Restore Driver Table 2 T0TDPREDCOV as t0_m·v

[seonghobae]

Summary

Independent Driver, Oud, and Voelkle (2017, JSS 77(5)) Table 2 restore of one named quantity: T0TDPREDCOV.

Table 2 names T0TDPREDCOV the n.latent × (Tpoints × n.TDpred) covariance matrix between latents at T0 and time-dependent predictors. Default of "auto" restricts covariance to 0. Table 3 names T0TDPREDEFFECT the first-occasion TD effect (a regression). The crate already recovers T0TDPREDEFFECT as t0_m.

The 2017-era ctFit.R (ctsem 2.5.0) places T0TDPREDCOV in the OpenMx S covariance block between first-occasion latents and TD predictors. The 2017-era summary.ctsemFit.R comments out TDPREDVAR / TDPREDVARstd and does not form T0TDPREDCOV in summary. SEM conversion: T0TDPREDEFFECT = T0TDPREDCOV * solve(TDPREDVAR), so the scalar covariance is t0_m · v after finite t0_m and v ≥ 0. Form t0_m first, then multiply by v. A zero coefficient or zero predictor variance is exact 0. A signed coefficient is a signed covariance. Free first-occasion covariance does not require stable a < 0.

This is not a std map. This crate does not invent TDPREDVARstd.

JSS PDF re-opened 2026-08-30T16:40Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104

Fail-closed / refuses

• unstandardised t0_m is not T0TDPREDCOV (equal numbers when v = 1 remain distinct named quantities)
• analog extra t0_m² v is not T0TDPREDCOV (equal numbers when t0_m = 1 remain distinct named quantities; Table 2 names the covariance, not that extra)
• TI analog t0_b · v is not T0TDPREDCOV even when t0_m = t0_b
• process m · v is TDPREDEFFECT × TDPREDVAR and is not this first-occasion map even when t0_m = m
• v < 0, non-event clock, overflow, and nonfinite inputs fail closed

Scope

Stays inside psychometric_core. Does not add a second invariance crate. Does not recreate #78 longitudinal_core or #80 irregular_time. Independent of open sibling std PRs (#299–#316). Register items 110–111 (1–105 are on the research note; 55–88 / 106–109 are queued elsewhere).

Still not a Kalman filter, not a matrix expm, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) and Mislevy (1991) remain unread (Unpaywall is_oa: false).

Verification

cargo test -p psychometric_core green. cargo clippy -p psychometric_core --all-targets -- -D warnings clean.

Do not merge on this author. Do not self-approve. Draft until independent non-author APPROVE + exact-head required-check success.

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