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

[seonghobae]

Stacked on #218 (T0MEANSstd). Next unique licensed map on this ancestry is footnote-4 standardisation of 2017-era MANIFESTMEANS. Do not duplicate #210 MANIFESTVARstd, #195 CINTstd, or #218 T0MEANSstd. TDPREDVARstd is commented out in the 2017-era source and is not recovered.

Driver, Oud, and Voelkle (2017, Table 2, p. 12; p. 16; footnote 4; Eq. 5, p. 5; JSS PDF re-opened 2026-08-25T05:04Z) print 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:

MANIFESTMEANS <- 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. The 2017-era dimnames(MANIFESTMEANS) <- list(manifestNames, manifestNames) assignment on an n.manifest × 1 matrix is a source bug and is not this map.

Recovery

• recover_standardised_manifest_mean(τ, θ, clock) forms strictly positive θ first, then divides τ by √θ.
• A zero mean is exactly zero.
• A larger positive θ yields a smaller |std|.
• Zero θ fails closed. Unstandardised MANIFESTMEANS is defined for a zero residual; standardised MANIFESTMEANS is not.
• Non-event clock fails closed.
• MANIFESTMEANS does not require stable a < 0.

Claim boundary

• Unstandardised MANIFESTMEANS is not MANIFESTMEANSstd.
• 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.
• T0MEANSstd recovers the same number when τ = μ_0 and θ = p_0 and remains a distinct named quantity.

Meredith (1993) and Mislevy (1991) remain closed (Unpaywall 2026-08-25T05:04Z: is_oa: false, 0 locations).

Do not merge without an independent APPROVE plus exact-head required-check success. Do not self-approve. Do not request Copilot.

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[seonghobae]

Superseded by consolidation: this slice's Driver et al.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.