T0TOTALVAR` as Table 2 `TRAITVAR`.
+pub use event_time::refuse_initial_total_variance_as_trait_variance;
 /// Refuse treating Driver Eq. 3–4 lagged latent covariance as `cov(y_t, y_{t-1})`.
 pub use event_time::refuse_latent_lagged_covariance_as_observed_covariance;
 /// Refuse treating Driver Eq. 5 latent mean as `E(y)`.