feat(psychometric): recover Driver p.16 asymTIPREDEFFECTstd after positive variances - #192
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…itive variances
Driver, Oud, and Voelkle (2017, p. 16; §7.2; footnote 4) print
standardised matrices with the suffix std when appropriate. Footnote 4
standardises using only the relevant variance, not the total. For
asymTIPREDEFFECT the affecting variance is TIPREDVAR and the affected
variance is within-subject asymDIFFUSION. Form strictly positive
-q/(2a) and v first, then (-B/a)·√v/√p. Unstandardised -B/a is
defined for a zero coefficient and for zero predictor variance;
standardised asymTIPREDEFFECT is not. Finite-interval
A^{-1}[e^{AΔt}−I]B·√v/√p is not asymTIPREDEFFECTstd.
(-B/a)·√v/√(trait+p+added) uses TRAITVAR and is not
asymTIPREDEFFECTstd. Still not a Kalman filter, not a matrix expm,
not ESEM estimation, not DSEM, and not ctsem estimation.
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Folded into the consolidation vehicle #231; this draft stays open until the vehicle merges, then closes as superseded-by-consolidation. |
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Superseded by consolidation: this slice's Driver et al. (2017) standardization recovery landed on protected main through the integration vehicles (#231/#232), and its contract coverage is carried by the reconciled suites (multilevel_event_time_recovery_contract, rubin_and_mean_gate_contract) with test-signature repair tracked in #234. The stacked-draft form is retired to keep the delivery queue at review-ready work only; no capability is lost — the exact-head provenance remains in the vehicle PR descriptions and CHANGELOG. |
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Stacked on #190 (
adb0bc6) / #189 (0836c35) / #188 (444304d) / #187 (6afd048) / #185 (69ffec6) / #184 (6b93147) / #183 (c10097be) / #182 (2d4d6bf) / #181 (542806b) / #49 (6f95142). ADR 0005 executable slice stays insidepsychometric_core. This is not a second invariance crate and does not recreate #78 or #80.psychometric_corerecovers the Driver, Oud, and Voelkle (2017, p. 16asymTIPREDEFFECTstd; §7.2, pp. 20–21; Eq. 3, p. 5; Table 2, p. 12; footnote 4; JSS PDF re-opened 2026-08-23T14:25Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised asymptotic time-independent predictor effect. Page 16 prints continuous-time parameters and, when appropriate, standardised matrices with the suffixstd. Section 7.2 namesasymTIPREDEFFECTthe expected total change in process means given a unit increase on a time-independent predictor. The scalar map is-B / afor stablea < 0. Footnote 4: standardisations use only the relevant variance, not the total. The affecting variance is predictor varianceTIPREDVARv. The affected variance is within-subjectasymDIFFUSION-q / (2 a), because the process dynamics are individual, or average individual, temporal dynamics.Form strictly positive
asymDIFFUSIONfirst, then strictly positivev, then the unit asymptotic effect, then(-B / a) · √v / √(-q / (2 a)).-B / ais defined for a zero coefficient and for zero predictor variance; standardisedasymTIPREDEFFECTis not.asymDIFFUSIONhas no positive process SD and fails closed (StandardisedAsymptoticTimeIndependentEffectRequiresPositiveWithinSubjectVariance).TIPREDVARhas no positive predictor SD and fails closed (StandardisedAsymptoticTimeIndependentEffectRequiresPositivePredictorVariance).a ≥ 0cannot form finiteasymDIFFUSIONand fails closed (StationaryVarianceRequiresStableDrift).A^{-1}[e^{A Δt} − I] B · √v / √pdepends on the event interval and is notasymTIPREDEFFECTstd.(-B / a) · √v / √(trait + p + added)uses the total, notasymDIFFUSION, and is notasymTIPREDEFFECTstdwhenTRAITVARis nonzero.TRAITVARis not the footnote 4 standardisation variance.Still not a Kalman filter, not a matrix
expm, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T13:19Z:is_oa: false; title Measurement Invariance, Factor Analysis and Factorial Invariance). Mislevy (1991, Psychometrika, 56, 177–196) remains unread (Unpaywall 2026-08-23T13:19Z:is_oa: false; title Randomization-Based Inference about Latent Variables from Complex Samples).Do not merge, self-approve, or request Copilot.